CN104698841B - Control system combining proportional-integral with state reset and implementation method - Google Patents

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

Control system and implementation method that a kind of combination proportional integral is reset with state

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：

$u\left(t\right)=k_{p}e\left(t\right)+k_i{\∫}_0^{t}e\left(\mathrm{\τ}\right)\mathrm{d\τ}$

Wherein, k_p,k_iIt 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：

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 transmission function of single order replacement controlling unit can be expressed asWherein a_r For resistance R₁Value, b_rFor resistance R₂Value, the value of electric capacity is

Further, the dynamical equation of single order replacement controlling unit is：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_r(t,j)=\frac{R_2}{R_1}\frac{1}{R_2\mathrm{Cs}+1}e\left(t\right),\mathrm{if}{x}_r(t,j)e\left(t\right)\≥0\\ x_r(t_{j+1},j+1)=0,\mathrm{if}{x}_r(t_{j+1},j)e\left(t_{j+1}\right)\≤0\end{array}\right.$

Wherein e (t) and x_r(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.t_j+1Represent that jth time resets the moment occurring, x_r(t_j+1, firstorder filter before j) expression resets State value, x_r(t_j+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

${\stackrel{\·}{v}}_C=-\frac{R_2}{R_1}\frac{1}{R_2\mathrm{Cs}+1}e.$

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 v_C1(t)≤0 and v_C2(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 R_dSo that v_C1T () is almost changed into v at once_C1(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) ＞ 0_C2T ()=0, as e (t) When≤0, circuit is changed into firstorder filter.V is known according to analysis_C1(t)≤0 and v_C2T () >=0 meets always, define x_r(t)=- v_C1(t)-v_C2(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 filter_dThe 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 filter_dWith 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：

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.

Single order reset controlling unit dynamical equation be：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_r(t,j)=\frac{R_2}{R_1}\frac{1}{R_2\mathrm{Cs}+1}e\left(t\right),\mathrm{if}{x}_r(t,j)e\left(t\right)\≥0\\ x_r(t_{j+1},j+1)=0,\mathrm{if}{x}_r(t_{j+1},j)e\left(t_{j+1}\right)\≤0\end{array}\right.$

E (t) and x_r(t, j) represents input and the output voltage of t Clegg integrator respectively.J represents and has occurred and that j Secondary replacement.t_j+1Represent that jth time resets the moment occurring, x_r(t_j+1, j) represent the state value of firstorder filter before replacement, x_r (t_j+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 x_r(t, j) will not contrary sign.If e T () ＞ 0 is thenBecause v_C1(t)≤0, so e (t) v_C1(t)≥0.During e (t) ＜ 0, similar analysis can obtain e (t) v_C2 (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 a_rFor resistance R₁ Value, b_rFor 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：

$P\left(s\right)=\frac{N_p\left(s\right)}{D_p\left(s\right)}$

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 k_p,k_i,a_r,b_r,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 $C\left(s\right)=\frac{k_p{s}^2+(k_p{a}_r+k_i{\mathrm{\λ}}_1+b_r{\mathrm{\λ}}_2)s+a{\mathrm{\λ}}_1{k}_i}{s^2+a_{r}s}=\frac{N_c\left(s\right)}{D_c\left(s\right)},$ 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 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 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 N_c(s)D_p(s)+N_p(s)D_cParameter a of FORE is adjusted s () is stable in the case that_r,b_rCarried 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：

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.

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 a_rFor resistance R₁Value, b_rFor 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：

$\left\{\begin{array}{ccc}{\stackrel{\·}{x}}_r(t,j)=\frac{R_2}{R_1}\frac{1}{R_{2}Cs+1}e\left(t\right),& if& x_r(t,j)e\left(t\right)\≥0\\ x_r(t_{j+1},j+1)=0,& if& x_r(t_{j+1},j)e\left(t_{j+1}\right)\≤0\end{array}\right.$

Wherein e (t) and x_r(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, t_j+1Represent that jth time resets the moment occurring, x_r(t_j+1, j) represent the state value of firstorder filter before replacement, x_r(t_j+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.