CN104698841A - 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 PDF

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Publication number
CN104698841A
CN104698841A CN201510058161.0A CN201510058161A CN104698841A CN 104698841 A CN104698841 A CN 104698841A CN 201510058161 A CN201510058161 A CN 201510058161A CN 104698841 A CN104698841 A CN 104698841A
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state
reset
controlling unit
control system
resets
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CN104698841B (en
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王景成
赵广磊
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Shanghai Jiaotong University
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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

A kind of control system of resetting in conjunction with proportional integral and state and implementation method
Technical field
The present invention relates to technical field of automatic control, be specifically related to control to reset with state the control system and implementation method that control (Reset Control) in conjunction with PI (PID:Proportional-Integral, proportional integral).
Background technology
Proportional integral (PI) controller is widely used in the various occasion needing Automated condtrol, and the output of PI controller comprises proportional, integration item two parts, and the form of PI algorithm can be described as:
u ( t ) = k p e ( t ) + k i ∫ 0 t e ( τ ) dτ
Wherein, k p, k ibe respectively proportional gain, storage gain.E (t) is the difference of setting value (SP:Set Point) and process variable (PV:Process Variable), and u (t) is the output of PI controller.
Resetting control system (Reset Control Systems) and refer to that controlled device is the dynamically system that controller existence resets continuous time, is a nonlinear systems.Replacement controller adds replacement rule by the linear of standard or gamma controller and forms, and namely when system state meets given replacement rule, controller state is reset to zero or the value relevant with state.Drive replacement behavior event to be called replacement condition, typical replacement condition is, when controller input zero passage or when controller input/output symbol is contrary, state is reset to zero.Reset and control to be the Clegg integrator proposed in 1958 by Clegg the earliest, compared to common integrator, but it has identical magnitude margin only has the delayed phase of 38.1 degree.Use the reason resetting and control to mainly contain two aspects: one is the transient performance in order to improved system; Two is reset to control to have the potential advantages that can overcome Linear Control performance boundary.
Prior art Vidal, A.Banos, J.C.Moreno, M.Berenguel, PI+CI compensationwith variable reset:Application on solar collector fields, IndustrialElectronics, 2008.IECON 2008.34th Annual Conference of IEEE, pp.321-326, the control method that a kind of proportional integral adds Clegg integrator is proposed in 2008., PI is utilized to control to eliminate the characteristic of error and the characteristic of Clegg integrator improved system dynamic property, but make PI+CI controller can realize controlling the same rise time overshoot with PI to reduce, thus reset by simple the dynamic property controlling the system that improves.Its shortcoming is: the Clegg integrator used the most simply resets control device, regulating parameter only has one, controller state is reset to zero when being controller input zero passage by the replacement rule adopted, and thus cannot analyze the robustness adopting this control method for disturbing signal.
Summary of the invention
The deficiency that the replacement control system model that is few and that adopt of regulating parameter in reset control method is not easy to robust analysis is added for existing PI, one object of the present invention is, proposes a kind of in conjunction with PI and the control system based on the FORE (First Order Reset Element) of hybrid model.
The invention provides a kind of control system reset in conjunction with proportional integral and state, as shown in Figure 2, wherein proportional integral link is compared with conventional proportional integral link and is added a coefficient lambda 1, FORE is the link comprising state replacement, and adds a coefficient lambda 2, λ 1and λ 2integral part and the ratio reset shared by part in u (t) is being exported for regulating.
The advantage that PI controls is that quick adjustment system is dynamic, and realizes zero steady-state error adjustment, but adjustment process may make to occur larger overshoot during error convergence fast, namely can realize good steady-state behaviour and dynamic property may be poor.And reset the dynamic property that the advantage controlled is to improve control system, but being used alone replacement control can not ensure zero steady-state error performance.Therefore, control in conjunction with PI and reset the advantage controlled, good stable state and dynamic property can be reached simultaneously.
The present invention also provides a kind of implementation method of the control system reset in conjunction with proportional integral and state.
Hybrid system mentioned here refers to that system dynamically comprises continuously system that is dynamic and Discrete Dynamic.
The invention provides a kind of control system reset in conjunction with proportional integral and state, comprise proportional plus integral control link, be input as error signal e (t), export u (t) for controlling controlled device P (s), the control system reset in conjunction with proportional integral and state also comprises state and resets controlling unit, it is in parallel with proportional plus integral control link that state resets controlling unit, when the output signal symbol that error signal e (t) and state reset controlling unit is different, the output signal that state resets controlling unit is reset to null value.
Further, the control system reset in conjunction with proportional integral and state also comprises the first regulating parameter and the second regulating parameter, and the first regulating parameter is connected with proportional plus integral control link, and the second regulating parameter and state reset controlling unit and connect.
Further, the first regulating parameter and the second regulating parameter and be 1.
Further, increase the ratio of the first regulating parameter and the second regulating parameter, to realize quick adjustment.
Further, reduce the ratio of the first regulating parameter and the second regulating parameter, to reduce overshoot.
Further, state resets controlling unit is that single order resets controlling unit.
Further, single order resets controlling unit and comprises the first linear filter in parallel and the second linear filter, first Capacitance parallel connection first diode of the first linear filter, second Capacitance parallel connection second diode of the second linear filter, first diode is contrary with the second diode direction, and the output that single order resets controlling unit is:
x r(t)＝-v C1(t)-v C2(t)
Wherein v c1t () is the output of the first linear filter, v c2t () is the output of the second linear filter.
Further, the continuous dynamic part transport function of single order replacement controlling unit can be expressed as wherein a rfor resistance R 1value, b rfor resistance R 2value, the value of electric capacity is
Further, the dynamic equation of single order replacement controlling unit is:
x · r ( t , j ) = R 2 R 1 1 R 2 Cs + 1 e ( t ) , if x r ( t , j ) e ( t ) ≥ 0 x r ( t j + 1 , j + 1 ) = 0 , if x r ( t j + 1 , j ) e ( t j + 1 ) ≤ 0
Wherein e (t) and x r(t, j) represents that t single order resets the input and output voltage of controlling unit respectively.J represents that occurring j time resets.T j+1represent that jth time resets the moment occurred, x r(t j+1, j) represent reset before the state value of firstorder filter, x r(t j+1, j+1) represent jth time reset after the value of firstorder filter.
Compared to Clegg integrator, single order resets controlling unit FORE and adds a regulating parameter, thus adds the degree of freedom resetting Controller gain variations; Single order resets the model of controlling unit FORE, as above-mentioned single order resets the dynamic equation of controlling unit, when the input/output symbol adopted is different, state is reset to the replacement rule of zero, when being different from Clegg integrator input zero passage state is reset to the replacement rule of zero, thus makes the robustness being easier to analyze this control method.
The present invention also provides a kind of implementation method of the control system reset in conjunction with proportional integral and state, comprises the following steps:
(1) do not consider that state resets the replacement behavior of controlling unit, consider that state resets the transport function of the continuous dynamic part of controlling unit, determine the parameter of the control system reset in conjunction with proportional integral and state, 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 is regulated, to reach the object of improvement system dynamic behaviour.
Compared with prior art, the invention provides a kind of control system of resetting in conjunction with proportional integral and state and implementation method has following beneficial effect:
First regulating parameter is connected with proportional integral link, and the second regulating parameter is connected with replacement controlling unit, regulates the first regulating parameter and the second regulating parameter, to realize quick adjustment, to reduce overshoot, reaches good stable state and dynamic property simultaneously.
Accompanying drawing explanation
Fig. 1 is the closed-loop control system structural drawing of the control system reset in conjunction with proportional integral and state of one embodiment of the present of invention;
Fig. 2 is the structural drawing of the control system reset in conjunction with proportional integral and state shown in Fig. 1;
The state that Fig. 3 is the control system reset in conjunction with proportional integral and state shown in Fig. 1 resets the circuit diagram of controlling unit;
Fig. 4 is the circuit diagram of first-order linear wave filter.
Embodiment
In order to make object of the present invention, technical scheme and advantage definitely, below in conjunction with Figure of description and specific embodiment, the present invention is described in more detail.
As shown in Figure 1, the control system reset in conjunction with proportional integral and state of one embodiment of the present of invention, comprising proportional plus integral control link PI, be input as error signal e (t), exporting u (t) for controlling controlled device P (s).
The control system reset in conjunction with proportional integral and state also comprises state and resets controlling unit FORE, it is in parallel with proportional plus integral control link PI that state resets controlling unit FORE, when the output signal symbol that error signal e (t) and state reset controlling unit FORE is different, the output signal that state resets controlling unit FORE is reset to null value.
As shown in Figure 2, the control system reset in conjunction with proportional integral and state also comprises the first regulating parameter λ 1with the second regulating parameter λ 2, the first regulating parameter λ 1connect with proportional plus integral control link PI, the second regulating parameter λ 2reset controlling unit FORE with state to connect.
First regulating parameter λ 1with the second regulating parameter λ 2and be 1.
Increase the first regulating parameter λ 1with the second regulating parameter λ 2ratio, to realize quick adjustment.
Reduce the first regulating parameter λ 1with the second regulating parameter λ 2ratio, to reduce overshoot.
It is that single order resets controlling unit that state resets controlling unit FORE.
FORE is by common first-order linear wave filter, as shown in Figure 4, expand, its concrete circuit structure as shown in Figure 3, according to this circuit structure, compare with first-order linear wave filter, the output of FORE is no longer dynamically linear, and shows the Hybrid dynamics behavior comprising continuously dynamic and Discrete Dynamic.
Known by the ABC of Circuits System, use ideal operational amplificr, firstorder filter can be realized by the resistance of the resistance of input channel and feedback channel and electric capacity.Pass between corresponding input and output ties up to time domain and can be expressed as
v · C = - R 2 R 1 1 R 2 Cs + 1 e .
Control to realize resetting, namely when firstorder filter input and output not jack per line time state is reset to zero, design single order as shown in Figure 3 resets Controlling model.It dynamically can be described below.First, owing to being ideal operational amplifier, input voltage always zero, two capacitance voltages meets v c1(t)≤0 and v c2(t)>=0 (otherwise the electric current in diode can make capacitor discharge).As e (t) < 0, the voltage no matter be present in electric capacity is above how many, above electric current in two diodes pass through R dmake v c1t () almost becomes v at once c1(t)=0.But, when e (t) >=0, circuit above corresponding to firstorder filter, owing to there is no electric current in diode.For circuit below, similar analysis can be known, has v as e (t) > 0 c2t ()=0, when e (t)≤0, circuit becomes firstorder filter.V is known according to analysis c1(t)≤0 and v c2t ()>=0 meets always, definition x r(t)=-v c1(t)-v c2(t).
Single order resets controlling unit and comprises the first linear filter (linear filter on top) in parallel, with the second linear filter (linear filter of bottom), first Capacitance parallel connection first diode of the first linear filter, second Capacitance parallel connection second diode of the second linear filter, the first diode is contrary with the second diode direction;
3rd resistance R in first linear filter dafter the 3rd Diode series, with the first resistance R of the first linear filter 1parallel connection, the 3rd diode is identical with the first diode direction; 3rd resistance R in second linear filter dafter the 4th Diode series, with the first resistance R of the second linear filter 1parallel connection, the 4th diode is identical with the second diode direction.
The output that single order resets controlling unit is:
x r(t)＝-v C1(t)-v C2(t)
Wherein v c1t () is the output of the first linear filter, v c2t () is the output of the second linear filter.
The dynamic equation that single order resets controlling unit is:
x &CenterDot; r ( t , j ) = R 2 R 1 1 R 2 Cs + 1 e ( t ) , if x r ( t , j ) e ( t ) &GreaterEqual; 0 x r ( t j + 1 , j + 1 ) = 0 , if x r ( t j + 1 , j ) e ( t j + 1 ) &le; 0
E (t) and x r(t, j) represents the input and output voltage of t Clegg integrator respectively.J represents that occurring j time resets.T j+1represent that jth time resets the moment occurred, x r(t j+1, j) represent reset before the state value of firstorder filter, x r(t j+1, j+1) represent jth time reset after the value of firstorder filter.
As can be seen from the relation of above firstorder filter input and output, e (t) and x r(t, j) can not contrary sign.If e (t) > 0, because v c1t ()≤0, so e (t) v c1(t)>=0.During e (t) < 0, similar analysis can obtain e (t) v c2(t)>=0.In addition, about e (t) ≠ 0, two parts circuit has at least one to play firstorder filter effect and another output is zero.
The continuous dynamic part transport function that single order resets controlling unit can be expressed as wherein a rfor resistance R 1value, b rfor resistance R 2value, the value of electric capacity is
For sake of convenience, now suppose that the transfer function model of controlled device P (s) is as follows:
P ( s ) = N p ( s ) D p ( s )
Step one: first do not consider the generation reset, the transport function of the continuous dynamic part of known FORE can be written as according to the controller architecture in Fig. 2, design correlation parameter k p, k i, a r, b r, λ 1, λ 2closed-loop system is made to be stable not occurring when resetting.Namely first the controller transfer function in Fig. 2 is expressed as C ( s ) = k p s 2 + ( k p a r + k i &lambda; 1 + b r &lambda; 2 ) s + a &lambda; 1 k i s 2 + a r s = N c ( s ) D c ( s ) , Wherein λ 1, λ 2for adjusting PI part and FORE ratio partly and meeting λ 1+ λ 2=1, can λ=0.5 be chosen as, λ 2=0.5, then design k p, k i, a r, b rmake closed loop transform function N c(s) D p(s)+N p(s) D cs the characteristic root of () is all arranged in the Left half-plane of complex plane (in lineary system theory, POLE PLACEMENT USING, quantitative feedback theory or LMI theory etc. can be used to complete this step parameter designing), and meet certain system performance index (as the dynamic performance index such as rise time, Time Created).
Step 2: the FORE device containing replacement behavior in Fig. 3 is joined the relevant position in Fig. 2, thus make controller have Hybrid dynamics behavior, according in summary of the invention, FORE is analyzed dynamically, when error signal e (t) and the output signal symbol of FORE are different, the output of FORE is reset to null value, thus the value of u (t) is reset.Further, at guarantee closed loop transform function N c(s) D p(s)+N p(s) D cthe parameter a of FORE is regulated s when () is stable r, b rto reach the object improving dynamic performance.
Step 3: because PI control section is mainly used in the object realizing zero steady-state error and adjustment rise time, and FORE is mainly used in the dynamic behaviour such as overshoot, speed of convergence of improvement system.Therefore, need the ratio of adjustment shared by two parts to reach the system performance of expectation, parameter lambda 1, λ 2exactly in order to realize this purpose.According to the adjustment of first two steps, other controller parameters are determined.Regulate λ 1, λ 2value, increase value to reach the performance of rise time fast, or reduce value export the performance of overshoot to reach to reduce.
The control system that resets in conjunction with proportional integral and state provided by the invention and implementation method, first regulating parameter is connected with proportional integral link, second regulating parameter is connected with replacement controlling unit, regulate the first regulating parameter and the second regulating parameter, to realize quick adjustment, to reduce overshoot, reach good stable state and dynamic property simultaneously.
More than describe preferred embodiment of the present invention in detail.Should be appreciated that those of ordinary skill in the art just design according to the present invention can make many modifications and variations without the need to creative work.Therefore, all technician in the art, all should by the determined protection domain of claims under this invention's idea on the basis of existing technology by the available technical scheme of logical analysis, reasoning, or a limited experiment.

Claims (10)

1. the control system reset in conjunction with proportional integral and state, comprise proportional plus integral control link, be input as error signal e (t), export u (t) for controlling controlled device P (s), it is characterized in that, the described control system reset in conjunction with proportional integral and state also comprises state and resets controlling unit, it is in parallel with described proportional plus integral control link that described state resets controlling unit, when the output signal symbol that error signal e (t) and described state reset controlling unit is different, the output signal that described state resets controlling unit is reset to null value.
2. as claimed in claim 1 in conjunction with the control system that proportional integral and state reset, it is characterized in that, the described control system reset in conjunction with proportional integral and state also comprises the first regulating parameter and the second regulating parameter, described first regulating parameter is connected with described proportional plus integral control link, and described second regulating parameter and described state reset controlling unit and connect.
3., as claimed in claim 2 in conjunction with the control system that proportional integral and state reset, it is characterized in that, described first regulating parameter and described second regulating parameter and be 1.
4. as claimed in claim 2 in conjunction with the control system that proportional integral and state reset, it is characterized in that, increase the ratio of described first regulating parameter and described second regulating parameter, to realize quick adjustment.
5. as claimed in claim 2 in conjunction with the control system that proportional integral and state reset, it is characterized in that, reduce the ratio of described first regulating parameter and described second regulating parameter, to reduce overshoot.
6. as claimed in claim 1 in conjunction with the control system that proportional integral and state reset, it is characterized in that, it is that single order resets controlling unit that described state resets controlling unit.
7. as claimed in claim 6 in conjunction with the control system that proportional integral and state reset, it is characterized in that, described single order resets controlling unit and comprises the first linear filter in parallel and the second linear filter, first Capacitance parallel connection first diode of described first linear filter, second Capacitance parallel connection second diode of described second linear filter, described first diode is contrary with described second diode direction, and the output that described single order resets controlling unit is:
x r(t)＝-v C1(t)-v C2(t)
Wherein v c1t () is the output of described first linear filter, v c2t () is the output of described second linear filter.
8. as claimed in claim 6 in conjunction with the control system that proportional integral and state reset, it is characterized in that, the continuous dynamic part transport function that described single order resets controlling unit can be expressed as wherein a rfor resistance R 1value, b rfor resistance R 2value, the value of electric capacity is
9. as claimed in claim 6 in conjunction with the control system that proportional integral and state reset, it is characterized in that, the dynamic equation that described single order resets controlling unit is:
x &CenterDot; r ( t , j ) = R 2 R 1 1 R 2 Cs + 1 e ( t ) , if x r ( t , j ) e ( t ) &GreaterEqual; 0 x r ( t j + 1 , j + 1 ) = 0 , if x r ( t j + 1 , j ) e ( t j + 1 ) &le; 0
Wherein e (t) and x r(t, j) represents that t single order resets the input and output voltage of controlling unit respectively.J represents that occurring j time resets.T j+1represent that jth time resets the moment occurred, x r(t j+1, j) represent reset before the state value of firstorder filter, x r(t j+1, j+1) represent jth time reset after the value of firstorder filter.
10. an implementation method for the control system reset in conjunction with proportional integral and state as described in claim 1-9, it is characterized in that, described implementation method comprises the following steps:
(1) do not consider that state resets the replacement behavior of controlling unit, consider that described state resets the transport function of the continuous dynamic part of controlling unit, determine the parameter of the control system reset in conjunction with proportional integral and state, 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 is regulated, to reach the object of improvement system dynamic behaviour.
CN201510058161.0A 2015-02-04 2015-02-04 Control system combining proportional-integral with state reset and implementation method Expired - Fee Related CN104698841B (en)

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CN111969647A (en) * 2020-07-24 2020-11-20 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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