CN104834211A - Thermal power plant control system internal model PID controller tuning method - Google Patents

Abstract

The invention relates to a thermal power plant control system internal model PID controller tuning method. According to the method, parametric expression of a PID controller is derived based on the PID controller tuning method of the internal model principles; and a filter time constant is tuned. The tuning process is divided into two aspects. According one aspect of the tuning process, analysis is performed from the aspect of the robust performance of a control system, and the conclusion is that the larger the value of the filter time constant is, the better the robust performance of the system is. According to the second aspect of the tuning process, analysis is performed from the aspect of the ITAE performance index of the control system, the conclusion is that the smaller the value of filter time constant is, the smaller the ITAE performance index is, and the better the control performance is. Based on the above two aspects of analysis, the selection of the filter time constant can refer to two aspects, selection of a too small or too large value for the value of lambda is not proper under the situation that the robustness, rapidity and accuracy of the system can be ensured; as indicated by a large quantity of simulation experiments and analysis, when it is determined that the ratio of the lambda to a delay time tau ranges from 0.8 to 1, the control performance of the system is good.

Description

Thermal power plant's control system Internal Model PID Controller setting method

Technical field

The invention belongs to industrial control field, be mainly used in online parameter tuning and the optimization of thermal power plant's control system.

Background technology

PID controller, i.e. proportional-integral derivative controller, be backfeed loop parts common in Industry Control Application, be made up of proportional unit P, integral unit I and differentiation element D.

For thermal power plant's industrial control system, because it bears all multitasks such as safety index, economic target, environmental protection index ensureing Power Plant Thermal Process equipment and electricity generation system, and controlled device is very complicated, running environment is difficult to determine, gives and controls accurately to bring very large difficulty.PID controller is all occupy very leading status in various control system and various control algolithm.In actual moving process, the load of machine or equipment etc. be in operation constantly change, noise also can intervene operation, and these reasons all can cause object model parameter to change a lot, so require that pid parameter can accomplish on-line tuning.

In research field at home, existing many methods of adjusting to pid parameter have been applied in industrial reality.As: Internal Model PID parameter tuning, adjust based on the PID of simplicial method, adjust etc. based on the pid parameter of ITAE (integral of time multiplied by the absolute value of error criterion) index.

In later stage nineteen fifties, Smith proposes time lag compensation device, and this is that the generation of internal model control provides main background.Internal model control is that the one of Smith prediction device increases expansion and supplements, and very simply clear during structure, interference free performance and robustness there has also been very large improvement.After this, the research of scholar both domestic and external to internal model control is just more and more extensive.Arrive nowadays, conventional inmould-method has started the future development to Based Intelligent Control, and also very abundant to improving one's methods of internal model control.When the design of the process in the face of some complexity, the thinking of internal model control and other multiple thinkings connect by many experts and scholars, as: fuzzy decision, adaptive control etc., so just substantially increase the advantage of internal model control in complex process.

But although achieve significant progress to the research of internal model control, a lot of research also just rests on simulation stage.Such as: nonlinear internal model control scheme is applied seldom in practice.And if when wanting to be applied in actual control system, the computer-controlled mode of many employings again, this just requires system discretize.If discrete time error process is improper, then can the effect controlled be affected.In addition, owing to lacking unified, detailed theoretical system, internal model control effect in the application of nonlinear system is also not fully up to expectations.

Summary of the invention

Not good and the problem of stability and rapidity etc. cannot be taken into account for solving in prior art the thermal power plant's practical application control system middle controller parameter tuning existed simultaneously, the invention discloses a kind of Internal Model PID Controller setting method based on robustness and ITAE performance index.

The present invention is concrete by the following technical solutions.

A kind of thermal power plant control system Internal Model PID Controller setting method, is characterized in that, said method comprising the steps of:

Step 1: design Internal Model PID Controller;

Step 2: the low-pass filter time constant of Internal Model PID Controller of adjusting according to robust performance index;

Step 3: the low-pass filter time constant of Internal Model PID Controller of adjusting according to ITAE performance index;

Step 4: the span of the index determination low-pass filter time constant of comprehensive two aspects.

In step 1, thermal power plant's control system equivalence of reality is become a naive model be made up of the PID controller of adjusting based on internal model principle and controlled device, and the expression formula of PID controller is as follows:

The transport function of controller: $C\left(s\right)=\frac{C_{\mathrm{IMC}}\left(s\right)}{1-G_{\mathrm{IMC}}\left(s\right)G_p\left(s\right)};$

Controller parameter expression formula: $K_p=\frac{T}{(\mathrm{\λ}+\mathrm{\τ})},T_I=T;$

Wherein, the parameter that needs are adjusted is low-pass filter time constant λ;

In formula: C (s) is the transport function of the PID controller of adjusting based on internal model principle, also referred to as feedback controller or

Internal Model PID Controller;

G _iMCs transport function that () is internal mode controller;

G _ps model that () is controlled device;

K _pfor the proportional gain of PID controller;

T _ifor the integration time constant of PID controller;

K is the gain of plant model;

T is the time constant of plant model;

τ is the time delay of plant model.

In step 2, following content is comprised according to the adjust filter time constant of Internal Model PID Controller of robust performance index:

The scope that can change to maintain this three parameters of system stability is derived respectively when K, T, τ tri-parameter mismatch of controlled device, and reach a conclusion: to increase the parameter variation range that can maintain system stability, namely improve the robustness of system, low-pass filter time constant λ need be increased.

In step 3, following content is comprised according to the adjust filter time constant of Internal Model PID Controller of ITAE performance index:

Choose ITAE performance index, namely the time takes advantage of absolute error criterion integration index, and control system performance is carried out to evaluation and adjusted, and ITAE performance index are as follows: $J_{\mathrm{ITAE}}={\∫}_0^{\mathrm{\τ}}(1-0)\mathrm{tdt}+\underset{t_e\→\∞}{\lim }{\∫}_{\mathrm{\τ}}^{t_e}{e}^{-\frac{t-\mathrm{\τ}}{\mathrm{\λ}}}\mathrm{tdt}=(\mathrm{\τ}-1)\mathrm{\λ}+\frac{1}{2}{\mathrm{\τ}}^2;$ Therefrom can find out that choosing less filter time constant λ can make ITAE performance index reduce, and namely can make the control performance of system relatively good.

In step 4, combine the analysis of step 2,3 pairs of low-pass filter time constant setting values, determine, when the ratio of λ and delay time T is between 0.8 ~ 1, the control performance of thermal power plant's control system can be guaranteed.

The present invention has following useful technique effect:

This PID controller setting method can improve stability and the rapidity of control system, especially also have good effect for the large delay controlled device in thermal power plant's control system, and randomness performance is also better.

Accompanying drawing explanation

Fig. 1 is the application based on the Internal Model PID Controller setting method schematic flow sheet of robustness and ITAE performance index;

Fig. 2 is the structural representation of the thermal power plant's control system simplified;

Fig. 3 is internal model principle block scheme;

Fig. 4 is internal model principle active feedback structural drawing;

In figure: G is actual controlled model; G _pfor controlled device mathematical model;

G _iMCfor internal mode controller; C is the feedback controller of equivalence;

Y, D, R are respectively the output of process, disturbance input and reference input.

Embodiment

Below in conjunction with Figure of description, technical scheme of the present invention is further described in detail.

Be the structural representation of thermal power plant's control system as shown in Figure 2, thermal power plant's control object is simplified to mathematical model, adopt Internal Model PID Controller, namely IMC-PID controller carries out single loop FEEDBACK CONTROL to it.And propose a kind of setting method for Internal Model PID Controller on this model.

Be the Internal Model PID Controller setting method schematic flow sheet based on robustness and ITAE performance index disclosed in the present application as shown in Figure 1, described PID controller setting method comprises the following steps:

Step 1: design thermal power plant control system internal mode controller;

In thermal power plant's control system loop, select Internal Model PID Controller, i.e. IMC-PID controller, Fig. 3 is the functional-block diagram of internal model control.In such an embodiment, the output of controller both outputted to control object, also delivered to internal model, the difference of the actual output of system and the output of internal model through backfeed loop and setting value comprehensive after as the input of controller.Be the inner structure of whole control system in dotted line frame in Fig. 3, available analog hardware or computer software realize.Due in this structure except there being internal mode controller G _iMCin addition, further comprises process model G _p, therefore internal model control gains the name.Can be the simple feedback control system form shown in Fig. 4 by its equivalent transformation,

By the feedback arrangement figure of Fig. 4, we can draw:

$Y\left(s\right)=\frac{G_{\mathrm{IMC}}\left(s\right)G\left(s\right)}{1+G_{\mathrm{IMC}}\left(s\right)[G\left(s\right)-G_p\left(s\right)]}R\left(s\right)+\frac{1-G_{\mathrm{IMC}}\left(s\right)G\left(s\right)}{1+G_{\mathrm{IMC}}\left(s\right)[G\left(s\right)-G_p\left(s\right)]}D\left(s\right)---\left(1\right)$

In formula, the output that Y (s) is system, the input that R (s) is system, the disturbance that D (s) is system, G _iMCs () is internal mode controller, G (s) is actual controlled device, G _ps model that () is controlled device.

From above formula, if controlled model can be expressed accurately, i.e. G _p(s)=G (s), and G _iMC(s)=G ^-1time (s), there is Y (s)=R (s).

Can find out, the output in thermal power plant's control system can accomplish that track reference inputs, and not by the impact of disturbance.But, if model G _pexpression formula when the RHP of s is with zero point or delayed item, the internal mode controller with above-mentioned desirable controller characteristic cannot realize.And in the middle of the control procedure of reality, in a lot of situation, people are difficult to set up accurate mathematical model, that is there is certain gap unavoidably between real process and model.But we can design internal mode controller G according to the feature of actual controlled device _iMCsystem is controlled.Design process is as follows:

First, plant model is made to do following decomposition:

G _p(s)＝G _p+(s)G _p-(s) (2)

Wherein: G _p+the transport function with minimum phase characteristic, G _p-be an all-pass filter comprising time lag and Right-half-plant zero, have

$\left|G_{p+}\left(s\right)\right|=1,\∀\mathrm{\ω}$

Secondly, a low-pass filter is added:

$F\left(s\right)=\frac{1}{{(\mathrm{\λs}+1)}^{\mathrm{\γ}}}---\left(3\right)$

Obtain internal mode controller: G _iMC(s)=G _p- ^-1(s) F (s) (4)

In formula, γ is object model G _prelative order.

Thus, the transport function obtaining the feedback controller of equivalence according to Fig. 2 is: (5)

The controller applied in this feedback controller i.e. thermal power plant's control system of equivalence.

Desirable PID controller transport function:

$G_c\left(s\right)=K_p(1+\frac{1}{T_{i}s}+T_{D}s)---\left(6\right)$

In formula: K _pfor the proportional gain of PID controller, T _ifor the integration time constant of PID controller, T _dfor the derivative time constant of PID controller

The feedback controller of before deriving and the relation of internal mode controller:

$C\left(s\right)=\frac{G_{\mathrm{IMC}}\left(s\right)}{1-G_{\mathrm{IMC}}\left(s\right)G_P\left(s\right)}$

This formula and desirable PID controller transport function are carried out equivalence, utilizes the principle that each term coefficient of s polynomial expression is equal, solve these three parameters of scale-up factor, integration time constant and derivative time constant namely obtaining IMC-PID controller.

With single order Taylor formula, similar process is carried out to the link of delaying in model, namely gets:

E ^{-τ s}≈ 1-τ s, the relative order due to object model is 1, so the exponent number of low-pass filter is 1, then plant model can be approximated to be:

$G_p\left(s\right)=\frac{K}{\mathrm{Ts}+1}(1-\mathrm{\τs})---\left(7\right)$

In formula: K is the gain of plant model, T is the time constant of plant model, and τ is the time delay of plant model.

By model decomposition: $\begin{array}{cc}{G}_{p-}\left(s\right)=\frac{K}{(\mathrm{Ts}+1)}& G_{p+}\left(s\right)=1-\mathrm{\τs}---\left(8\right)\end{array}$

In like manner can obtain, feedback controller is:

$C\left(s\right)=\frac{G_{\mathrm{IMC}}\left(s\right)}{1-G_{\mathrm{IMC}}\left(s\right)G_p\left(s\right)}=\frac{1}{G_{p-}\left(s\right)F^{-1}\left(s\right)-G_p\left(s\right)}$

Formula (2-3), (2-8) are brought into:

$C\left(s\right)\frac{(\mathrm{Ts}+1)}{K(\mathrm{\λ}+\mathrm{\τ})s}=\frac{1}{K}\frac{T}{\mathrm{\λ}+\mathrm{\τ}}(1+\frac{1}{\mathrm{Ts}})$

The corresponding parameters that can obtain IMC-PID controller is:

$K_p=\frac{T}{K(\mathrm{\λ}+\mathrm{\τ})},T_I=T---\left(9\right)$

So we obtain the parameter expression of IMC-PID controller.Can find out, in expression formula, unique parameter needing adjustment is low-pass filter time constant λ.So we will pass through the analysis to robustness and ITAE performance index two aspect, the value of filter time constant of roughly adjusting.

Above-mentioned (5), (6) two relational expression equivalences, so we can sum up the step of following design IMC-PID controller:

1st step: by thermal power plant controlled system mathematical model G _ps () is broken down into minimum phase part G _p+(s) and all-pass part G _p-(s)

G _p(s)＝G _p+(s)G _p-(s)， $G_p\left(s\right)=\frac{K}{\mathrm{Ts}+1}(1-\mathrm{\τs})$

G _p+(s)＝1-τs， $G_{p-}\left(s\right)=\frac{K}{(\mathrm{Ts}+1)}$

Wherein: G _p+the transport function with minimum phase characteristic, G _p-be an all-pass filter comprising time lag and Right-half-plant zero, K is the gain of plant model, and T is the time constant of plant model, and τ is the time delay of plant model;

2nd step: utilize formula (4) and (5) to obtain internal mode controller G _iMC(s) and feedback controller C (s); Internal mode controller G _iMCs the transport function of () is: G _iMC(s)=G _p- ^-1(s) F (s)

The transport function of feedback controller C (s) is: $C\left(s\right)=\frac{G_{\mathrm{IMC}}\left(s\right)}{1-G_{\mathrm{IMC}}\left(s\right)G_p\left(s\right)}$

Wherein: F (s) is low-pass first order filter, G _ps () is plant model;

3rd step: feedback controller and the PID controller form selected are carried out equivalence, obtains two parameters of IMC-PID controller;

$K_p=\frac{T}{K(\mathrm{\λ}+\mathrm{\τ})},T_1=T$

4th step: after drawing the expression formula of controller parameter, filter time constant λ is the unique variable in expression formula, need adjust to it.

Step 2: the filter time constant of Internal Model PID Controller of adjusting according to robust performance index

Control system robust analysis:

The robustness of control system refers to the ability that system can keep stability, progressive adjustment and dynamic perfromance constant.Consider the factors such as operating mode complicated in thermal power plant's control system, when model mismatch, we just should consider the robustness of control system.

During model mismatch, controlled device can be described as following form:

G'(s)＝G _p(s)+ΔG(s) (10)

Wherein, G'(s) be the model after mismatch, the variable quantity that Δ G (s) is model;

When identification model mates with actual controlled device, have iMC controller can be designed, obtain: $G_{\mathrm{IMC}}=\left(s\right)=\frac{\mathrm{Ts}+1}{K(\mathrm{\λs}+1)}---\left(11\right)$

(1) when model changes, variation delta G can do following expression:

$\mathrm{\ΔG}\left(s\right)=\frac{\∂G_p\left(s\right)}{\∂K}\mathrm{\ΔK}+\frac{\∂G_p\left(s\right)}{\∂T}\mathrm{\ΔT}+\frac{\∂G_p\left(s\right)}{\∂\mathrm{\τ}}\mathrm{\Δ\τ}$

Wherein, Δ K, Δ T, Δ τ is respectively proportional gain, integration time constant, the variable quantity of derivative time constant.

Derivative in above formula is obtained:

$\mathrm{\ΔG}\left(s\right)=\frac{K{e}^{-\mathrm{\τs}}}{\mathrm{Ts}+1}(\frac{\mathrm{\ΔK}}{K}-\frac{\mathrm{\ΔTs}}{\mathrm{Ts}+1}-\mathrm{\Δ\τs})---\left(12\right)$

Obtained by Fig. 1, the closed loop transform function of this IMC-PID control system is:

1+G _IMC(s)[G _p(s)-G′(s)]＝0 (13)

Formula (4), (12) are brought into, and single order Taylor expansion are carried out to Time Delay, after abbreviation, obtain following form:

$1+\frac{1-\mathrm{\τs}}{\mathrm{\λs}+1}(\frac{\mathrm{\ΔK}}{K}-\frac{\mathrm{\ΔTs}}{\mathrm{Ts}+1}-\mathrm{\Δ\τs})=0$

So we a point situation can make following discussion:

When gain mismatch, K' ≠ K, T'=T, τ '=τ, formula (14) becomes

Abbreviation obtains: (λ K-τ Δ K) s+K+ Δ K=0 (Δ K=K'-K)

By Routh Criterion, system to remain stable, the span of K:

$K^{\′}\≤\frac{\mathrm{\λ}+\mathrm{\τ}}{\mathrm{\τ}}K---\left(15\right)$

Can obtain, when λ increases, make the span of the gain coefficient K that system can be stable larger, that is, improve the stability that filter time constant can strengthen system.

(2) when time constant mismatch: K'=K, T' ≠ T, τ '=τ, formula (2-14) becomes

Abbreviation obtains: (λ T+ τ Δ T) s ²+ (λ+T-Δ T) s+1=0 (Δ T=T'-T)

By Routh Criterion, system to remain stable, the span of K:

$(1-\frac{\mathrm{\λ}}{\mathrm{\τ}})T\≤T^{\′}\≤2T+\mathrm{\λ}---\left(16\right)$

Can obtain, when λ increases, on the left of inequality, have the trend of reduction, on the right side of equation, have the trend of increase.Namely system can keep the span of stable time constant T larger.That is, the stability that filter time constant can strengthen system is improved.

(3) when delay time mismatch, K'=K, T'=T, τ ' ≠ τ, formula (2-14) becomes

Abbreviation obtains: τ Δ τ s ²+ (λ-Δ τ) s+1=0 (Δ τ=τ '-τ)

By Routh Criterion, system to remain stable, the span of K:

τ≤τ'≤τ+λ (17)

Can obtain, when λ increases, the left side of inequality is constant, and right side increases.Namely system can keep the span of stable delay time τ larger.That is, the stability that filter time constant can strengthen system is improved.

By above analysis, we can draw, the one order inertia of model mismatch delays object, and its stability condition and filter time constant λ have very large relation.To improve the robustness of system, then should suitably increase filter time constant λ.For determining the span of λ further, we analyze from ITAE performance index aspect it again.

Step 3: the filter time constant of Internal Model PID Controller of adjusting according to ITAE performance index

Control system ITAE Performance Analysis:

Integral of time multiplied by the absolute value of error criterion (ITAE) performance index:

$J_{\mathrm{ITAE}}={\∫}_0^{\∞}t\left|e\left(t\right)\right|\mathrm{dt}=\min ---\left(18\right)$

This formula is used as the target of evaluation, the dynamic response capability of controlled device and controller and quiet can be assessed simultaneously

Performance during state, can reflect the accuracy of the hierarchy of control, can react again in time portion at the absorption part of error

The rapidity of the hierarchy of control, has good selectivity and practicality.

The above-mentioned approximation method of same selection carries out IMC-PID attitude conirol, and feedback controller C (s) is as follows:

$C\left(s\right)=\frac{\mathrm{Ts}+1}{K(\mathrm{\λ}+\mathrm{\τ})s}$

According to Fig. 3, obtain closed loop transfer function:

$\frac{Y\left(s\right)}{R\left(s\right)}=\frac{C\left(s\right)G_p\left(s\right)}{1+C\left(s\right)G_p\left(s\right)}=\frac{e^{-\mathrm{\τs}}}{(T+\mathrm{\τ})s+e^{-\mathrm{\τs}}}---\left(19\right)$

Continue application Taylor single order to above formula to launch:

$\frac{Y\left(s\right)}{R\left(s\right)}=\frac{C\left(s\right)G_p\left(s\right)}{1+C\left(s\right)G_p\left(s\right)}=\frac{e^{-\mathrm{\τs}}}{\mathrm{Ts}+1}$

Under time domain Stepped Impedance Resonators output response can be obtained by Laplace inverse transformation:

$y\left(t\right)=(1-e^{-\frac{t-\mathrm{\τ}}{\mathrm{\λ}}})---\left(20\right)$

Be taken to ITAE performance index with in expression formula, obtain:

$J_{\mathrm{ITAE}}={\∫}_0^{\mathrm{\τ}}(1-0)\mathrm{tdt}+\underset{t_e\→\∞}{\lim }{\∫}_{\mathrm{\τ}}^{t_e}{e}^{-\frac{t-\mathrm{\τ}}{\mathrm{\λ}}}\mathrm{tdt}=(\mathrm{\τ}-1)\mathrm{\λ}+\frac{1}{2}{\mathrm{\τ}}^2---\left(21\right)$

As can be seen from the above equation, choose less filter time constant λ and ITAE performance index can be made to reduce, the control performance of system namely can be made relatively good.

Step 4: combining step 2,3 determines the span of filter time constant

The comprehensively analysis of above-mentioned two aspects, choosing of filter time constant can with reference to two aspects, under can ensureing that system robustness can ensure again the rapidity of system and the condition of accuracy, the value of λ should not be chosen too small or excessive, according to a large amount of emulation experiments and analysis, determine that the control performance of system is reasonable when the ratio of λ and delay time τ is between 0.8 ~ 1.

Claims (5)

1. thermal power plant's control system Internal Model PID Controller setting method, is characterized in that, said method comprising the steps of:

Step 1: design Internal Model PID Controller;

Step 2: the low-pass filter time constant of Internal Model PID Controller of adjusting according to robust performance index;

Step 3: the low-pass filter time constant of Internal Model PID Controller of adjusting according to ITAE performance index;

Step 4: the span of the index determination low-pass filter time constant of comprehensive two aspects.

2. Internal Model PID Controller setting method according to claim 1, is characterized in that:

In step 1, thermal power plant's control system equivalence of reality is become a naive model be made up of the PID controller of adjusting based on internal model principle and controlled device, and the expression formula of PID controller is as follows:

The transport function of controller: $C\left(s\right)=\frac{G_{\mathrm{IMC}}\left(s\right)}{1-G_{\mathrm{IMC}}\left(s\right)G_p\left(s\right)};$

Controller parameter expression formula: $K_p=\frac{T}{K(\mathrm{\λ}+\mathrm{\τ})},T_I=T;$

Wherein, the parameter that needs are adjusted is low-pass filter time constant λ;

In formula: C (s) is the transport function of the PID controller of adjusting based on internal model principle, also referred to as feedback controller or Internal Model PID Controller;

G _iMCs transport function that () is internal mode controller;

G _ps model that () is controlled device;

K _pfor the proportional gain of PID controller;

T _ifor the integration time constant of PID controller;

K is the gain of plant model;

T is the time constant of plant model;

τ is the time delay of plant model.

3. Internal Model PID Controller setting method according to claim 2, is characterized in that:

In step 2, following content is comprised according to the adjust filter time constant of Internal Model PID Controller of robust performance index:

Derive when K, T, τ tri-parameter mismatch of controlled device respectively and stablize to maintain thermal power plant control system the scope that this three parameters can change, and reach a conclusion: the stable parameter variation range of described control system can be maintained to increase, namely improve the robustness of system, low-pass filter time constant λ need be increased.

4. the Internal Model PID Controller setting method according to claim 1 or 3, is characterized in that:

In step 3, following content is comprised according to the adjust filter time constant of Internal Model PID Controller of ITAE performance index:

Choose ITAE performance index, namely the time takes advantage of absolute error criterion integration index, and control system performance is carried out to evaluation and adjusted, and ITAE performance index are as follows: $J_{\mathrm{ITAE}}={\∫}_0^{\mathrm{\τ}}(1-0)\mathrm{tdt}+\underset{t_e\→\∞}{\lim }{\∫}_{\mathrm{\τ}}^{t_e}\mathrm{tdt}=(\mathrm{\τ}-1)\mathrm{\λ}+\frac{1}{2}{\mathrm{\τ}}^2;$ Wherein, τ is the time delay of plant model, and λ needs the parameter of adjusting to be low-pass filter time constant; Therefrom can find out that choosing less filter time constant λ can make ITAE performance index reduce, and namely can make the control performance of system relatively good.

5. the Internal Model PID Controller setting method according to claim 1 or 4, is characterized in that:

In step 4, combine the analysis of step 2,3 pairs of low-pass filter time constant setting values, determine, when the ratio of λ and delay time τ is between 0.8 ~ 1, the control performance of thermal power plant's control system can be guaranteed.