CN104020663A - Digital PID parameter self-tuning method based on principle of statistics - Google Patents

Abstract

The invention provides a PID parameter self-tuning method based on the principle of statistics. The method mainly comprises the steps of (1) initializing a program and reading the initialization parameter of a sensor; (2) conducting parameter self-tuning, wherein for a mathematical model as described in the specification, (u(t))' serves as a matrix Y, (K, 1/Ki, Kd) serves as a matrix B, the expression as described in the specification serves as a matrix X, and then the equation Y=BX+b is true and the parameter to be estimated is calculated by means of the matrix computation formula B=(Y-b)/X=(Y-b)*inv(X); (3) calculating the proportion term Ke(t), the integral term (as described in the specification) and the differential term (as described in the specification); (4) obtaining the summation of the proportion term, the integral term and the differential term; (5) conducting suitability judgment on the tuned parameter after a controller runs for a certain period of time. The parameter self-tuning method can be realized in the PID algorithm, the number of occupied computation resources is small, accuracy is high, parameter tuning is achieved totally automatically without manual intervention, output signal convergence time is theoretically reduced by half compared with the Ziegler-Nichols, and performance is far better than that of the Cohen-Coon method.

Description

A kind of Digital PID Parameters automatic setting method based on Principle of Statistics

Technical field

The invention belongs to automation control area, be specifically related to a kind of Digital PID Controller methods of self-tuning based on Principle of Statistics.

Technical background

PID self-actuated controller has been widely used since invention.In the automatic control equipment of current new installation, there is PID controller or the algorithm of having adopted over half.PID controller is controlled and is developed so far from initial simulating signal, and major part is replaced by digital control approach.In the design of Digital PID Controller, the new algorithm that development parameters is adjusted, becomes the important means of improving its performance.While being stablized by the metric characteristic of control target, the parameter of self-actuated controller is also determined, but when constantly being changed by the metric characteristic of control target, controller parameter by experiment data obtains.The setting algorithm of parameters of PID controller is a kind of method of automatic acquisition control procedure empirical parameter.The method that is usually used in obtaining pid parameter has try and error method and curve cycle method.Current application has Ziegler-Nichols and two kinds of methods of Cohen-Coon the most widely, and Ziegler-Nichols method can be for control closed circuit and open circuit, and Cohen-Coon method is conventionally only for the control of opening a way.The quality of pid parameter setting algorithm can be weighed by output valve in a period of time and the standard deviation of setting value difference.Equation (1) is a kind of general mathematical model of PID controller.From mathematical model, can find out, when application the method is controlled industrial process, have across weights and measures (as, by flow control liquid level; By size of current, control temperature etc.), automatic returning adapts to the excellent characteristics such as physical model (needs do not obtain in advance by the accurate mathematical model of control object).

$u\left(t\right)=K(e\left(t\right)+\frac{1}{K_i}{\∫}_0^{t}e\left(t^{\′}\right){\mathrm{dt}}^{\′}+K_d\frac{\mathrm{de}\left(t\right)}{\mathrm{dt}}+b)--------\left(1\right)$

In formula, u: control output signal;

E: currency and setting value difference;

K: parameter is controlled in proportional gain;

K _i: storage gain is controlled parameter;

K _d: the differential gain is controlled parameter;

T: input sample time;

B: output offset.

In practical application, also need additionally to add some parameters.The control signal that exceeds topworks's processing power may cause distorted signals or device damage.For example: a noise bandwidth parameter N is set _b, when input value with value difference be set be less than N _btime, parameter e zero setting, this can effectively prevent output signal shake, increases controller stability; A dead band parameter D is set _z, prevent excessive or too small output signal.

Problem maximum in practical application is K, K _i, K _ddetermining of three parameters.In commercial production, post operation personnel often cannot reasonably adjust the parameter of PID controller.Because the characteristic of control object is varied, veteran technician also will be taken plenty of time adjustment controller parameter.And along with the variation of control object characteristic, PID controller parameter probably needs to readjust.And adopt the artificial PID setting method of adjusting parameter conventionally can not find in time the migration of industry control condition, cause controller long-time running under inaccurate state.

Ziegler-Nichols PID Tuning first integration and differentiation gain is set to 0, and then proportional gain is started from scratch increases gradually, until reach the limit of gain K _u, this Time Controller output valve is vibrated with steady state value.According to different types, parameter K, K in P, PI, tri-kinds of control modes of PID have been provided _i, K _dwith K _urelation.This setting method needs the long period to determine K _u.During manual shift, most of controller can not draw control signal curve, is difficult to accurately judge K _uvalue, in the algorithm from setting parameter is realized, the fit procedure of control signal curve is had relatively high expectations to computational resource, and microprocessor is difficult to satisfy the demand conventionally.Cohen-Coon method only needs output signal rising (or reduction) then stable, can calculate setting parameter, speed.Only has in theory 1/4 of Ziegler-Nichols method setting time.But this method is only suitable for controlling in open circuit, and accuracy is not high.

Summary of the invention

The object of the invention is to a difficult problem that is difficult to adjust for PID controller parameter, a kind of pid parameter automatic setting method based on Principle of Statistics is provided.

For this reason, the present invention adopts following technical scheme:

A Digital PID Parameters automatic setting method based on Principle of Statistics, comprises the steps:

(1) initialize routine, read sensor initiation parameter;

(2) parameter tuning: to mathematical model $u\left(t\right)=K(e\left(t\right)+\frac{1}{K_i}{\∫}_0^{t}e\left(t^{\′}\right){\mathrm{dt}}^{\′}+K_d\frac{\mathrm{de}\left(t\right)}{\mathrm{dt}}+b)$ ①，

In formula, u: control output signal, e: currency and setting value difference, K: parameter, K are controlled in proportional gain _i: storage gain is controlled parameter, K _d: the differential gain is controlled parameter, t: input sample time, b: output offset;

Make (u (t)) ' be matrix Y, (K, 1/K _i, K _d) be matrix B, for matrix X, there is equation Y=BX+b to set up, wherein, matrix X, Y are experiment image data, and matrix B is pid parameter to be estimated;

Utilize following matrix computations formula to calculate and treat estimated parameter:

B＝(Y–b)/X＝(Y–b)*inv(X)②

When tuning process starts, set three different controller output valve y ₁, y ₂, y ₃, calculate respectively corresponding input value x ₁, x ₂, x ₃; Controller output valve Y=(y ₁, y ₂, y ₃) and input value X=(x ₁, x ₂, x ₃) respectively substitution formula 2. in, can calculate and treat estimated parameter K, K _i, K _d;

(3) calculate respectively ratio phase Ke (t), integration phase with differential phase

(4) ratio phase, integration phase are sued for peace mutually with differential;

(5) after controller operation certain hour, the parameter after adjusting is carried out to suitability judgement, establish discriminant function in formula, u: controller output signal, e: currency and setting value difference, σ: the standard deviation of e value normal distribution;

If E < is 4 σ, illustrate that the parameter after adjusting is suitable, can carry out controller control signal output and use; If E > is 4 σ, represent that variation has occurred the characteristic of control object, current pid parameter is inapplicable, and by abovementioned steps, parameter is adjusted again.

Due to after controller parameter completes and adjust, move one period, to be controlled Properties of Objects may change, current parameter can not adapt to control requirement.This just need to judge at any time the adaptability of parameter by after date when controller moves one section by a kind of method.Because PID controller completes after adjust, the e in step 1 mathematical model meets normal distribution, and the mathematical expectation distributing is PID setting value, and the standard deviation sigma of distribution is to weigh the adaptive important indicator of pid parameter.Probability density function according to normal distribution, when e value exceeds four standard deviation 4 σ in average left and right, can think that small probability event occurs, this represents that variation has occurred to be controlled Properties of Objects, current pid parameter is inapplicable, need to use above-mentioned parameter automatic setting method again to adjust.

Adopt the inventive method PID, minimum need to be near 3 stable input signals sampling, more PID of sampled value integration performance is better.In the situation that sensor sample frequency is higher, can increases and adopt quantity to improve the performance of parameter tuning.Many group input values are averaged, and then calculate input matrix X.This method can effectively suppress input signal noise.

Beneficial effect of the present invention is: methods of self-tuning of the present invention is different from the parameter tuning instrument of existing plug-in type, can occupy computational resource few in the inner realization of pid algorithm, and accuracy is good.The essence of setting method is application experiment statistic law, and the linear operation by statistics can calculate parameter to be estimated; In addition, the inventive method PID full automation, does not need manual intervention; Output signal convergence time in theory than Ziegler-Nichols method few half, performance is obviously better than Cohen-Coon method; The inventive method also has good hardware adaptive mechanism, can stable operation in embedded system.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of pid parameter automatic setting method of the present invention.

Embodiment

As shown in Figure 1, a kind of pid parameter automatic setting method based on Principle of Statistics, comprises the steps:

(1) initialize routine, read sensor initiation parameter;

(2) parameter tuning: to mathematical model $u\left(t\right)=K(e\left(t\right)+\frac{1}{K_i}{\&Integral;}_0^{t}e\left(t^{\&prime;}\right){\mathrm{dt}}^{\&prime;}+K_d\frac{\mathrm{de}\left(t\right)}{\mathrm{dt}}+b)$ ①，

In formula, u: control output signal, e: currency and setting value difference, K: parameter, K are controlled in proportional gain _i: storage gain is controlled parameter, K _d: the differential gain is controlled parameter, t: input sample time, b: output offset;

Make (u (t)) ' be matrix Y, (K, 1/K _i, K _d) be matrix B, for matrix X, there is equation Y=BX+b to set up, wherein, matrix X, Y are experiment image data, and matrix B is pid parameter to be estimated;

Utilize following matrix computations formula to calculate and treat estimated parameter:

B＝(Y–b)/X＝(Y–b)*inv(X)②

When tuning process starts, controller output valve is set to respectively to 50%, 10%, 90%, calculates respectively corresponding input value x ₁, x ₂, x ₃; Then controller output valve and input value X=(x ₁, x ₂, x ₃) respectively substitution formula 2. in, can calculate and treat estimated parameter K, K _i, K _d;

(3) calculate respectively ratio phase Ke (t), integration phase with differential phase

(4) ratio phase, integration phase are sued for peace mutually with differential;

(5) after controller operation certain hour, the parameter after adjusting is carried out to suitability judgement, establish discriminant function in formula, u: controller output signal, e: currency and setting value difference, σ: the standard deviation of e value normal distribution;

If E < is 4 σ, illustrate that the parameter after adjusting is suitable, can carry out controller control signal output and use; If E > is 4 σ, represent that variation has occurred the characteristic of control object, current pid parameter is inapplicable, and by abovementioned steps, parameter is adjusted again.

In order to verify control effect of the present invention, adopt Matlab to realize respectively Ziegler-Nichols method, Cohen-Coon method and PID automatic setting method effect mentioned above.Control parameter tuning method for three kinds and adopt identical pid algorithm and D _z, N _betc. parameter.Stack sine, square wave, random number undesired signal respectively in input value, to simulate the variation of control object characteristic in commercial production.Investigation is the adaptability to undesired signal from setting algorithm.Setting time used is with | e|<N _bbe as the criterion.Test result is as shown in table 1 below:

Three kinds of PID controller parameters of table 1 are from the simulation test of setting algorithm

In table 1, P1 section is noiseless section, and P2 section is introduced sinusoidal wave interference, and P3 section is introduced square wave and disturbed, and P4 section is introduced random number and disturbed.T1, T2, T3, T4 are respectively the setting time that P1, P2, P3, P4 time period used, and σ is that respective standard is poor.From data, can find out that the pid parameter based on Principle of Statistics is better than first two method from Tuning algorithm adaptability.

Claims (1)

1. the Digital PID Parameters automatic setting method based on Principle of Statistics, is characterized in that, comprises the steps:

(1) initialize routine, read sensor initiation parameter;

(2) parameter tuning: to mathematical model 1.,

In formula, u: control output signal, e: currency and setting value difference, K: parameter, K are controlled in proportional gain _i: storage gain is controlled parameter, K _d: the differential gain is controlled parameter, t: input sample time, b: output offset;

Make (u (t)) ' be matrix Y, (K, 1/ K _i, K _d) be matrix B, for matrix X, there is equation Y=BX+b to set up, wherein, matrix X, Y are experiment image data, and matrix B is pid parameter to be estimated;

Utilize following matrix computations formula to calculate and treat estimated parameter:

B?=?(Y?–b)/?X?=?(Y?–?b?)?*?inv?(?X?)?②

When tuning process starts, set three different controller output valve y1, y2, y3, calculate respectively corresponding input value x1, x2, x3; Controller output valve Y=(y1, y2, y3) and input value X=(x1, x2, x3) respectively substitution formula 2. in, can calculate and treat estimated parameter K, K _i, K _d;

(3) calculate respectively ratio phase Ke (t), integration phase with differential phase ;

(4) ratio phase, integration phase are sued for peace mutually with differential;

(5) after controller operation certain hour, the parameter after adjusting is carried out to suitability judgement, establish discriminant function , in formula, u: controller output signal, e: currency and setting value difference, σ: the standard deviation of e value normal distribution;

If E < is 4 σ, illustrate that the parameter after adjusting is suitable, can carry out controller control signal output and use; If E > is 4 σ, represent that variation has occurred the characteristic of control object, current pid parameter is inapplicable, and by abovementioned steps, parameter is adjusted again.