CN104698841B - Control system combining proportional-integral with state reset and implementation method - Google Patents
Control system combining proportional-integral with state reset and implementation method Download PDFInfo
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- CN104698841B CN104698841B CN201510058161.0A CN201510058161A CN104698841B CN 104698841 B CN104698841 B CN 104698841B CN 201510058161 A CN201510058161 A CN 201510058161A CN 104698841 B CN104698841 B CN 104698841B
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Abstract
The invention provides a control system combining proportional-integral with state reset. The control system comprises a proportional-integral control link and a state reset control link, input is an error signal e (t), output u (t) is used for controlling a controlled object P (s), the state reset control link is parallelly connected with the proportional-integral control link, and an output signal of the state reset control link is reset to zero when symbols of the error signal e (t) are different from those of the output signal of the state reset control link. The invention further provides an implementation method of the control system combining proportional-integral with state reset. A first adjusting parameter is serially connected with the proportional-integral control link, a second adjusting parameter is serially connected with the state reset control link, the first adjusting parameter and the second adjusting parameter are adjusted to realize rapid adjustment and decrease overshoot, and fine steady-state and dynamic performances are achieved.
Description
Technical field
The present invention relates to technical field of automatic control is and in particular to combine PI (PID:Proportional-
Integral, proportional integral) control control system and the implementation method resetting control (Reset Control) with state.
Background technology
Proportional integral (PI) controller is widely used in the various occasions needing Automated condtrol, the output of PI controller
Including proportional, two parts of integral term, the form of PI algorithm can be described as:
Wherein, kp,kiIt is respectively proportional gain, storage gain.E (t) is setting value (SP:Set Point) and process variable
(PV:Process Variable) difference, u (t) is the output of PI controller.
Resetting control system (Reset Control Systems) refers to controlled device for dynamically controller continuous time
The system that existence resets, is nonlinear systems.Reset controller is increased by the linearly or nonlinearly controller of standard
Put rule composition, when system mode meets given replacement rule, controller state is reset to zero or related with state
Value.Drive replacement behavior event referred to as reset condition, typical replacement condition be when controller input zero passage when or
State is reset to zero when contrary by controller input/output symbol.Resetting control is to be proposed in 1958 by Clegg earliest
Clegg integrator, compared to common integrator, but it has the delayed phase of identical magnitude margin only 38.1 degree.
Control the reason mainly have two aspects using resetting:One is the transient performance in order to improve system;Two is to reset control to have
The potential advantages of Linear Control performance boundary can be overcome.
Prior art Vidal, A.Banos, J.C.Moreno, M.Berenguel, PI+CI compensation with
variable reset:Application on solar collector fields,Industrial Electronics,
2008.IECON 2008.34th Annual Conference of IEEE, proposes a kind of ratio in pp.321-326,2008.
Integration plus the control method of Clegg integrator, control the characteristic that can eliminate error and Clegg integrator to improve system using PI
But the characteristic of system dynamic property is so that PI+CI controller is capable of controlling the same rise time overshoot to reduce with PI,
Thus by the simple dynamic property resetting and controlling the system that improves.Its shortcoming is:The Clegg integrator being used is
Simple replacement control device, regulation parameter only one of which, the replacement rule being adopted is will to control during controller input zero passage
Device state is reset to zero, thus cannot analyze the robustness for disturbing signal using this control method.
Content of the invention
Add for existing PI that regulation parameter in reset control method is few and replacement control system model that adopted is not easy to
The deficiency of robust analysis, it is an object of the present invention to propose a kind of combination PI and FORE based on hybrid model
The control system of (First Order Reset Element).
The present invention provides the control system that a kind of combination proportional integral is reset with state, as shown in Fig. 2 wherein proportional integral
Link is compared with conventional proportional integral link and be increased a coefficient lambda1, FORE is the link comprising state replacement, and increases
One coefficient lambda2, λ1And λ2The ratio partly shared with replacement for adjusting integral part in output u (t).
The advantage that PI controls is quick regulation system dynamics, and realizes zero steady-state error regulation, but quick regulation
Process may make to occur larger overshoot during error convergence, that is, be capable of preferable steady-state behaviour and dynamic property may
Poor.And the advantage resetting control be improve control system dynamic property, but be single use replacement control it cannot be guaranteed that
Zero steady-state error performance.Therefore, the advantage controlling in conjunction with PI control and replacement, can reach preferable stable state and dynamic simultaneously
Energy.
The present invention also provides the implementation method of a kind of combination proportional integral and the control system of state replacement.
Hybrid system mentioned here refers to that system dynamics include continuously dynamic and Discrete Dynamic system.
The present invention provides the control system that a kind of combination proportional integral is reset with state, including proportional plus integral control link,
Input as error signal e (t), export u (t) and be used for controlling controlled device P (s), the control resetting with state in conjunction with proportional integral
System also includes state and resets controlling unit, and state replacement controlling unit is in parallel with proportional plus integral control link, works as error signal e
When the output signal symbol of () and state replacement controlling unit is different t, the output signal that state resets controlling unit is reset to zero
Value.
Further, the control system resetting with state in conjunction with proportional integral also includes the first regulation parameter and the second regulation
Parameter, the first regulation parameter is connected with proportional plus integral control link, and the second regulation parameter resets controlling unit with state and connects.
Further, the first regulation parameter and the second regulation parameter and be 1.
Further, increase the ratio of the first regulation parameter and the second regulation parameter, to realize quick regulation.
Further, reduce the ratio of the first regulation parameter and the second regulation parameter, to reduce overshoot.
Further, state resets controlling unit and resets controlling unit for single order.
Further, single order resets the first linear filter and the second linear filter that controlling unit includes parallel connection, the
First electric capacity parallel connection the first diode of one linear filter, second electric capacity parallel connection the second diode of the second linear filter,
First diode is in opposite direction with the second diode, and single order resets controlling unit and is output as:
xr(t)=- vC1(t)-vC2(t)
Wherein vC1T () is the output of the first linear filter, vC2T () is the output of the second linear filter.
Further, the continuous dynamic part transmission function of single order replacement controlling unit can be expressed asWherein ar
For resistance R1Value, brFor resistance R2Value, the value of electric capacity is
Further, the dynamical equation of single order replacement controlling unit is:
Wherein e (t) and xr(t, j) represents that t single order resets input and the output voltage of controlling unit respectively.J represents
Have occurred and that j replacement.tj+1Represent that jth time resets the moment occurring, xr(tj+1, firstorder filter before j) expression resets
State value, xr(tj+1, j+1) represent jth time reset after firstorder filter value.
Compared to Clegg integrator, single order resets controlling unit FORE and increased a regulation parameter, thus increased weight
Put the degree of freedom of controller design;Single order resets the model of controlling unit FORE, such as above-mentioned single order resets the dynamic of controlling unit
State is reset to zero replacement rule, inputted different from Clegg integrator by equation when the input/output symbol of employing is different
When zero, state is reset to zero replacement rule, so that being easier to analyze the robustness of this control method.
The present invention also provides the implementation method of a kind of combination proportional integral and the control system of state replacement, walks including following
Suddenly:
(1) do not consider that state resets the replacement behavior of controlling unit it is considered to state resets the continuous dynamic state part of controlling unit
The transmission function divided, determines the parameter combining the control system that proportional integral is reset with state so that closed-loop control system is stablized;
(2) consider that state resets the replacement behavior of controlling unit, determine that state resets the parameter of controlling unit;
(3) adjust proportional plus integral control link and the ratio resetting controlling unit, improve system dynamics behavior to reach
Purpose.
Compared with prior art, a kind of combination proportional integral of present invention offer is reset with state control system and realization side
Method has the advantages that:
First regulation parameter is connected with proportional integral link, and the second regulation parameter connect with resetting controlling unit, regulation the
One regulation parameter and the second regulation parameter, to realize quick regulation, to reduce overshoot, reach preferable stable state and dynamic simultaneously
Energy.
Brief description
Fig. 1 is the closed loop control system with the control system of state replacement for the combination proportional integral of one embodiment of the present of invention
System structure chart;
Fig. 2 is the structure chart of the control system that the combination proportional integral shown in Fig. 1 is reset with state;
Fig. 3 is the electricity of the state replacement controlling unit of the control system that the combination proportional integral shown in Fig. 1 is reset with state
Lu Tu;
Fig. 4 is the circuit diagram of first-order linear wave filter.
Specific embodiment
In order that the objects, technical solutions and advantages of the present invention are definitely, with reference to Figure of description and specifically in fact
Apply example, the present invention is described in more detail.
As shown in figure 1, the control system that the combination proportional integral of one embodiment of the present of invention is reset with state, including ratio
Example integration control link PI, inputs as error signal e (t), exports u (t) and is used for controlling controlled device P (s).
The control system being reset with state in conjunction with proportional integral is also included state and resets controlling unit FORE, and state resets control
Link FORE processed is in parallel with proportional plus integral control link PI, when the output of error signal e (t) and state replacement controlling unit FORE
When signal code is different, the output signal that state resets controlling unit FORE is reset to null value.
As shown in Fig. 2 the control system resetting with state with reference to proportional integral also includes the first regulation parameter λ1With second
Regulation parameter λ2, the first regulation parameter λ1Connect with proportional plus integral control link PI, the second regulation parameter λ2Reset with state and control
Link FORE is connected.
First regulation parameter λ1With the second regulation parameter λ2And be 1.
Increase the first regulation parameter λ1With the second regulation parameter λ2Ratio, to realize quick regulation.
Reduce the first regulation parameter λ1With the second regulation parameter λ2Ratio, to reduce overshoot.
State resets controlling unit FORE and resets controlling unit for single order.
FORE is by common first-order linear wave filter, as shown in figure 4, expanding, its specific circuit structure such as Fig. 3
Shown, according to this circuit structure, compare with first-order linear wave filter, the output of FORE is no longer dynamically linear, and shows bag
Include continuously dynamic and Discrete Dynamic Hybrid dynamics behavior.
Known by the ABC of Circuits System, using ideal operational amplificr, firstorder filter can be by input channel
Resistance and the resistance of feedback channel and electric capacity realize.Pass between corresponding input and output ties up to time domain and can be expressed as
In order to realize resetting control, when the input and output not jack per line of firstorder filter, state is reset to zero, design
Single order as shown in Figure 3 resets Controlling model.It dynamically can be described as follows.Firstly, since being ideal operational amplifier, input voltage is always
Zero, two capacitance voltages meet vC1(t)≤0 and vC2(t) >=0 (otherwise the electric current in diode can make electric capacity discharge).Work as e
T, during () < 0, the voltage no matter being present in electric capacity above is how many, the electric current in both the above diode passes through RdSo that
vC1T () is almost changed into v at onceC1(t)=0.However, when e (t) >=0, circuit above corresponds to firstorder filter, due to two
There is no electric current in pole pipe.For following circuit, similar analysis is it is recognised that have v as e (t) > 0C2T ()=0, as e (t)
When≤0, circuit is changed into firstorder filter.V is known according to analysisC1(t)≤0 and vC2T () >=0 meets always, define xr(t)=-
vC1(t)-vC2(t).
Single order resets the first linear filter (linear filter on top) that controlling unit includes parallel connection, linear with second
Wave filter (linear filter of bottom), first electric capacity parallel connection the first diode of the first linear filter, the second linear filtering
Second electric capacity parallel connection the second diode of device, the first diode is in opposite direction with the second diode;
3rd resistor R in first linear filterdThe first electricity after the 3rd Diode series, with the first linear filter
Resistance R1Parallel connection, the 3rd diode is identical with the first diode direction;3rd resistor R in second linear filterdWith the 4th diode
First resistor R after series connection, with the second linear filter1Parallel connection, the 4th diode is identical with the second diode direction.
Single order resets controlling unit and is output as:
xr(t)=- vC1(t)-vC2(t)
Wherein vC1T () is the output of the first linear filter, vC2T () is the output of the second linear filter.
Single order reset controlling unit dynamical equation be:
E (t) and xr(t, j) represents input and the output voltage of t Clegg integrator respectively.J represents and has occurred and that j
Secondary replacement.tj+1Represent that jth time resets the moment occurring, xr(tj+1, j) represent the state value of firstorder filter before replacement, xr
(tj+1, j+1) represent jth time reset after firstorder filter value.
The relation being inputted and exported by above firstorder filter can be seen that e (t) and xr(t, j) will not contrary sign.If e
T () > 0 is thenBecause vC1(t)≤0, so e (t) vC1(t)≥0.During e (t) < 0, similar analysis can obtain e (t) vC2
(t)≥0.In addition, at least one, two parts circuit plays that firstorder filter acts on and another is output as about e (t) ≠ 0
Zero.
The continuous dynamic part transmission function that single order resets controlling unit can be expressed asWherein arFor resistance R1
Value, brFor resistance R2Value, the value of electric capacity is
For sake of convenience, it is now assumed that the transfer function model of controlled device P (s) is as follows:
Step one:Do not consider that reset occurs it is known that the transmission function of the continuous dynamic part of FORE can be written as firstAccording to the controller architecture in Fig. 2, design relevant parameter kp,ki,ar,br,λ1,λ2Make closed loop system that weight is not occurring
It is stable when putting.First the controller transfer function in Fig. 2 is expressed as
Wherein λ1,λ2It is for adjusting the ratio of PI part and FORE part and meeting λ1+λ2=1, λ=0.5, λ can be chosen as2=
0.5, then design kp,ki,ar,brMake closed loop transform function Nc(s)Dp(s)+Np(s)DcS the characteristic root of () is all located at complex plane
Left half-plane (in lineary system theory, it is possible to use POLE PLACEMENT USING, quantitative feedback theory or LMI are theoretical
Walk parameter designing etc. completing this), and meet certain system performance index (as the dynamic properties such as rise time, setup time refer to
Mark).
Step 2:FORE device containing the behavior of replacement in Fig. 3 is added to the relevant position in Fig. 2, so that
Controller has Hybrid dynamics behavior, according to the dynamic analysis for FORE in content of the invention, as error signal e (t) and FORE
Output signal symbol different when, the output of FORE is reset to null value, so that the value of u (t) resets.Further,
Ensureing closed loop transform function Nc(s)Dp(s)+Np(s)DcParameter a of FORE is adjusted s () is stable in the case thatr,brCarried with reaching
The purpose of high dynamic performance.
Step 3:Because PI control section is mainly used in realizing zero steady-state error and the purpose of regulation rise time, and
FORE is mainly used in the dynamic behaviours such as the overshoot of improvement system, convergence rate.Accordingly, it would be desirable to the ratio shared by regulation two parts
To reach desired systematic function, parameter lambda1,λ2Exactly in order to realize this purpose.According to the regulation of first two steps, other controllers
Parameter has determined.Adjust λ1,λ2Value, increaseThe performance to reach the quick rise time for the value, or reduce's
Value reduces the performance of output overshoot to reach.
Control system and implementation method that combination proportional integral and the state that the present invention provides resets, the first regulation parameter with
Proportional integral link is connected, and the second regulation parameter is connected with resetting controlling unit, adjusts the first regulation parameter and adjusts ginseng with second
Number, to realize quick regulation, to reduce overshoot, reaches preferable stable state and dynamic property simultaneously.
The preferred embodiment of the present invention described in detail above.It should be appreciated that those of ordinary skill in the art is no
Need creative work just can make many modifications and variations according to the design of the present invention.Therefore, all technology in the art
It is available that personnel pass through logical analysis, reasoning, or a limited experiment under this invention's idea on the basis of existing technology
Technical scheme, all should be in the protection domain being defined in the patent claims.
Claims (8)
1. the control system that a kind of combination proportional integral is reset with state, including proportional plus integral control link, inputs as error letter
Number e (t), output u (t) is used for controlling controlled device P (s) it is characterised in that the control that resets with state of described combination proportional integral
System processed also includes state and resets controlling unit, and described state replacement controlling unit is in parallel with described proportional plus integral control link,
When the output signal symbol of error signal e (t) and described state replacement controlling unit is different, described state resets controlling unit
Output signal be reset to null value;
Described state resets controlling unit and resets controlling unit for single order;
Described single order resets the first linear filter and the second linear filter that controlling unit includes parallel connection, and described first is linear
First electric capacity parallel connection the first diode of wave filter, second electric capacity parallel connection the second diode of described second linear filter, institute
State the first diode in opposite direction with described second diode, described single order resets controlling unit and is output as:
xr(t)=- vC1(t)-vC2(t)
Wherein vC1T () is the output of described first linear filter, vC2T () is the output of described second linear filter.
2. combination proportional integral as claimed in claim 1 and state reset control system is it is characterised in that described combination ratio
The control system that example integration is reset with state also includes the first regulation parameter and the second regulation parameter, described first regulation parameter with
Described proportional plus integral control link series connection, described second regulation parameter resets controlling unit with described state and connects.
3. the control system that combination proportional integral as claimed in claim 2 and state reset is it is characterised in that described first adjusts
JIESHEN number and described second regulation parameter and be 1.
4. combination proportional integral as claimed in claim 2 and state reset control system is it is characterised in that increase described the
One regulation parameter and the ratio of described second regulation parameter, to realize quick regulation.
5. combination proportional integral as claimed in claim 2 and state reset control system is it is characterised in that reduce described the
One regulation parameter and the ratio of described second regulation parameter, to reduce overshoot.
6. combination proportional integral as claimed in claim 1 and state reset control system is it is characterised in that described single order weight
The continuous dynamic part transmission function putting controlling unit is expressed asWherein arFor resistance R1Value, brFor resistance R2Value,
The value of electric capacity is
7. combination proportional integral as claimed in claim 1 and state reset control system is it is characterised in that described single order weight
The dynamical equation putting controlling unit is:
Wherein e (t) and xr(t, j) represents that t single order resets the input of controlling unit and output voltage respectively, and j represents and sent out
Raw j replacement, tj+1Represent that jth time resets the moment occurring, xr(tj+1, j) represent the state value of firstorder filter before replacement,
xr(tj+1, j+1) represent jth time reset after firstorder filter value;R1Represent resistance R1Value, R2Represent resistance R2Value, C
Represent the value of electric capacity C.
8. the realization side of the control system that the combination proportional integral as described in a kind of as arbitrary in claim 1-7 one is reset with state
Method is it is characterised in that described implementation method comprises the following steps:
(1) do not consider that state resets the replacement behavior of controlling unit it is considered to described state resets the continuous dynamic state part of controlling unit
The transmission function divided, determines the parameter combining the control system that proportional integral is reset with state so that closed-loop control system is stablized;
(2) consider that state resets the replacement behavior of controlling unit, determine that state resets the parameter of controlling unit;
(3) proportional plus integral control link and the ratio resetting controlling unit are adjusted, to reach the purpose improving system dynamics behavior.
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DE102016011865A1 (en) * | 2016-10-01 | 2018-04-05 | Khd Humboldt Wedag Gmbh | Regulating device with adjustability of the control behavior |
CN109581861B (en) * | 2017-09-29 | 2022-02-15 | 上海微电子装备(集团)股份有限公司 | Motion stage control system, motion stage system, and exposure apparatus |
CN111969647B (en) * | 2020-07-24 | 2022-08-02 | 南方电网科学研究院有限责任公司 | Converter transient instability stabilization control method and device based on state resetting |
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KR100973210B1 (en) * | 2010-04-16 | 2010-07-30 | 국방과학연구소 | Pid equivalent controller that does not include derivative and method thereof |
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Non-Patent Citations (4)
Title |
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Luca Zaccarian, Dragan Neˇsic´and Andrew R. Teel.《First order reset elements and the Clegg integrator revisited》.《2005 American Control Conference》.2005,第563-568页. * |
PI+CI compensation with variable reset:;Angel Vidal,Jose C.;《IEEE》;20081231;第321-326页 * |
Reset Control for Passive Bilateral Teleoperation;Alejandro Fernández Villaverde, Antonio Barreiro Blas;《IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS》;20110730;第58卷(第7期);第3037-3045页 * |
Tuning rules for a reset PI compensator with variable rese;Alfonso Ba˜nos and Miguel A. Dav;《IFAC Conference on Advances in PID Control》;20120330 * |
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