CN1024953C - Two degree of freedom controller - Google Patents

Two degree of freedom controller Download PDF

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CN1024953C
CN1024953C CN 90107699 CN90107699A CN1024953C CN 1024953 C CN1024953 C CN 1024953C CN 90107699 CN90107699 CN 90107699 CN 90107699 A CN90107699 A CN 90107699A CN 1024953 C CN1024953 C CN 1024953C
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order lag
output
difference
point
freedom
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CN1050270A (en
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広井和男
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Toshiba Corp
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Toshiba Corp
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Priority claimed from JP1344366A external-priority patent/JP2845534B2/en
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Abstract

A two degree of freedom PID controller which comprises setpoint filter means (20) for performing a derivative operation (D) on a process disturbance signal in accordance with a setpoint value (SV) and a control value (PV) of a controlled system, thereby outputting a setpoint signal (SV0), PI-control operation means (22) for determining a deviation (E) between the setpoint signal and the control value, and performing a PI-control operation on the deviation, thereby outputting a manipulative signal (MV), and adder means (24) for adding the process disturbance signal to the manipulative signal output by the PI-control operation means, thus obtaining a sum signal, and for supplying the sum signal to the controlled system.

Description

Two degree of freedom controller
The present invention relates to a kind of two degree of freedom controller, the Optimal Control of sort controller energy complete process disturbance, and can Optimal Control tracking target process values or set-point value.
The PID controller has been applied to the every field of industry.In recent years, the application of digital pid controller constantly increases and substitutes analog pid controller, and has become indispensable a member now in control factory.Digital pid controller is carried out following basic operation:
MV（S）＝K p｛1+1/（T IS）+（T DS）/（1+ηT DS）｝E（S） …（1）
Here being a manipulated variable MV(S), is a deviation (amount) E(S), and Kp is proportional gain, T IBe integral time, T DBe derivative time (derivative time), S is a Laplacian, and η is that coefficient and 1/ η are the differential gains.Equation (1) has been determined the PID control of a deviation (amount).This control generally is called " deviation PID control ".
But in deviation PID control, the variation of set point SV is that phase step type changes (Stepwise) in many cases.Because the step of set-point value SV changes, the PID controller is often carried out an excessive D(differential) operation, so manipulated variable MV alters a great deal, and the result, the PID controller gives the system that is controlled an impact.Perhaps, the setting point tracking characteristic of PID controller has overshoot, and therefore, controller is carried out a kind of vibration operation inevitably.
In recent years, a kind of novel PID controller is carried out the D operation to PV, rather than deviation (amount) is carried out the D operation.This PID controller has dropped into actual use.Operation below this PID controller is carried out:
MV（S）＝K p[｛1+1/（T IS）｝E（S）
-｛（T DS）/（1+ηT DS）｝PV（S）] …（2）
Here be controlling value PV(S) from controlled system.
Equation (1) and (2), each has all determined the PID control operation of one degree of freedom.Only there is one group of pid parameter to be set.In the control system of reality, the best pid parameter of best control procedure disturbance has different values with the best pid parameter of best tracking set point.
1963, Yi Saisi I He Luowazi (Issac I.Horowitz) discloses a kind of two-freedom PID(2DOF PID) algorithm, wherein can set two groups of parameters independently, this algorithm not only makes the control procedure disturbance effectively of PID controller, and can accurately follow the tracks of the value of set point.After this, this algorithm is used in many PID controllers, and these controllers are carrying out high-caliber control to factory in actual use.In this 2DOF pid algorithm, the best pid parameter of control procedure disturbance is set at first.When set-point value changed, then pid parameter automatically changed according to the coefficient for the selected set-point filter of new settings point value.
Fig. 1 is the block scheme of the 2DOF PID controller of routine.This controller comprises set-point filter device H(S) and PID controller (PV differential).As shown in Figure 1, set-point filter device H(S) link the input end of PID controller, this filter apparatus H(S) comprise: lead-lag device 1; First-order lag device 2; Incomplete differential device 3; Subtracter device 4; Incomplete integrating gear 5; Adder unit 6.Leading or hysteresis adds to set-point value SV to this lead-lag device 1 one.This first-order lag device 2 adds to set-point value SV to first hysteresis (delay).3 pairs of differential gains of this incomplete differential device are provided with a higher limit, and also postpone derivation operation.This subtracter device 4 cuts the output of first-order lag device 2 from the output of incomplete differential device 3.The output of 5 pairs of subtracter device 4 of this incomplete integrating gear postpones.This adder unit 6 is with the output of lead-lag device 1 and the output addition of incomplete differential device 5.The output SV of adder unit 6 or set-point filter device H(S) output SV be added on the PID controller as a set point.
The PID controller of PV derivative-type (PV is carried out differential) comprises: deviation calculation device 7; Non-linear device 8; PI control operation device 9; Subtracter device 10 and incomplete differential device 11.This deviation calculation device 7 receives the output SV of adder unit 6 OReach the controlling value PV that controlled system 12 is provided, according to output SV OCalculate a deviation (amount) E with controlling value PV.The deviation E that is obtained is input to non-linear device 8 then.8 couples of deviation E of this non-linear device carry out nonlinear operation, and this operation comprises: the dead band nonlinear operation, deviation square operation and change in gain operation produce an output then.The output of device 8 is input to PI control operation device 9.The PI control operation is carried out in the output of 9 pairs of non-linear devices 8 of this operating means, and described PI control operation is determined by first on the right of equation (2), produced a PI controlling value thus.This PI controlling value is added to subtracter device 10.
Therebetween, controlling value PV is added to incomplete differential device 11 from controlled system 12.11 couples of controlling value PV of this incomplete differential device carry out an incomplete derivation operation, and described incomplete derivation operation is determined by second on the right of equation (2), produced an incomplete differential value thus.This incomplete differential value is input to subtracter device 10.This subtracter device 10 cuts the incomplete differential value from the PI controlling value, obtain a manipulated variable MV thus.
This manipulated variable MV is added to totalizer 13, and process disturbance signal D also is added to this totalizer 13.Totalizer 13 is with variable MV and signal D addition.Variable MV and signal D " with " being input to controlled system 12, system's 12 Be Controlled become and set-point value SV controlling value PV thus OEquate, i.e. SV O=PV.
Therefore, the algorithm C of control procedure disturbance D(S) be expressed from the next:
C D（S）＝K p｛1+1/（T IS）+（T DS）/（1+ηT DS）｝ …（3）
On the other hand, the algorithm C of control set-point value SV(S) represent by (4) formula:
C SV（S）＝K p[α+｛1/（T IS）-β o/（1+T I·S）｝
+（γ OT DS）/（1+ηT DS）] …（4）
At first, parameter K P, T IAnd T DPlace the value that can make 2DOF PID controller that optimum process perturbation control characteristic is arranged, then, decision 2DOF factor alpha, β O, and γ OMake 2DOF PID controller have best setting point tracking characteristic.In case 2DOF PID controller has optimum process perturbation control characteristic and best some tracking characteristics, the then parameter K adjusted P, T IAnd T DJust can be according to factor alpha, β OAnd γ OAnd change, thereby catch up with the variation of controlling value PV.The result is that controller can be carried out the PIP control of two-freedom.
Aforesaid two-freedom PIP control has superiority in many aspects, but also has the shortcoming of following several respects.
1. can find out 2DOF factor alpha, β significantly from equation (4) OAnd γ OUncorrelated mutually, and they were should be associated mutually originally.So when factor alpha changes, factor beta OAnd γ OMust change independently.Be adjustment factor β like this OAnd γ OWant the expensive time.
2. as previously mentioned, set-point filter device H(S) and PID controller (PV derivative-type) have first-order lag device and incomplete differential device, in most of the cases in order to control a factory, will carry out tens to several thousand 2DOF PID controls.Therefore, a plant control system needs a large amount of first-order lag devices and a large amount of incomplete differential devices.System load is very big, and the system that makes is difficult to high-speed cruising, and system will do very greatly inevitably.
3. in order to control a factory, deviation (amount) will be carried out nonlinear operation in many cases.This nonlinear operation can easily, accurately or at will acquisition.
In other words, in order to control a factory, will carry out nonlinear operation to deviation in many cases, this is that factory can not only control according to departure E because of the characteristic owing to controlled system 12.This be why non-linear device 8 be connected to PI control operation device 9 input end to finish reason to the nonlinear operation of departure E, nonlinear operation comprises dead band nonlinear operation, departure square operation, change in gain operation and gap (gap) operation etc.Because incomplete differential device 11 switches to the output terminal of PI control operation device 9, the output of incomplete differential device 11 is without nonlinear operation.Therefore, the result of nonlinear operation is coarse, has reduced the reliability of two-freedom PID control inevitably.
It is a kind of when the 2DOF of proportional gain factor alpha changes that first purpose of the present invention is to provide, and can change the two degree of freedom controller of differential term gain automatically.
Second purpose of the present invention is to provide a kind of and uses a small amount of time element and volume is little, load light and two degree of freedom controller that can high speed operation.
The 3rd purpose of the present invention be to provide a kind of energy simple and easy, accurately, freely comprise the nonlinear operation of derivation operation, thereby the controller of the two-freedom of control system efficiently.
For finishing the foregoing invention purpose, according to the invention provides a kind of two degree of freedom controller, this controller comprises:
The set-point filter device is used for according to the controlling value of set-point value and controlled system the process disturbance signal being carried out derivation operation, exports a set point signal thus;
PI control operation device is used for determining the departure between set point signal and the described controlling value and this departure is carried out the PI control operation, exports a control signal thus; With
Adder unit is used for the process disturbance signal is added to control signal by PI control operation device output, thus obtain one " with " signal and should " with " signal adds to controlled system.
PI control operation device can comprise the non-linear device that is used for departure is carried out nonlinear operation.
Therefore, set-point filter device and PI control operation device combine, and realize two-freedom PID control at an easy rate.
The set-point filter device is connected to the input end of PI control operation device, and the process disturbance signal is carried out derivation operation according to set-point value and controlling value, PI control operation device can accurately, freely carry out nonlinear operation, thereby finishes the PID control of two-freedom.
In the preferred embodiment of the present invention, the set-point filter device comprises:
The gain coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of proportional gain, exports first product thus;
First subtracter device, it is used for cutting first product from set-point value, exports first difference thus;
First first-order lag device, it has the two-freedom coefficient of integral time, is used for first difference is carried out the first-order lag operation, exports first result of first-order lag operation thus;
Derivative time the coefficient multiplier, it is used for first product be multiply by the two-freedom coefficient of a derivative time, exports second product thus;
Second subtracter device, it is used for cutting controlling value from second product, exports second difference thus;
The incomplete differential device, it is used to receive second difference and this second difference is carried out the incomplete differential operation, exports an incomplete differential operating result thus;
The 3rd subtracter device, the result that it is used for deducting from first result of first-order lag operation the incomplete differential operation exports the 3rd difference thus;
Second first-order lag device, it is used for the 3rd difference is carried out the first-order lag operation, exports second result of first-order lag operation thus;
The first adder device, it is used for second result of first-order lag operation is added to the result of incomplete differential operation, export first thus " with "; With
The second adder device, it be used for first " with " be added to first product, obtain second thus " with ", and with this second " with " be added on the PI control operation device as set point signal.
In another preferred embodiment of the present invention, the set-point filter device comprises:
The gain coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of proportional gain, exports first product thus;
First subtracter device, it is used for deducting first product from set-point value, exports first difference thus;
First first-order lag device, it has the two-freedom coefficient of integral time, is used for first difference is carried out the first-order lag operation, exports first result of first-order lag operation thus;
Derivative time the coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of a derivative time, exports second product thus;
Second subtracter device, it is used for deducting controlling value from second product, exports second difference thus;
Incomplete derivator, it is used to receive second difference and this second difference is carried out the incomplete differential operation, exports the result of incomplete differential operation thus;
The 3rd subtracter device, it is used for deducting the incomplete differential operation from first result of first-order lag operation result exports the 3rd difference thus;
Second first-order lag device, it is used for the 3rd difference is carried out the first-order lag operation, exports second result of first-order lag operation thus;
The first adder device, it is used for second result of first-order lag operation is added to the result of incomplete differential operation, export first thus " with "; With
The second adder device, it be used for first " with " be added to first product, obtain second thus " with ", and with this second " with " be added on the PI control operation device as set point signal.
Perhaps, in order to Comparative Examples gain with realize that the set-point filter device that two-freedom is controlled can comprise derivative time:
The gain coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of proportional gain, exports first product thus;
First subtracter device, it is used for deducting first product from set-point value, exports first difference thus;
Derivative time the coefficient multiplier, it is used for first product be multiply by the two-freedom coefficient of derivative time, exports second product thus;
Second subtracter device, it is used for deducting controlling value from second product, exports second difference thus;
The incomplete differential device, it is used to receive second difference and this second difference is carried out the incomplete differential operation, exports the result of incomplete differential operation thus;
The 3rd subtracter device, the result that it is used for deducting from first difference incomplete differential operation exports the 3rd difference thus;
The first-order lag device, it is used for the 3rd difference is carried out the first-order lag operation, exports the result of first-order lag operation thus;
The first adder device, it is used for the result of first-order lag operation is added on the result of incomplete differential operation, export first thus " with "; With
Second adder, it be used for first " with " be added to first product, obtain second thus " with ", and this device be used for second " with " be added on the PI control operation device as set point signal.
According to two degree of freedom controller provided by the present invention, it comprises the set-point filter device and a PI control operation device of the differential term that receives a controlling value.This PI control operation device comprises: the departure calculation element; The PI control device; And being connected non-linear device between departure calculation element and the PI control device, it is used for finishing the nonlinear operation to differential term.
In order to finish above-mentioned purpose, comprise according to two degree of freedom controller provided by the present invention:
The set-point filter device, it is used to receive set-point value and produces set point signal, and this device comprises:
The coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of proportional gain, exports a product thus;
The first-order lag device, it has the two-freedom coefficient of an integral time at least, and is designed to deduct from set-point value this product, produces a difference thus; With
Adder, it is used for above-mentioned product is added to this difference, exports set point signal thus;
PI control operation device, it is used for determining the departure between the controlling value that set point signal and controlled system provide, and this departure is carried out the PI control operation, exports a control signal thus; With
Adder unit, it is used for the process disturbance signal is added to control signal by PI control operation device output, obtain then one " with " signal, and should " with " signal is added on the controlled system.
For finishing above-mentioned purpose, comprise according to another two degree of freedom controller provided by the present invention:
The set-point filter device, it is used to receive set-point value and produces a set point signal, and this device comprises:
The coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of proportional gain, exports a product thus;
First first-order lag device, it is used for deducting this product from set-point value, produces a difference thus;
Second first-order lag device, it has the two-freedom coefficient of an integral time at least, and its set-point value of being used to postpone set-point value and output delay; With
Adder, it is used for above-mentioned product is added to by on the set-point value after the delay of second first-order lag device output, exports set point signal thus;
PI control operation device, it is used for determining the departure between the controlling value of set point signal and controlled system, and this departure is carried out the PI control operation, exports a control signal thus; With
Adder unit, it is used for the process disturbance signal is added to control signal by PI control operation device output, obtain thus one " with " signal, and " with " signal is added on the controlled system.
Be appreciated that according to above-mentioned, for two-freedom being added to the proportional gain of the set-point filter that is used for traditional controller, one lead-lag device resolves into two parts, first is proportional to the static compensation part of input and second portion is the dynamic compensation part that changes, with respect to input delay.One single order lagging device and dynamic compensation part are in series, and therefore, two first-order lag devices are used to finish 2DOF PI control.Two-freedom is also given integral time in addition, like this, when the two-freedom index variation of proportional gain, the degree of freedom value of integral time is changed with suitable direction.
Therefore, the required proportional gain factor of the Optimal Control of maintenance process disturbance is constant, and the two-freedom coefficient of the proportional gain that the proportional gain of set-point value can be by changing the coefficient multiplier changes.In addition, the integral time of maintenance process disturbing signal is constant, as long as change the integral time that the two-freedom coefficient of the integral time of first-order lag device just can correspondingly change set-point value.Thereby realize a two-freedom PI control completely.By changing the two-freedom coefficient of proportional gain, can change integral time with suitable direction.In addition, as long as use two first-order lag devices just can realize two-freedom PI control completely.
Comprise according to another one two degree of freedom controller provided by the invention:
The gain coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of proportional gain, exports first product thus;
Derivative time the coefficient multiplier, it is used for set-point value be multiply by the two-freedom coefficient of derivative time, exports second product thus;
First first-order lag device, it is used for set-point value is carried out the first-order lag operation, exports first result of first-order lag operation thus;
Integral time the coefficient multiplier, it is used for the result of first-order lag operation be multiply by the two-freedom coefficient of integral time, exports the 3rd product thus;
The incomplete differential device, it is used for the controlling value that the second sum of products controlled system is provided is carried out the incomplete differential operation, exports the result of incomplete differential operation thus;
Second first-order lag device, it is used for the result of first product, the operation of the 3rd sum of products incomplete differential is carried out the first-order lag operation, exports second result of first-order lag operation thus;
The first adder device, it is used for first and second results added with the first-order lag operation, exports set point signal thus;
PI control operation device, it is used for the departure between definite set point signal and the controlling value, and this departure is carried out the PI control operation, exports a control signal thus; With
The second adder device, it is used for process disturbance signal and control signal addition, thereby obtain " with " signal, and this " with " signal is added to controlled system.
This two degree of freedom controller can add to proportional gain, derivative time and integral time to two-freedom completely.
Other purpose of the present invention and advantage will be set forth in the following description, and wherein a part of purpose and advantage will be apparent by explanation, perhaps by practice of the present invention is understood.Utilize the means and the combination thereof that particularly point out in the appended claims, can realize and obtain these purposes of the present invention and advantage.
Accompanying drawing constitutes the part of this instructions, and they show the present preferred embodiment of the present invention.Accompanying drawing with top given description and below the explanation of details of the preferred embodiment of being about to provide, be used for setting forth principle of the present invention.
Fig. 1 is the block scheme of the traditional two-freedom PID controller of expression;
Fig. 2 represents the block scheme according to the PID controller of the first embodiment of the present invention;
Fig. 3 A and 3B explain that the lead-lag device is the figure of equivalent transformation how;
Fig. 4 A and 4B explain that incomplete integrating gear is the figure of equivalent transformation how;
Fig. 5 is the relation curve between 2DOF factor alpha and the β on the one hand, has represented the characteristic of the system that controlled by PID controller shown in Figure 2 on the other hand;
Fig. 6 is the block scheme that shows according to the PID controller of second embodiment of the present invention;
Fig. 7 is the block scheme of the PI controller of third embodiment of the invention;
Fig. 8 explains that set-point filter is the curve map that how to respond the step variation of set-point value;
Fig. 9 be explain when the process disturbance control characteristic of the PI controller shown in Fig. 7 when tuning, the curve map of the setting point tracking characteristic that this controller had;
Figure 10 is the block scheme of set-point filter used in the PI controller of the fourth embodiment of the present invention;
Figure 11 is the block scheme of set-point filter device used in the PI controller of fifth embodiment of the invention;
Figure 12 is the block scheme of set-point filter device used in the PI controller of sixth embodiment of the invention;
Figure 13 is the block scheme of the PID controller of seventh embodiment of the invention;
Figure 14 A and 14B explain that the incomplete differential device is the figure of equivalent transformation how;
Figure 15 is the block scheme of the PID controller of eighth embodiment of the invention;
Figure 16 is the block scheme of the PID controller of ninth embodiment of the invention;
Figure 17 is the block scheme of the imagination structure of set-point filter device used in the PID controller shown in Figure 16;
Figure 18 is the block scheme of the practical structures of set-point filter device used in the PID controller of Figure 16;
Figure 19 is a kind of block scheme of set-point filter device that is only constituted, can be used for the PID controller of Figure 16 by the first-order lag device.
The 2DOF PID controller of first embodiment of the invention is described below with reference to Fig. 2,3,3A, 3B, 4A and 4B.
As shown in Figure 2,2DOF PID controller comprise a set-point filter device 20 ,-PI algorithm operating part 22 and adder unit 24.Totalizer 24 is connected to the system 26 that is controlled by 2DOF PID controller.
Set-point filter 20 is used for receiving set-point value SV and this value SV is operated, and thus two-freedom is added to proportional gain K P, integral time T IWith T derivative time DPI-algorithm operating part 22 comprises: departure calculation element 28, non-linear device 30 and PI control device 32.Departure calculation element 28 receives the output SV of set-point filter device 20 O, reach controlling value PV by controlled system 26, and from output SV ODeduct controlling value PV, obtain departure E thus; Device 28 carries out subtraction SV O-PV=E.If required, 30 couples of departure E of non-linear device carry out nonlinear operation, thereby produce an output.The PI control operation is carried out in the output of 32 pairs of non-linear devices 30 of PI control device, produces manipulated variable MV thus.
Adder unit 24 is used for process disturbance signal D is added on the manipulated variable MV that is produced by PI-algorithm operating part 22, and this " with " value gives controlled system 26.Controlled and the SV=SV of system 26 as a result O=PV.
As shown in Figure 2, set point filtration unit 20 comprises: gain coefficient multiplier 34, be connected to the first adder device 36 of the output terminal of this multiplier 34, also be connected to first subtracter device 38 of the output terminal of this multiplier 34, second subtracter device 40, be coupled to first first-order lag device 42 of the output terminal of second subtracter device 40, be connected to the second adder device 44 of the output terminal of device 42, the time coefficient multiplier 46 that is connected with multiplier 34, be coupled to the 3rd subtracter device 48 of the output terminal of multiplier 46, be coupled to the incomplete differential device 50 of the output terminal of the 3rd subtracter device 48, and be connected second first-order lag device 52 between first subtracter device 38 and second subtracter device 40.
As described, set-point filter device 20 is given proportional gain, integral time and derivative time with two-freedom.For two-freedom being added to these, incomplete differential device 11(Fig. 1) its output terminal one of switching to PI control operation device 9 of differential term one be added to set-point filter device 20.In addition, by the integration of common use controlling value, integration and differential, the proportional gain of set-point value and the first-order lag of integral time of set-point value, needed device is than will lack in traditional 2DOF PID controller (Fig. 1).
At first how interpreting means 20 imposes on proportional gain to two-freedom below.Gain coefficient multiplier 34 multiply by set-point value SV the 2DOF factor alpha of proportional gain.The output of multiplier 34, be that the product of SV and α is added to the first adder device 36 and first subtracter device 38.First subtracter device 38 deducts output α SV from set-point value SV.The output of first subtracter device 38, be poor between SV and the α SV, be input to first adder device 36 by second first-order lag device 52, second subtracter device 40, first first-order lag device 42 and second adder device 44.First adder device 36 is added to the output of second adder device 44 in the output of gain coefficient multiplier 34, thereby two-freedom is imposed on proportional gain.
Interpreting means 20 is how two-freedom to be imposed on derivative time now.The output of gain coefficient multiplier 34 inputs to time coefficient multiplier 46, and the 2DOF coefficient gamma of derivative time is set up in this device 46.Time coefficient multiplier 46 will install 34 output and multiply by coefficient gamma, obtain product α γ SV.This product is input to the 3rd subtracter device 48.The 3rd subtracter 48 deducts the controlling value PV of system 26 from product α γ SV, thereby obtains difference α γ SV-PV.This difference is added to second subtracter 40 and second adder device 44 by incomplete differential device 50.The output of second subtracter device 40 is added to second adder device 44 through first first-order lag device 42, and the output of the 3rd subtracter device 48 is added to second adder 44 through incomplete differential device 50.Second adder device 44 is with the output of first first-order lag device 42 and the output addition of incomplete differential device 50, thus acquisition and number.Should and number be input to first adder device 36, the output of gain coefficient multiplier 34, be that α SV also is added to this device 36.Therefore, the output of the output of first adder device 36 output gain coefficient multipliers 34 and second adder device 44 and the number.As above-mentioned result, two-freedom was applied in to derivative time.
Explain how two-freedom is imposed on integral time now.The output of first subtracter device 38 is second first-order lag device 52 that SV-α SV adds to the 2DOF factor beta that comprises integral time.The output of device 52 by second substracting unit 40, first first-order lag device 42 and second adder device 44, is input to first adder device 36.First adder device 36 produces an output SV with the output addition of multiplier 34 and second adder device 44 O, it is as the output of set-point filter device 20.
What is interpreted as now will uses aforesaid set-point filter device 20, please referring to Fig. 3 A, 3B, 4A, 4B and 5.
In traditional 2DOF PID controller (Fig. 1) employed and roughly be illustrated in lead-lag device 1 among Fig. 3 A can be transformed into equivalently shown in Fig. 3 B like that.In other words, device 1 can be expressed as (1+ α T IS)/(1+T IS), it can be converted to:
（1+αT IS）/（1+T IS）
＝（α+αT IS+1-α）/（1+T IS）
＝α+（1-α）/（1+T IS） …（5）
Therefore, functional block diagram is represented shown in the available Fig. 3 B of equation (5).
In traditional PID controller (Fig. 1) employed and roughly be illustrated in incomplete integrating gear 5 among Fig. 4 A can be transformed to equivalently shown in Fig. 4 B like that.In other words, device 5 can be expressed as (T IS)/(1+T IS), it can be converted to:
T IS/（1+T IS）＝（1+T IS-1）/（1+T IS）
＝1-1/（1+T IS） …（6）
Therefore, functional block diagram is represented shown in the available Fig. 4 B of equation (6).
Clearly visible from Fig. 3 B and 4B and Fig. 2, first first-order lag device 42 can also can be used as incomplete integrating gear 5 as lead-lag device 1.In other words, use the functional block of Fig. 3 B and 4B and some new technological concepts to design the set-point filter device 20 shown in Fig. 2.
The algorithm C of control procedure disturbance D(S) provide by following formula:
C D（S）＝MV/PV
＝K P[1+1/（T IS）+T DS/（1+ηT DS）] …（7）
On the other hand, the algorithm C of control set-point value SV(S) represent with following formula:
C SV（S）＝MV/SV
＝K P｛α+[1/（T IS）-（1-α）β/（1+βT IS）]
+αγT DS/（1+ηT DS）｝ …（8）
Can be clear that from formula (7) and formula (8), when the 2DOF of proportional gain factor alpha changes, the proportional gain K of the algorithm of retentive control process disturbance pConstant, can change the proportional gain K in the algorithm of controlling set-point value pα.Equally, when the 2DOF of integral time factor beta changed, the integral time of the algorithm of retentive control process disturbance was constant, can change the integral time in the algorithm of controlling set-point value.Equally, when the 2DOF of derivative time coefficient gamma changed, the derivative time in the algorithm of retentive control process disturbance was constant, can change the derivative time in the algorithm of controlling set-point value.In brief, can constitute 2DOF PID control completely.
Therefore, the 2DOF PID controller among Fig. 2 only needs 3 time devices, and the traditional PID controller of the 2DOF among Fig. 1 needs 5 time devices.Therefore, the load of the PID controller of Fig. 2 has reduced with comparing of the conventional PID controllers shown in Fig. 1 with expense, and the PID controller of Fig. 2 compares with the conventional PID controllers shown in Fig. 1, the former descend by volume and operating speed faster.Controller shown in Fig. 2 can also carry out 2DOF PID control completely to system 26.
The 2DOF factor alpha of the 2DOF PID controller shown in Fig. 2, its proportional gain, the 2DOF factor beta of integral time and the 2DOF coefficient gamma of derivative time can separate settings.So just be easy to be provided with these coefficients.
And, be easy to regulate 2DOF factor beta and γ with the 2DOF PID controller shown in Fig. 2.This is that these 2DOF coefficients are adjusted automatically because when the 2DOF factor alpha changes, and this point is readily appreciated that from formula (8).
Moreover the 2DOF PID controller shown in Fig. 2 can carry out nonlinear operation easily and accurately.This is because this 2DOF PID controller need be corresponding to incomplete differential device 11(Fig. 1) part, this device 11 is bypassed to PI control operation device 9(Fig. 1) output, and because the differential term of controlling value is included within the set-point filter device 20.
Fig. 5 represents the optimum value of 2DOF factor alpha and β is how to change along with the characteristic of the system 26 that is controlled by the 2DOF PID controller of Fig. 2.The characteristic of system 26 is defined as L/T, and wherein L is the idle time (idling time) of system 26, and T is the time constant of system 26.As can be seen from Figure 5, the PID controller of Fig. 2 in actual applications, 2DOF factor alpha and β can only be half of setting value.In actual applications, the value of 2DOF factor alpha, β and γ is preferably:
α＝0，β＝4，γ＝1.25
The PID controller of first embodiment of the invention can improve the basis of control PID system of factory, brings up to two degree of freedom of generation from producing one degree of freedom, thus the every field in the industry is made contributions.
Please, the set-point filter device 20 of the 2DOF PID controller of second embodiment of the invention is described below referring to Fig. 6.
In first embodiment (Fig. 2), the output of gain coefficient multiplier 34 is multiplied each other with the 2DOF coefficient gamma of derivative time.In second embodiment shown in Fig. 6, set-point value SV is input to the 2DOF coefficient gamma is set o Time coefficient multiplier 56 in.Except this point, the device 20 of set-point filter shown in Fig. 6 identical with shown in Fig. 2, and in Fig. 6, use same numbering with the same section shown in Fig. 2, no longer it is explained in detail here.
In 2DOF PID controller, use, in order to the algorithm C(S of control procedure disturbance) with first embodiment (Fig. 2) in employed identical, this algorithm is determined by equation (7).On the other hand, in 2DOF PID controller, use, in order to control set-point value algorithm C SV(S) provide by following formula:
C SV（S）＝MV/SV
＝K P｛α+[1/（T IS）-（1-α）β/（1+βT IS）]
+γ OT DS/（1+ηT DS）｝ …（9）
In the present embodiment, when the 2DOF factor alpha changed, the gain of differential term can not change automatically, and this point is different with first embodiment.
Referring to Fig. 7.Among the figure the 3rd embodiment of 2DOF PI controller of the present invention.Except the set-point filter device 120 of present embodiment does not have the differential term at all, all the other are identical with the 2DOF PID controller shown in Fig. 2.Therefore, in Fig. 7, all use identical numbering, no longer it is explained in detail with the same section shown in Fig. 2.
As shown in Figure 7, set-point filter 120 comprises: the 2DOF coefficient multiplier 34 that set-point value SV be multiply by the 2DOF coefficient of proportional gain, deduct the subtracter device 38 of device 34 output from set-point value SV, the output that is connected in series, gives subtracter device 38 is with two first- order lag devices 52 and 42 of suitable first-order lag.With adder unit 36 with the output addition of the output of 2DOF coefficient multiplier 34 and first-order lag device 42.The output of adder unit 36 is as set-point value SV OBe input to PI control device 32.
Set-point filter device 120 receives set-point value SV and according to this set-point value Comparative Examples gain with carry out the two-freedom operation integral time, produces single-degree-of-freedom (1DOF) thus and control needed set-point value SV OSet-point value SV OBe input to departure calculation element 28, also be input to device 28 from a controlling value PV of controlled system 26.Device 28 is from set-point value SV OIn deduct this controlling value PV, and obtain departure E.This departure E is added to PI control device 32.32 couples of departure E of PI control device carry out the PI control operation, thereby produce manipulated variable MV.The manipulated variable MV that is obtained is input to adder unit 24, and process disturbance signal D also adds auto levelizer 24.Adder unit 24 is variable MV and signal D addition, produce thus one " with " signal.Should " with " signal is added to system 26.The result makes system 26 controlled: SV=SV O=PV.
Below with reference to Fig. 8 and Fig. 9, the operation of the 2DOF PI controller among Fig. 7 is made an explanation.
When set-point value SV a1 line was as shown in Figure 8 done the step variation, the equivalent electrical circuit shown in Fig. 3 B was owing to the transport function of being determined by equation (5) produces output SV, shown in line b1.The output characteristics that line b1 represents at first is proportional to factor alpha and changes, and (1-α) continues according to 1/(1+T IS) change.Therefore, when a big overshoot is arranged by the determined response characteristic of line b1, if first-order lag device 62 is added to (a 1-α), then output characteristics will change shown in line c1.This output characteristics of being represented by line c1 has a less overshoot than the response characteristic of being determined by line b1.
Explain now set-point filter device 120 and PI control device 32 are how to cooperate to constitute 2DOF PI control completely.
Can see the algorithm C of control procedure disturbance from Fig. 7 D(S) be:
C D（S）＝MV/PV＝C（S）＝K P｛1+1/（T IS）｝ …（10）
Also can see the algorithm C of control set-point value from Fig. 7 SV(S) be:
C SV（S）＝F（S）C（S）
＝｛α+（1-α）/[（1+βT IS）（1+T IS）]｝
×K P｛1+1/（T IS）｝
＝K P｛α[1+1/（T IS）]
+（1-α）/[（T IS）（1+βT IS）]｝
＝K P｛α[1+1/（T IS）]
+（1-α）×[1/（T IS）-β/（1+βT IS）]｝
＝K P｛α+[1/（T IS）-（1-α）β/（1+βT IS）]｝ …（11）
Apparent from equation (10) and (11), the proportional gain K of maintenance process disturbance PConstant, the proportional gain α K of set-point value PCan change by changing the 2DOF factor alpha.In case K PAnd T IBe arranged on such value, 2DOF PI controller (Fig. 7) just has an optimum process perturbation control characteristic.And, T integral time of maintenance process disturbance IConstant, β T integral time of set-point value ICan change by changing the 2DOF factor beta, in case K PAnd T IBe arranged on such value, 2DOF PI controller (Fig. 7) just has optimum process perturbation control characteristic.Like this, the 2DOF PI controller among Fig. 7 just can carry out 2DOF PI control completely.
Therefore, the integral I of set-point value SV(S) provide by following formula:
I SV＝1/（T IS）-（1-α）β/（1+βT IS） …（12）
From equation (12), can obtain:
(a) when β=0, I SV(S)=1/(T IS) (integral time is constant)
(b) when β＞0, I SV(S)＜1/(T IS) (lengthening integral time)
(c) when β＜0, I SV(S)＞1/(T IS) (shortening integral time)
Obviously, keep T integral time IConstant, as long as change T integral time IThe 2DOF factor beta just can corresponding change process disturbance β T integral time I
Therefore, if the transport function G(S of system 26) be arranged on e -2sStep changes to obtain the optimum process perturbation control by regulating the PI parameter for/1+5S and set-point value SV, and the 2DOF PI controller that then is shown in Fig. 7 will have the response characteristic that is shown in Fig. 9.The curve a2 that is shown in Fig. 9 represents if α=1 and β=0, that is, if do not have set-point filter device 120 thereby obtain be the PI control of one degree of freedom the time, the response characteristic that 2DOF PI controller will present.A2 can clearly be seen that from curve, and this response characteristic has bigger overshoot.
The curve b2 that is shown in Fig. 9 represents if α=0.4 and β=0, that is, if only P is obtained the control of two degree of freedom, the response characteristic that 2DOF PI controller will present.The response characteristic represented by curve b2 also has overshoot, only do not have curve a2 big like that.
Curve c2 represents when α=0.4 and β=0.35, that is, when P and I are all obtained the control of two degree of freedom, the response characteristic that 2DOF PI controller is presented.C2 can clearly be seen that from curve, and this response characteristic has only very little overshoot.
Again, the curve d2 that is shown in Fig. 9 represents if α=0 and β=0, that is, if when P and I all obtained the control of one degree of freedom, the response characteristic that 2DOF PI controller will present.Obviously, this response characteristic is not enough, and 2DOF PI controller is too slow to the variation response of set-point value SV.Can understand from Fig. 9,2DOF PI controller illustrated in fig. 7 all can be finished best two-freedom control to P and I.
From equation (11) also as can be seen, when the 2DOF of proportional gain factor alpha changed, did corresponding change in suitable direction integral time.Or rather, factor alpha is big more, and integral time is short more, and factor alpha is more little, and integral time is long more.In other words, change with the direction different integral time with the response speed of 2DOF PI controller.When factor alpha fixedly the time, only just can change integral time by changing factor beta.
Apparent from Fig. 7, set-point filter device 120 only comprises two first- order lag devices 42 and 52 but can carry out control to the two-freedom of system 26 reliably, and set point filter device 120 is simple in structure.Thereby it is light that the duty factor on the 2DOF PI controller is shown in the load of PID controller of routine of Fig. 1, and the PI controller can move soon than conventional controller.One be used to control factory, comprise the 2DOF PI system of tens to several thousand 2DOF PI controllers same as shown in Figure 7 thereby can do smallerly to have lighter load and can at full speed move.
Figure 10 to Figure 12 is three set-point filter devices that are used for two 2DOF PI controllers according to the of the present invention the four, the five and the 6th embodiment.Each set-point filter device all has two first-order lag devices.
Be shown in the set-point filter device 120 of Figure 10, be characterized in, first-order lag device 58 and adder unit 60 are connected to the output of subtracter device 38, and this subtracter device deducts the output of coefficient multiplier device 34 from set-point value SV.Adder unit 60 the output addition of the output of subtracter device 38 and first-order lag device 58 is produced one " with ".Should " with " be input to first-order lag device 42.The output of first-order lag device 42 offers subtracter device 62, and the output of first-order lag device 58 also offers it.Thereby subtracter device 62 deducts the output of first-order lag device 42 from the output of first-order lag device 58, thereby obtains one " poor ".This " poor " is input to adder unit 36.
Be used for algorithm C Figure 10 set-point filter device 120, control set-point value SV SV(S) determine by following formula:
C SV（S）＝K P〔α+1/T IS）-（1-α）β/（1+T IS）〕 …（13）
Obviously, two first- order lag devices 42 and 58 are used to finish two-freedom PI control.
Explanation set-point filter device 120 also has two first- order lag devices 42 and 52 among Figure 11.Its characteristics are that subtracter device 64 is connected to the output terminal of subtracter device 38, and subtracter device 38 deducts the output of coefficient multiplier device 34 from set-point value SV.Subtracter device 64 deducts the output of first-order lag device 52 from the output of subtracter device 38, the described output of device 52 obtains by postponing set-point value SV.Signal by subtracter device 64 outputs is input to first-order lag device 42.
Algorithm C set-point filter device 120, that control this set-point value that is used for Figure 11 SV(S) determine by following formula:
C SV（S）＝K P｛α+〔1/（T IS）-β/（1+βT IS）]｝ …（14）
Figure 12 has done some changes to the set-point filter device 120 shown in Figure 10.The dissimilarity of the device 120 among it and Figure 10 is, is that the output of set-point value SV rather than subtracter device 38 is input to first-order lag device 58.Employed therein algorithm C SV(S) be
C SV（S）＝K P｛α+〔1/（T IS）-β/（1+T IS）〕｝ …（15）
Therefore, can finish the control of two-freedom according to the of the present invention the 6th embodiment, 2DOF PID controller with the set-point filter device that is shown in Figure 12.
2DOF PID controller according to the 7th embodiment of the present invention describes now with reference to Figure 13.The parts identical with Fig. 2 with identical representing with reference to numbering, do not give a detailed account to these identical parts in Figure 13.
The 2DOF PID controller that is shown in Figure 13 except not with Fig. 2 in employed first-order lag device 52 equivalences parts and with parts 70,72 and the 74 replacement incomplete differential devices 50, all the controller with Fig. 2 is identical for all the other.In other words, this 2DOF PID controller comprises set-point filter device 220, PI algorithm actuating unit 22 and adder unit 24.The system 26 of this 2DOF PID controller control links the output terminal of adder unit 24.
This set-point filter device 220 receives set-point values and operates, thus, two degree of freedom give proportional gain Kp and derivative time T D
PI algorithm actuating unit 22 comprises deviation calculation device 28, non-linear device 30 and PI control device 32.The output SVo of setting value filter device 220 and the controlling value PV that is provided by controlled system 26 are provided deviation calculation device 28.And deduct controlling value PV from output SVo, thus, obtain deviation E, promptly it carries out subtraction: SVo-PV=E.30 couples of deviation E of non-linear device carry out nonlinear operation, thereby produce output.The PI control operation is carried out in the output of 32 pairs of non-linear devices 30 of PI control device, produces thus to handle alter MV.
Adder unit 24 is added to process disturbance signal D on the manipulated variable MV that is produced by PI algorithm operating part 22, output thus " with " to controlled system 26.As a result, system 26 is controlled so as to SV=SVo=PV.
As mentioned above, set-point filter device 220 gives proportional gain and derivative time two degree of freedom.For this purpose, bypass is to incomplete differential device 11(Fig. 1 of the output of PI control operation device 9) differential term be provided for set-point filter device 220.
At first, illustrate how device 220 gives proportional gain two degree of freedom.Gain coefficient multiplier device 34 multiplies each other the 2DOF factor alpha of set-point value SV and proportional gain.The output of multiplier 34 is the long-pending of SV and α, offers the first adder device 36 and first subtracter device 38.First subtracter device 38 deducts this output α SV from set-point value SV.The output of first subtracter device 38, promptly SV and α SV's is poor, inputs to first adder device 36 through second subtracter device 40, second first-order lag device 42 and second adder device 44.First adder device 36 so just gives proportional gain the output addition of the output of second adder device 44 and gain coefficient multiplier device 34 two degree of freedom.
To illustrate now how device 220 gives derivative time two-freedom.The output of gain coefficient multiplier device 34 is input to time coefficient multiplier device 46, and the 2DOF coefficient gamma of derivative time is set to device 46.The output and the coefficient gamma of time coefficient multiplier device 46 handle assemblies 34 multiply each other, and obtain long-pending α γ SV.This long-pending the 3rd subtracter device 48 that is input to.The 3rd subtracter device 48 deducts the controlling value PV of system 26 from long-pending α γ SV, obtain difference α γ SV-PV like this, and this difference offers divider means 70.The output of divider means 70 is directly inputted to the 4th subtracter device 74.It is also through the 3rd first-order lag device 72 inputs the 4th subtracter device 74.The 4th subtracter device 74 deducts the output of the 3rd first-order lag device 72 from the output of divider means 70.Second adder device 44 is directly imported in the output of the 4th subtracter device 74.It also inputs to second adder device 44 through second subtracter device 40 and first first-order lag device 42.Second adder device 44 is the output addition of the output of first first-order lag device 42 and the 4th subtracter device 74, thereby obtain " with ".This " with " be input to first adder device 36, the output of gain coefficient multiplier device 34, promptly α SV also offers it.Thereby, the output of first adder device 36 output gain coefficient multiplier devices 34 and second adder device 44 " with ".Like this " with ", promptly the output SVo of set-point filter device 220 inputs to the deviation calculation device 28 of PI algorithm operating part 22.
The incomplete differential device 50 that is used for the 1st embodiment of Fig. 2 can be used (TDS)/(1+ η T DS) equivalently represented, shown in Figure 14 A this equivalent mathematical notation formula, this algebraic symbol (expression) can change as follows:
T DS/（1+ηT DS）＝（1/η）ηT DS/（1+ηT DS）
＝（1/η）〔1-T Ds/（1+ηT Ds）〕 …（16）
Equation (16) can be by the block representation of Figure 14 B.Thereby incomplete differential device 50 is equivalent to the combination of the divider means 70 that is shown in Figure 13, the 3rd first-order lag device 72 and the 4th subtracter device 74.Therefore, the algorithm C of control procedure disturbance D(S) can provide by following formula.
C D（S）＝MV/PV
＝C（S）+〔T DS/（1+ηT DS）〕
×〔（T IS）/（1+T IS）〕C（S）
＝K P[1+1/（T IS）〕+〔T DS/（1+ηT DS）〕
×〔T IS/（1+T IS）〕×K P〔1+1/（T IS）〕
＝K P〔1+1/（T IS）+T DS/（1+ηT DS）〕 …（17）
On the other hand, the algorithm C of control set-point value SV SV(S) determine by following formula:
C SV（S）＝MV/SV
＝〔（1+αT IS）/（1+T IS）〕C（S）
+〔αγT DS/（1+ηT DS）〕
×〔T IS/（1+T IS）〕C（S）
＝〔（1+αT IS）/（1+T IS）〕K P〔1+1/（T IS）〕
+〔αγT DS/（1+ηT DS）〕
×〔T IS/（1+T IS）〕K P〔1+1/（T IS）〕 …（18）
Apparent from formula (17) and (18), keep the proportional gain Kp of process disturbance constant, by changing the proportional gain α Kp that the 2DOF factor alpha just can change set-point value.On the other hand, the derivative time of the algorithm of retentive control process disturbance is constant, and just can change by the 2DOF coefficient gamma that changes derivative time the derivative time of the algorithm of control set-point value SV.Briefly, the 2DOF PID controller that is shown in Figure 13 can all be carried out two-freedom control completely to P and D.
Thereby the 2DOF PID controller that is shown in Figure 13 only needs two time devices, and conventional 2DOF PID controller need have four time devices.Thereby it can be with lower cost manufacturing, and the volume after making is less, and load is lighter, and can high speed motion.
In addition,, the 2DOF factor alpha of proportional gain and the 2DOF coefficient gamma of derivative time are set easily with 2DOF PID controller shown in Figure 13, fixed because these two 2DOF coefficients can be put independently of one another.In addition, regulate these 2DOF coefficients easily, because when the 2DOF of proportional gain factor alpha changes, the gain of differential term is can be self-regulating.
Also have, differentiating unit can carry out nonlinear operation reliably in 2DOF PID controller.This is because controller is not equivalent to the incomplete differential device 11(Fig. 1 that switches to PI control operation device 9) parts, and the differential term of controlling value PV is input to set-point filter device 220.
Be arranged on according to the set-point filter device 220 in the 2DOF PID controller of the 8th embodiment of the present invention referring now to Figure 15 narration.This set-point filter device 220 and the set-point filter device 20 that is shown in Fig. 6 different are two aspects.At first, it is not equivalent to the parts of first-order lag device 52.Second point, its is with divider means 70, first-order lag device 72 is identical with those parts of the 7th embodiment that is used for Figure 13 with subtracter device 74() replacement is arranged on set-point filter device 20(Fig. 6) in the incomplete differential device.
Thereby, be applied to the algorithm C of the 8th embodiment of control procedure disturbance D(S) represent by equation (17).And be used to control the algorithm C of setting value SV SV(S) determine by following formula:
C SV（S）＝MV/SV
＝K P〔α+γT DS/（1+ηT DS）〕+K P/（T IS） （19）
Can know clearly that from formula (19) when the 2DOF of proportional gain factor alpha changed, the gain of differential term can not be regulated automatically.In this respect, the set-point filter device 220 of Figure 15 is different from the set-point filter device (Figure 13) of seventh embodiment of the invention.
Referring now to the 2DOF PID controller of Figure 16 to Figure 19 narration according to the ninth embodiment of the present invention.Figure 16 is the block diagram of explanation 2DOF PID controller; Figure 17 is the block diagram of the structure of table expression a kind of imagination of being arranged on the set-point filter device 320 in the PID controller that is shown in Figure 16; Figure 18 is the block diagram of expression set-point filter device 320 practical structures; Figure 19 be only comprise the first-order lag device to installing 320 block diagrams that change to some extent.
The basic structure of the 9th embodiment is narrated below with reference to Figure 16.As shown in figure 16,2DOF PID controller comprises that a set-point filter device 320, is coupled to the PI algorithm operating part 22 and the adder unit 24 that is connected to these operating part 22 output terminals of filter apparatus 320 output terminals.Be connected to the output of adder unit 24 by the system 26 of PID controller control.PI algorithm operating part 22 comprises a deviation calculation device 28, links the non-linear device 30 of device 28 output terminals and links the PI control device 32 of non-linear device 30 output terminals.
Set-point filter device 320 receives set-point value SV and controlling value PV, and controlling value PV is carried out derivation operation and 2DOF operation, produces set-point value SVo thus.This set-point value SVo offers PI algorithm operating part 22; More particularly, it is input to deviation calculation device 28.Device 28 deducts controlling value PV from set-point value SVo, so just obtain deviation E.Deviation E is input to non-linear device 30.30 couples of deviation E of non-linear device carry out all nonlinear operations and produce output.Have in these nonlinear operations: the dead band operation, the deviation square operation, gain changes operation and gap operating.The output of non-linear device 30 offers PI control device 32.The PI control operation is carried out in the output of 32 pairs of non-linear devices 30 of control device, produces manipulated variable MV thus.Adder unit 24 is process disturbance signal D and the manipulated variable MV addition that is produced by PI algorithm operating part 22, thus, output " with " to controlled system 26.
It is complexity like this that the inside of set-point filter device 320 constitutes, so that be difficult to get across.Constitute in order to narrate this inside, let us suppose device 320 comprises transport function 80,82,84,86,88 and 90, adder unit 92, and subtracter device 96 and totalizer one subtracter device 94, as shown in figure 17.
At first, determine transport function 80,82,84,86,88 and 90.The operation that PI control device 32 is carried out is determined by following formula:
C O（S）＝K P〔1+1/（T IS）〕 …（20）
Response to controlling value PV is expressed from the next:
PV＝｛（H（S）+H（S）P（S）R（S）+M（S）R（S）+
N（S）Q（S）R（S））Co（S）G（S）/〔1+（1+Q（S）R（S））
Co（S）G（S）〕｝SV+｛G（S）/〔1+（1+Q（S）R（S））
Co（S）G（S）〕｝D（S） …（21）
Formula (21) expression, controlling value PV is SV component and D(S) combination of component.Formula (21) is applied to the control algolithm of selected a kind of needs, and it will be by process disturbance D(S) change and control procedure disturbance best.In second of equation (21), the transport function G(S of Be Controlled system 26) and process disturbance D(S) be known variables.Thereby, the algorithm C of control procedure disturbance D(S) can be selected by using following common pid algorithm:
C D（S）＝｛1+Q（S）R（S）｝Co（S）
＝K P〔1+1/（T IS）+T DS/（1+ηT DS）〕 …（22）
From formula (20), (21) and (22), we obtain:
Co（S）Q（S）R（S）＝（T DS）/（1+ηT DS） …（23）
Q（S）R（S）＝〔（T DS）/（1+ηT DS）〕
×〔（T IS）/（1+T IS）〕 …（24）
And then from formula (24), we obtain by the definite transport function 88 and 90 of following formula:
Q（S）＝（T DS）/（1+ηT DS） …（25）
R（S）＝（T IS）/（1+T Is） …（26）
Then, the selected control algolithm that best set point following feature (Setpoint-following characteristic) is given 2DOF PID controller (Figure 16) that is applicable to.In first the SV component of formula (21), G(S) can not change with SV, the algorithm of formula (22) can not change.Thereby, the algorithm C of control set-point value SV SV(S) can provide by following formula:
C SV（S）＝〔H（S）+H（S）P（S）R（S）+M（S）R（S）
+N（S）Q（S）R（S）]Co（S）
＝K P｛α 1+〔1/（T IS）-β 1/（1+T IS）〕
+γ 1T DS/（1+ηT DS）〕 …（27）
In the formula, α 1, β 1 and γ 1 are the 2DOF coefficients and have following meanings:
(1) factor alpha 1
This is one proportional gain Kp is converted to proportional gain Kp *Coefficient, Kp is the required proportional gain of Optimal Control process disturbance, Kp *It is the proportional gain that is used for the optimum set point following feature is given the PID controller.This coefficient and Kp and Kp *Have following relationship:
α 1·K P＝K P ＊→α 1＝K P ＊/K P…（28）
(2) coefficient gamma 1
This coefficient is used for T derivative time DBe converted to T derivative time D *, T DBe required derivative time of Optimal Control process disturbance, T D *It is the derivative time that is used for best set point following feature is given the PID controller.Coefficient gamma 1With Kp, Kp *, T DAnd T D *Have following relationship:
K P·γ 1·T D＝K P ＊·T D ＊→γ 1＝α 1·（T D ＊/T D） …（29）
(3) factor beta 1
This be one T integral time IBe converted to T integral time I *Coefficient, T IBe required integral time of Optimal Control process disturbance, T I *It is the integral time that is used for best set point following feature is given the PID controller.
Optimal proportion gain Kp *Can obtain by gain Kp be multiply by α, and the best T derivative time D *Can pass through T derivative time DMultiply by γ 1/ α 1 and obtain.
But, give best set point following feature the PID controller required T I *Can not pass through T integral time IMultiply by coefficient and obtain.In order to give integral time two-freedom, must take special measure, be similar to the equation of formula (23) such as application class.For example, integral time T I *Can change T integral time by changing the value of β 1 then of equal valuely IAnd obtain.More particularly, give best set point following feature the PID follower required integral I *(S) determine by following formula:
I *(S)=I(S)-saturation device
＝I（S）-β 1/（1+T IS）
＝1/（T IS）-β 1/（1+T IS） …（30）
Annotate: saturation device is to give the optimum process perturbation control required integral I(S) corresponding to the first-order lag device.
In formula (30), β 1 is set to such value:
(a) if β is 1=0, I *(S)=I(S), thus remain unchanged integral time.
(b) if β 1＞0, I *(S)＜I(S), thereby, corresponding increase integral time.
(c) if β 1＜0, I *(S)＞I(S), thereby, corresponding minimizing integral time.
In other words, by formula (26) determined integral time the value with selected factor beta 1 change.Formula (23) is applied to formula (27), and transport function 84 or N(S) place coefficient gamma 1, that is, and N(S)=and γ 1, thus, eliminate differential term.As a result, we obtain:
〔H（S）+H（S）P（S）R（S）+M（S）R（S）〕Co（S）
＝K P｛α 1+〔1/（T IS）-β 1/（1+T IS）〕｝ …（31）
When formula (20) was applied to formula (31), formula (31) became:
H（S）+H（S）P（S）R（S）+M（S）R（S）
＝1/（1+T IS）+〔-β 1/（1+T IS）〕〔T IS/（1+T IS）〕
+α 1T IS/（1+T IS） …（32）
By formula (26) and formula (32), transport function 80,86 and 82 will be:
H（S）＝1/（1+T IS）
P（S）＝-β 1
M（S）＝α 1…（33）
Point out formula (25), (26) and (33): set-point filter device 320 can only be made up of first-order lag device and lead-lag device, as shown in Figure 18.
T IS/(1+T IS) and T DS/(1+T DS) can rewrite as follows:
T IS/（1+T IS）＝1-1/（1+T IS） …（34）
T DS/（1+ηT DS）
＝（1/η）〔1-1/（1+ηT DS）〕 （η≠0） …（35）
Thereby set-point filter device 320 can have structure as shown in figure 19.As shown in figure 19, transport function 88 can be by subtracter device 88a, and first-order lag device 88b and subtracter device 88c form, and transport function 90 is made up of first-order lag device 90a and subtracter device 90b.Like this, set-point filter device 320 only comprises three first- order lag devices 80,88b and 90.
As mentioned above, the control section of 2DOF PID controller that is shown in Figure 16 to 19 is according to the work of PI algorithm, and its filter segment has set-point filter device 320, and it receives set-point value SV and controlling value PV and according to desirable and selected control algolithm execution derivation operation.Thereby the PID controller can be carried out the 2DOF pid algorithm.In addition, if 2DOF factor alpha 1, β 1 and γ 1 are placed in the value of following table regulation, and the PID controller just can be carried out the PID control of one degree of freedom, incomplete two degree of freedom PID control and 2DOF PID control completely.
Table
NO α 1 β 1 γ 1 control algolithm control category
General PID control 1DOF
1 1 0 0
(differential PID) PID
PI-D controls 1DOF
2 1 0 0
To PV differential PID
1DOF
3000 I-PD control
PID
P-I-PD control not exclusively
4 α 00 (only carry out 2DOF to P
2DOF control) PID
PD-I-PD control not exclusively
5 α O γ (only carry out 2DOF to PD
2DOF control) PID
PI-PID control not exclusively
6 α β 0 (only carry out 2DOF to PI
2DOF control) PID
Fully
7 α β γ PID-PID control
2DOF
Just as already noted, Chang Gui 2DOF PID controller comprises the set-point filter device and has the control section of non-linear device and be designed to carry out PV derivative-type PID is controlled.The combination of set-point filter device and control section can not be carried out nonlinear operation completely to deviation.And not having the derivation operation device according to the control section of 2DOF PID controller of the present invention at all, its set-point filter device receives set-point value and controlling value and according to desired and selected control algolithm execution derivation operation.The output of set-point filter device offers control section, and it finishes nonlinear operation and PI control operation.Thereby 2DOF PID controller of the present invention can be carried out nonlinear operation to P, I and D, have simple and easy, accurately and the advantage of degree of freedom.2DOF PID controller of the present invention can efficiency operation.
Moreover, only need three first-order lag devices according to 2DOF PID controller of the present invention, and conventional 2DOF PID controller (Fig. 1) need have six first-order lag devices.Thereby 2DOF PID controller of the present invention can be done to such an extent that compare the little and simple of routine, helps improving the basis of the PID system that controls factory.Thus, the present invention can go far towards the every field of industry.
The above embodiments have non-linear device 30.Yet the present invention can be applied to not have the 2DOF controller of non-linear device.
Those skilled in the art is easy to concept imagine according to the present invention and goes out many variations and improvement, thereby the present invention is not limited to details described herein, representative device and the description thereof shown in also being not limited to here.Above-mentioned many variations and revise still falls within spirit of the present invention and the scope, and protection scope of the present invention should be as described in the appended claims.

Claims (20)

1, a kind of two-freedom PID controller is characterized in that comprising:
Controlling value (PV) according to set-point value (SV) and controlled system (26) is carried out derivation operation (D) to the process disturbance signal, exports the set-point filter device (20,220) of set point signal (SVo) thus;
Determine the deviation (E) between described set point signal and the described controlling value and this deviation carried out the PI control operation, export the PI control operation device (22) of a control signal (MV) thus; With
Process disturbance signal and control signal addition by the output of described PI control operation device, thereby obtain " with " signal and this and signal are offered the adder unit (24) of Be Controlled system.
2, PID controller as claimed in claim 1 is characterized in that, described PI control operation device comprises the non-linear device (30) of described deviation being carried out nonlinear operation.
3, PID controller as claimed in claim 1 is characterized in that, described set-point filter device (20) comprising:
The two-freedom multiplication of set-point value and proportional gain, export the gain coefficient multiplier (34) of first product thus;
From set-point value, deduct described first product, export first subtracter device (38) of first difference thus;
Have for integral time and two degree of freedom, be used for described first difference is carried out the first-order lag operation, exported first first-order lag device (52) of first result of first-order lag operation thus;
The two-freedom multiplication of described first product and derivative time, thereby export coefficient multiplier derivative time (46) of second product;
From second product, deduct described controlling value, thereby export second subtracter device (48) of second difference;
Receive described second difference and described second difference is carried out the incomplete differential operation, export the incomplete differential device (50) of incomplete differential operating result thus;
From first result of first-order lag operation, deduct the result of incomplete differential operation, export the 3rd subtracter device (40) of the 3rd difference thus;
Described the 3rd difference is carried out the first-order lag operation, thus second first-order lag device (42) of second result of output first-order lag operation;
The results added that second result of first-order lag operation and incomplete differential are operated, thus export first " with " first adder device (44);
First " with " thus obtain second with the first product addition " with ", and this second " with " offer the second adder device (36) of described PI control operation device as set point signal.
4, PID controller as claimed in claim 3 is characterized in that, described incomplete differential device (50) comprising:
To described second the difference divided by predetermined number, thereby export one merchant divider means (70);
Merchant by described divider means output is carried out the first-order lag operation, thereby produce the 3rd the first-order lag device (72) of an output; With
From described merchant, deduct the output of described the 3rd first-order lag device, thereby produce described incomplete differential device output, it is offered the 4th subtracter device (74) of described the 3rd subtracter device and described first adder device.
5, PID controller as claimed in claim 3 is characterized in that, described PI control operation device comprises the non-linear device (30) of described deviation being carried out nonlinear operation.
6, PID controller as claimed in claim 1 is characterized in that, described set-point filter device (20) comprising:
The two-freedom multiplication of set-point value and proportional gain, thereby export the gain coefficient multiplier (34) of first product;
From set-point value, deduct described first product, thereby export first subtracter device (38) of first difference;
Two-freedom coefficient with an integral time is operated in order to described first difference is carried out first-order lag, thereby exports first first-order lag device (52) of first result of described first-order lag operation;
The two-freedom multiplication of set-point value and derivative time, thereby export coefficient multiplier derivative time (56) of second product;
From described second product, deduct controlling value, thereby export second subtracter device (48) of second difference;
Receive second difference and described second difference is carried out the incomplete differential operation, export the result's of incomplete differential operation incomplete differential device (50) thus;
From first result of first-order lag operation, deduct the result of incomplete differential operation, thereby export the 3rd subtracter device (40) of the 3rd difference;
Described the 3rd difference is carried out the first-order lag operation, thus second first-order lag device (42) of second result of output first-order lag operation;
The results added that second result of first-order lag operation and incomplete differential are operated, thus export first " with " first adder device (44); With
Described first " with " with the first long-pending addition, thereby obtain second " with " and this second " with " offer the second adder device (36) of described PI control operation device as set point signal.
7, PID controller as claimed in claim 6 is characterized in that, described incomplete differential device (50) comprising:
Thereby described second difference is exported a merchant's divider means (70) divided by predetermined number;
Thereby the described merchant by described divider means output is carried out the first-order lag operation produce the 3rd the first-order lag device (72) of an output; With
From described merchant, deduct the output of described the 3rd first-order lag device, thereby produce the output of described incomplete differential device and it is offered the 4th subtracter device (74) of described the 3rd substracting unit and described first adder device.
8, PID controller as claimed in claim 6 is characterized in that, described PI control operation device comprises the non-linear device (30) of described deviation being carried out nonlinear operation.
9, PID controller as claimed in claim 1 is characterized in that, described set-point filter device (20) comprising:
Thereby the two-freedom multiplication of set-point value and proportional gain is exported the gain coefficient multiplier (34) of first product;
Thereby from set-point value, deduct first subtracter device (38) that described first product is exported first difference;
Thereby the two-freedom multiplication of described first product and a derivative time is exported second long-pending coefficient multiplier derivative time (46);
Thereby from described second amasss, deduct second subtracter device (48) that controlling value is exported second difference;
Receive described second difference and thereby this second difference is carried out the incomplete differential device (70,72,74) that the incomplete differential operating result is exported in the incomplete differential operation;
From described first difference, deduct the result of incomplete differential operation, thereby export the 3rd subtracter device (40) of the 3rd difference;
Described the 3rd difference is carried out the first-order lag operation, thus the first-order lag device (42) of output first-order lag operating result;
The result and the addition of incomplete differential operating result of first-order lag operation, thus export first " with " first adder device (44); With
First " with " thus obtain second with the described first long-pending addition " with " and this second " with " offer the second adder device (36) of described PI control operation device as set point signal.
10, PID controller as claimed in claim 9 is characterized in that, described incomplete differential device (50) comprising:
Thereby described second difference is exported a merchant's divider means (70) divided by predetermined number;
Thereby the described merchant from described divider means output is carried out the first-order lag operation produce second first-order lag device (72) of an output; With
From described merchant, deduct the output of described second first-order lag device, thereby produce the output of described incomplete differential device and it is offered the 4th subtracter device (74) of described the 3rd subtracter device and described first adder device.
11, PID controller as claimed in claim 9 is characterized in that, described PI control operation device comprises the non-linear device (30) of deviation being carried out nonlinear operation.
12, PID controller as claimed in claim 1 is characterized in that, described set-point filter device (20) comprising:
Thereby the two-freedom multiplication of set-point value and proportional gain is exported the first long-pending gain coefficient multiplier (34);
Thereby from set-point value, deduct described first long-pending first subtracter device (38) of exporting first difference;
Thereby the two-freedom multiplication of set-point value and a derivative time is exported second long-pending coefficient multiplier derivative time (56);
Thereby from described second amasss, deduct second subtracter device (48) that controlling value is exported second difference;
Receive described second difference and this second difference is carried out the incomplete differential operation, thus the incomplete differential device (70,72,74) of output incomplete differential operating result;
Thereby the result who deducts the incomplete differential operation from described first difference exports the 3rd subtracter device (40) of the 3rd difference;
Thereby described the 3rd difference is carried out the first-order lag device (42) of first-order lag operation output first-order lag operating result;
The results added that the result of first-order lag operation and incomplete differential are operated, thus export first " with " first adder device (44); With
Described first " with " thus obtain second with the described first long-pending addition " with " and this second " with " offer the second adder device (36) of PI control operation device as set point signal.
13, PID controller as claimed in claim 12 is characterized in that, described incomplete differential device (50) comprising:
Thereby described second difference is exported a merchant's divider means (70) divided by a predetermined number;
Merchant by described divider means output is carried out the first-order lag operation, thereby produce second first-order lag device (72) of an output; With
Thereby the output that deducts described second first-order lag device from described merchant produces the output of described incomplete differential device, and it is offered the 4th subtracter device (74) of described the 3rd subtracter device and described first adder device.
14, PID controller as claimed in claim 13 is characterized in that, described PI control operation device comprises the non-linear device (30) of deviation being carried out nonlinear operation.
15, a kind of controller of two-freedom is characterized in that comprising:
Receive set-point value and produce the set-point filter device (120) of set point signal, described set-point filter device comprises:
The two-freedom multiplication of a set-point value and a proportional gain is exported a long-pending coefficient multiplier (34) thus;
Thereby have the two-freedom coefficient of an integral time at least and be designed to from set-point value, deduct the described long-pending first-order lag device (38,52,58,42) that produces difference; With
Thereby the device (36) of described long-pending and described poor addition output set point signal;
Deviation between the controlling value of determining set point signal and being provided by the Be Controlled system is also carried out the PI control operation to this deviation, thereby exports the PI control operation device (28,32) of a control signal; With
Process disturbance signal and control signal addition by the output of described PI control operation device, thus obtain " with " signal and this " with " signal offers the adder unit (24) of described Be Controlled system.
16, controller as claimed in claim 15 is characterized in that, described first-order lag device comprises:
Thereby from set-point value, deduct the described long-pending subtracter device (34) of exporting a difference; With
Series connection also receives two first-order lag devices (52,42) of described difference, and one of them has the two-freedom coefficient of integral time.
17, a kind of two degree of freedom controller is characterized in that it comprises:
Receive set-point value and produce the set-point filter (120) of set point signal, described set-point filter device comprises:
The two-freedom multiplication of a described set-point value and a proportional gain, thus the long-pending coefficient multiplier (34) of output;
Thereby from described set-point value, deduct described long-pending first first-order lag device (42) that produces difference; With
Have one integral time two-freedom coefficient and postpone set-point value and second first-order lag device of the set-point value that output is delayed (52,58); With
Amass and the set-point value addition that postpones by described second first-order lag device described, thus the device (36) of output set point signal;
Deviation between the controlling value of determining set point signal and being provided by the Be Controlled system is also carried out the PI control operation to this deviation, thus the PI control operation device (28,32) of output control signal; With
Process disturbance signal and control signal addition by the output of described PI control operation device, thus obtain " with " signal and this " with " signal offers the adder unit (24) of Be Controlled system.
18, a kind of two-freedom PID controller is characterized in that it comprises:
Thereby the two-freedom multiplication of a set-point value and a proportional gain is exported the first long-pending gain coefficient multiplier (82);
The two-freedom multiplication of set-point value and a derivative time, thereby export second long-pending coefficient multiplier derivative time (84);
Thereby described set-point value is carried out the first-order lag operation export first first-order lag device (80) that this first-order lag is operated first result;
The result of first-order lag operation with one integral time the two-freedom multiplication, thereby export the 3rd coefficient multiplier integral time (86) that amasss;
To described second long-pending and carry out the incomplete differential operation by the controlling value that the Be Controlled system provides, thus the output result's of output incomplete differential operation incomplete differential device (88,96);
To first long-pending, the 3rd result long-pending and the incomplete differential operation carries out the first-order lag operation, thus second first-order lag device (94,90) of second result of output first-order lag operation;
Thereby the first adder device (92) of first and second results added output set point signal of first-order lag operation;
Determine the deviation between set point signal and the controlling value and this deviation carried out the PI control operation, thereby export the PI control operation device (28,30,32) of a control signal; With
Process disturbance signal and control signal addition, thus obtain " with " signal and this " with " signal offers the second adder device (24) of Be Controlled system.
19, PID controller as claimed in claim 18 is characterized in that, described PI control operation device comprises the non-linear device (30) of deviation being carried out nonlinear operation.
CN 90107699 1989-09-11 1990-09-11 Two degree of freedom controller Expired - Fee Related CN1024953C (en)

Applications Claiming Priority (5)

Application Number Priority Date Filing Date Title
JP1234959A JP2772059B2 (en) 1989-09-11 1989-09-11 2-DOF PID controller
JP234959/89 1989-09-11
JP315486/89 1989-12-06
JP1344366A JP2845534B2 (en) 1989-12-28 1989-12-28 2-DOF adjustment device
JP344366/89 1989-12-28

Publications (2)

Publication Number Publication Date
CN1050270A CN1050270A (en) 1991-03-27
CN1024953C true CN1024953C (en) 1994-06-08

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CN 90107699 Expired - Fee Related CN1024953C (en) 1989-09-11 1990-09-11 Two degree of freedom controller

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