CN110865540A

CN110865540A - Mutual coupling PI cooperative control theory new method

Info

Publication number: CN110865540A
Application number: CN201911194390.XA
Authority: CN
Inventors: 曾喆昭
Original assignee: Individual
Current assignee: Individual
Priority date: 2019-11-28
Filing date: 2019-11-28
Publication date: 2020-03-06

Abstract

Aiming at the problem that the gain robustness and the disturbance resistance robustness of various PI controllers are poor, a Mutual Coupling PI (MCPI) cooperative control theory new method is invented. According to the method, all internal and external complex factors of a system are defined as sum disturbance, so that a nonlinear complex system is mapped into an equivalent linear uncertain system, and a controlled error system under the inverse excitation of the sum disturbance is constructed; and obtaining the value range of the transition process time according to the dynamic characteristic test of the unknown controlled object, and designing a minimum speed factor model and a self-adaptive speed factor model according to the value range. The overall robust stability of the MCPI cooperative control system is theoretically analyzed. The invention can provide scientific theoretical basis for the technical evaluation and technical upgrade of various current PI controllers, is easy to realize the zero-distance rail connection of the MCPI cooperative control theory and the actual control engineering, and has wide application value in the control field of a first-order linear or nonlinear system and a multi-input multi-output system.

Description

Mutual coupling PI cooperative control theory new method

Technical Field

The present invention relates to a first-order system or a multiple-input multiple-output (MIMO) system control, and more particularly, to a Mutual-Coupling PI (MCPI) cooperative control.

Background

The PI controller is the oldest classic controller in the PID control family, and is mainly applied to control of a first-order linear or nonlinear system or a multiple-input multiple-output (MIMO) system due to the lack of a differential link. For known first order linear systems, the tuning of the PI may be achieved using a maximum phase margin tuning rule, however, the proportional gain k_pAnd integral gain k_iBoth depend on the characteristic angular frequency of the controlled object, and for the controlled objects with different differences, the two gains of the PI controller are also different, which shows that the two gains of the PI controller are closely related to the controlled objects; for a first-order nonlinear object or an MIMO nonlinear system, a phase margin setting rule cannot be used for setting PI gain, and generally, various intelligent optimization algorithms can be only used for online optimization and adjustmentAnd (4) determining. From the existing various PI setting methods, the gain robustness and the disturbance resistance robustness are poor, and the main reason is that the proportional gain k is ignored_pAnd the physical property of the PI control force u.

In fact, the students at home and abroad, whether engaged in the classical control theory or the modern control theory, only pay attention to the research of the controller gain setting method, but neglect the physical properties of the controller gain and the physical properties of the control force, and disregard the objective existence of the actual controlled object. Although various control methods can control individual case objects through gain setting, the method lacks wide scientific guiding significance and is only in the technical level of repeated application of the existing calculation method and control technology. Considering the wide application of the PI controller in the field of actual control engineering, the following comprehensive and deep analysis is mainly carried out around the limitation of the PI control theory, and the aim is to invent an advanced new control theory method, namely an MCPI cooperative control theory new method.

Disclosure of Invention

The invention aims to solve the technical problem of overcoming the defects in the prior art and provides a novel MCPI cooperative control theory method which is simple in model structure, easy in controller setting and good in dynamic quality and steady-state performance.

The technical scheme adopted by the invention for solving the technical problem is that the novel method for the MCPI cooperative control theory is characterized by comprising the following steps of:

step A: measuring unit step response characteristic of unknown nonlinear system, and obtaining transition process time T of controlled object according to dynamic characteristic information_rThe value range of (a) is in seconds;

and B: the transition process time T obtained according to the step A_rEstablishing a minimum central speed factor model as follows:

z_cm＝20α/T_r

wherein 1 is<α≤10，T_rThe transient process time of the controlled object from the dynamic state to the steady state;

and C: according to a given desired output y_dCombining unknown non-linesActual output y of the sexual object, establishing a tracking error e₁And its integral e₀Respectively as follows:

e₁＝y_d-y，e₀＝∫e₁dt

step D: obtaining z according to step B and step C, respectively_cmAnd e₁Then, in order to avoid overshoot and oscillation phenomena caused by integral saturation, an adaptive speed factor model z is established_cComprises the following steps:

z_c＝z_cmexp(-β|e₁|)

wherein z is_cm＝20α/T_r，1<α≤10，β＝1+0.1α；

Step E: obtaining e according to step C and step D respectively₁、e₀And z_cThen, an integral control force u is established_iProportional control force u_pAnd the MCPI cooperative control force u is respectively as follows:

u_p＝2z_ce₁/b₀，

wherein, b₀Not equal to 0 is the control channel gain estimate, 0 ≦ σ<1 is a factor of the rate of deviation of the center velocity, the greater the value of which, the integral control force u_iThe weaker the action of (a), otherwise,

is the desired output y_dDifferentiation of (1);

step F: obtaining an integral control force u according to step E_iAfter the MCPI is cooperated with the control force u, considering the phenomena of overshoot and oscillation caused by integral saturation and the condition of limited input of an actual physical system, the integral control force u is required_iAnd the cooperative control force u carries out amplitude limiting respectively, and the specific steps are as follows:

|u_i|≤0.8u_m，|u|≤u_m

wherein u is_mIs the maximum amplitude of the MCPI cooperative control force u.

The method defines all unknown uncertain complex factors such as unknown controlled system dynamics, internal uncertainty, external disturbance and the like as a total disturbance, establishes a controlled error system under the reverse excitation of the total disturbance according to the error between the given expected output and the actual output, further establishes an MCPI cooperative controller model, determines the value range of the transition process time of a controlled system by measuring the dynamic response characteristic of an unknown complex nonlinear system, further establishes a minimum speed factor model and an adaptive speed factor model, and analyzes the overall robust stability of the MCPI closed-loop control system from a complex frequency domain.

Drawings

Fig. 1 is a block diagram of an MCPI cooperative control system.

Fig. 2 is a diagram of the dynamics of an unknown controlled object.

FIG. 3 is an external perturbation.

Fig. 4 shows the cosine tracking control result of the unknown nonlinear system, (a) track tracking, (b) control input, (c) tracking control error, and (d) error local amplification effect.

Fig. 5 shows the step tracking control result of the unknown nonlinear system, (a) track tracking, (b) control input, (c) tracking control error, and (d) error local amplification effect.

Detailed Description

Analysis of the limitations of PI controllers

In order to facilitate understanding of the theoretical defects of the PI controller, first, the physical attributes of the control input u of the controlled object are known from the controlled object.

1) Problem background

Setting a certain order of unknown nonlinear disturbed system:

wherein, y₁Is the measurable state of the system, u and y are the control input and the actual output of the system, respectively, f (y)₁ξ) is a systemUnknown smooth function, ξ are model parameters (consider the time-varying case), b is the control channel time-varying gain, and d is the externally bounded perturbation.

2) Physical attributes of control force input in a controlled system

In the system (1), y is assumed to be y₁Is a generalized "displacement" quantity, such as: temperature in a temperature-dependent system, flow in a flow system, angle in a rotating system, displacement in a moving system, etc. Obviously, the control force bu in the system (1) is a physical quantity having a generalized "speed" dimension, and therefore, for any first order system, the control force bu has a generalized "speed" dimension, and thus, the control force bu formed by a PI controller or other type of controller should also have a generalized "speed" dimension.

After the physical attribute of the generalized speed is grasped by the control force input bu of any first-order system, the control force bu formed by various controllers should have corresponding matched physical attributes. However, because the existing control theory methods neglect the physical properties of the gain and control force bu of various controllers, the classical control theory represented by the "control theory" and the modern control theory represented by the "model theory" both disregard the objective existence of the actual controlled object, so that the existing various controllers are only suitable for the application technology level of the specific controlled object and lack scientific theoretical guiding significance.

3) Limitation analysis of PI controllers

Considering the wide application of PI controllers, detailed analysis is only performed below around PI control strategies, analyzing the root cause of PI limitations and their elimination methods.

Let r and y be the expected output and the actual output of the controlled object, respectively, then there are tracking errors and their integrals as: e.g. of the type₁＝r-y，e₀＝∫e₁dt, from which the PI control force can be derived:

u＝k_p(e₁+e₀/T_i)/b (2)

or

u＝(k_pe₁+k_ie₀)/b (3)

Wherein k is_p>0 and k_i＝k_p/T_iProportional and integral gains, respectively; t is_iIs the integration time constant.

The information available from the PI control force model (2) or (3) is very limited, only k is known_p>0，k_i＝k_p/T_iAnd the like, so the PI control strategy has the following historical legacy problems:

① lack of physical properties for proportional gain

PI is published so far, only k is given_p>0, no well-defined physical property is defined for it, and the proportional gain k is often given_pTreated as dimensionless independent variables;

② PI control force has only generalized displacement dimension

Assuming that r and y are both physical quantities of generalized displacement, then the error e₁R-y is also a generalized displacement, and e₀＝∫e₁The dt dimension is the generalized displacement per second, so that T is introduced into the PI control force prototype (2)_iAfter this time constant, the objective is to make the expression: u. of₀＝e₁+e₀/T_iHave the same dimension (generalized displacement) so as to satisfy the basic arithmetic operation rule, and then sum the result u₀Amplification of k_pK is multiplied by b to form a control force u_pu₀/b。

If k is_pDimensionless, the control force bu ═ k formed by the PI prototype (2) or (3)_pu₀Only generalized displacement dimension is adopted, but conflict occurs with the control input bu required by any first-order system with generalized speed dimension, which indicates that the PI control force model has obvious theoretical defect;

③ integral time constant

In the PI prototype (2), T_iHow is the value of? T is_iIs it related to the controlled object? Scholars at home and abroad rarely pay attention to the two problems, but in any situation, PI control law models in the shape of (3) are generally used, and only k is generally concerned_pAnd k_iTwo-gain online optimization algorithm, T is rarely concerned_iThe existence of (2), thus often leading to the integration time constant as true or false;

④ PI two gains independent of each other

Although k is_pAnd k_iThe mutual relationship is established between the following components: k is a radical of_i＝k_p/T_iHowever, if k_pIs an independent variable without attributes, T_iIs an independent time variable, then k_pAnd k is_iThe above-mentioned relationship between them has a great uncertainty, and belongs to a loose relationship. In fact, in pair k_pAnd k_iIn the online optimization process, it is usually treated as two gain variables independent of each other, which are actually two independent gains.

4) Adverse consequences that may arise from limitations of PI controllers

As can be seen from the historical legacy problems with the PI controllers above, if T_iIs an independent time variable, proportional gain k_pAnd is also an independent variable without physical properties, the following principle error or uncoordinated control mechanism can be caused to occur in the PI control law model:

① principle errors in dimension mismatch between PI control force and control input of controlled object

If k is_pIs an independent variable without attribute, and the proportional control force bu of PI_p＝k_pe₁And integral control force bu_i＝k_ie₀Are all control forces in the generalized "displacement" dimension, so PI control forces: bu ═ k_p(e₁+e₀/T_i) Or bu ═ k_pe₁+k_ie₀And are also control forces in a generalized "displacement" dimension.

However, the control force input bu of any one-order system is required to have a generalized "speed" dimension, so if a PI controller is used to control any one-order system, a principle error of dimension mismatch between the PI control force bu and the controlled object control force input bu may be caused, or it may be difficult for the PI control capability to exert a good control effect;

② uncoordinated control mechanism reduces dynamic quality and steady state performance

If k is_pIs an independent variable without physical property, T_iIs an independent time variable, then k_pAnd k_iAre actually independent of each other, so that the proportional control force bu of the PI is generated_p＝k_pe₁And integral control force bu_i＝k_ie₀Mutually independent and independent uncoordinated control mechanisms are presented in the control process. This is true of the fact that it is difficult for the PI control system to achieve good dynamic quality and steady state performance.

In summary, if k_pIs an independent variable without physical property, T_iThe PI control method is an independent time variable, so that not only can a principle error of control force class mismatch occur and the control capability of the PI be reduced, but also two different physical links of the PI can show an uncoordinated control mechanism in the control process, and therefore, the PI control system is difficult to obtain good dynamic quality and steady-state performance. In addition, an uncoordinated control mechanism can only ensure that a local transient steady state exists in the PI control system, and once an expected track mutation occurs, or a model parameter is time-varying or external disturbance exists, the PI gain needs to be re-set to enter another local transient steady state, which is a root cause of poor PI gain robustness, poor time-varying robustness and poor disturbance resistance robustness.

2. Mapping concept from unknown nonlinear system to linear uncertain system

1) Total perturbation definition

In order to solve the control problem of the unknown nonlinear system (1), the unknown nonlinear system is mapped into an equivalent linear uncertain system by using a sum disturbance concept, and the controller of the linear uncertain system is designed to realize the effective control of the unknown nonlinear system (1).

Definition 1. assume b is the control channel time-varying gain, and b ═ b₀+ △ b, the location of the non-linear disturbed system (1) will not be knownHaving a complex set of factors using a sum perturbation y₂To indicate that:

y₂＝f(y₁,ξ)+bd+△bu (4)

2) mapping of non-linear disturbed systems to linear uncertain systems

From equation (4), the sum of the disturbances y₂Not only contains the unknown internal dynamics f (y)₁ξ) and an external disturbance d, and further including uncertainty control force information △ bu, the unknown nonlinear disturbed system (1) can be mapped to an equivalent linear uncertainty system according to the definition of the sum disturbance (4):

wherein, b₀Not equal to 0 is an estimate of the control channel gain (accuracy is not required).

Since the linear uncertain system (5) is an equivalent mapping of the unknown nonlinear disturbed system (1), the control force u constructed by the system (5) can be directly applied to the control input of the unknown nonlinear disturbed system (1).

Assumption 1. if and only if a globally valid control strategy is used, the sum perturbation defined by equation (4) is always bounded: | y₂|<∞。

And (3) proving that: from equation (4), y is disturbed due to the sum₂Uncertain control force information △ bu is included, so that, as long as a globally valid control strategy is used to form the control force u, it is guaranteed that the total disturbance is bound | y₂|<And if not, indicating that the control strategy used is not effective.

3) Sources of sum perturbation concepts

Summation disturbance is a creative concept proposed by researchers in hangjing, korea, in 20 years ago, and achieves the purpose of auto-disturbance rejection by using an Extended State Observer (ESO) to perform observation estimation on the summation disturbance, feeding forward an estimation value to a control input end so as to counteract the influence of the summation disturbance as much as possible, and inventing an auto-disturbance rejection controller (ADRC). However, ADRC has a complex structure, involves too many parameters, and is computationally expensive. In addition, although robust and stable, the closed loop control system formed by ADRC has difficulty in theoretically analyzing the robust and stable. Therefore, the invention designs a global robust stable MCPI cooperative control system, which avoids a high-gain ESO functional module and simplifies the structure of the MCPI cooperative controller.

4) Theoretical significance of sum perturbation concept

From definition 1 of the sum perturbation: the sum perturbation definition has a general meaning since any unknown nonlinear complex system can be mapped into the form of an equivalent linear uncertain system (5). Moreover, the sum disturbance definition also completely weakens the concepts of system characteristic classification such as linearity and nonlinearity, determination and uncertainty, time variation and time invariance and the like, so that various problems of how to design an effective control strategy of different types of controlled systems which are always entangled by two control theory systems of a control theory and a model theory for a long time can be effectively solved.

The invention aims to solve the defects of the PI control force model by adopting the scientific assumption that: as long as the proportional gain k is defined_pWith the generalized velocity dimension, the theoretical defect of the PI control force can be easily solved. How to apply globally effective control force to an unknown nonlinear system (1) or an equivalent linear uncertain system (5) is the core control strategy of the invention, namely the MCPI cooperative control strategy.

MCPI cooperative control strategy

1) Design of MCPI cooperative controller

Aiming at the control problem of the linear uncertain system (5), the expected output and the actual output are respectively set as y_dAnd y, from which a tracking control error e can be defined₁And its integral e₀Respectively as follows: e.g. of the type₁＝y_d-y，e₀＝∫e₁dt, binding system (5), thus:

thus, a controlled error system under the summed perturbed inverse excitation can be established:

in order to globally stabilize the controlled error system (7), an integral control force u is defined_iProportional control force u_pAnd the MCPI cooperative control force u is respectively as follows:

wherein z is₁>0 and z₂>0 are respectively two speed factors of the MCPI cooperative controller, and the dimensions of the two speed factors are 1/second, b₀Not equal to 0 is an estimated value of the control channel gain, the same as below.

From the MCPI cooperative control force (8), two velocity factors z₁And z₂The proportional link and the integral link of the error are closely coupled together, so that the two different physical links show a cooperative control mechanism with different functions and consistent targets in the control process, and the PI control force is corrected

Two different links in the control process are independent from each other and respectively form an array of uncoordinated control behaviors. Therefore, the emergence of the MCPI cooperative controller (8) is a remarkable revolution of the control theory system.

2) MCPI tuning rules

According to the MCPI cooperative control force (8), the setting rule of the MCPI cooperative controller is as follows:

as can be seen from the MCPI cooperative tuning rule (9), z₁And z₂Not only the core coupling factor of the proportional and integral elements, but also the proportional gain k_pAnd integral gain k_iEquivalent conversion factor of (c). Due to k_pIs "1/second", k_iIs 1/second²", thusEnsures the proportional control force u shown by the MCPI control force (8)_p＝(z₁+z₂)e₁/b₀And the integral control force u_i＝z₁z₂e₀/b₀All having the same generalized velocity dimension.

4. Closed loop control system stability analysis

Theorem 1. from assumption 1, as long as the sum perturbation is bounded: | y₂|<Infinity, then if and only if z₁>0 and z₂>At 0, the closed-loop control system composed of the MCPI cooperative controller shown in the formula (8) is globally asymptotically stable and has good disturbance resistance robustness.

And (3) proving that:

1) stability analysis

The MCPI cooperative control force (8) is substituted for a controlled error system shown in an expression (7), and an MCPI closed-loop control system comprises the following components:

it is apparent that the closed loop control system (10) is actually a disturbance y in the sum₂Dynamic error system under inverse excitation. Considering the initial state:

a single-sided Laplace transform is taken for the MCPI closed-loop control system (10), and the method comprises the following steps:

finishing to obtain:

obviously, the first term of the closed loop control system (12) is the zero input response:

the second term is the zero state response:

the transfer function defining the closed loop control system is:

according to the complex frequency domain analysis theory, if and only if z₁>0、z₂>At 0, the system transfer function (13) has two poles on the real axis of the left complex half plane: -z₁And-z₂The error transmission system (13) and thus the closed loop control system (12) are stable. And because of z₁And z₂Are independent of model parameters of the controlled object, and the closed loop control system (12) is thus globally asymptotically stable.

2) Robust analysis of disturbance rejection

Substituting system (13) into system (12), the closed loop control system can be represented as:

when z is₁≠z₂The unit impulse response of the system (13) is:

wherein k is₁＝z₁/(z₂-z₁)，k₂＝z₂/(z₁-z₂)。

When z is₁＝z₂The unit impulse response of the system (13) is:

thus, the time domain solution available from the closed loop control system (14) is:

wherein "+" denotes a convolution integral operation.

When z is₁>0、z₂>At 0 time, due to

Thus, as long as the sum perturbation is bounded: | y₂|<Infinity, then must be:

i.e. the tracking error e of the controlled system₁(t) can be taken from any initial state other than zero

The zero point of the stable balance point is approached gradually, and accurate control can be realized theoretically. And because e₁(t) → 0 and y only₂|<Infinity, and with the sum perturbation y₂The MCPI closed-loop control system has good total disturbance robustness resistance, including model robustness, time-varying robustness, external disturbance robustness and the like, and the verification is complete.

Speed factor setting method and control force amplitude limiting of MCPI

Although theorem 1 proves that if and only if z₁>0、z₂>At 0, the MCPI cooperative control system is globally asymptotically stable, so that two speed factors z of the MCPI are theoretically indicated₁And z₂Has a large setting margin. From the formula (15), z₁And z₂Velocity factors, z, which are respectively the approximation of 0 for the two parts of the unit impulse response_jThe larger (j ═ 1,2) indicates that the unit impulse response h (t) approaches 0 more rapidly, or the tracking error e₁The faster (t) approaches 0. However, how to adjust z₁And z₂It is a key scientific problem that the present invention needs to solve.

1) Mapping of velocity factor to center velocity factor

For practical purposes, two speed factors are mapped to:

z₁＝(1-σ)z_c，z₂＝(1+σ)z_c(18)

wherein z is_cIs the center velocity factor, σ is the center velocity deviation ratio, and z_c>0，0≤σ<1。

Therefore, the MCPI cooperative control force (8) is rewritten as:

the MCPI setting rule (9) is rewritten as:

the central speed factor z is known from the MCPI setting rule (20)_cNot only two gains k in MCPI cooperative controller_pAnd k_iIs also an internal link factor between two different physical links of proportion and integral. Due to z_cThe proportion and the integral are closely coupled together, so that the two physical links with different attributes show a cooperative control mechanism with different functions and consistent targets in the control process, and the uncoordinated control behaviors which are independent and independent from each other and are independent of each other in the control process of the two different physical links of the traditional PI controller are overturned.

Furthermore, the larger σ, the weaker the integral control force will act, and vice versa. Due to z_cThe setting rule of the MCPI cooperative controller is established together with the sigma, so that the setting problem of the traditional PI can be effectively solved, and a scientific theoretical basis can be provided for technical evaluation and technical upgrading of the existing PI controller, so that the MCPI controller has important scientific significance.

2)z_cAnd T_iInter-related relationship between

Considering k in PI controller_pAnd k_iThe relationship between: k is a radical of_i＝k_p/T_iAnd combined with the setting rule (20) of the MCPI, the center can be obtainedThe speed factor is:

obviously, z is_cT by PI controller_iIs set, and the dimension is 1/second, T_iThe smaller, z_cThe larger the size, otherwise the opposite is true. However, to date, scholars at home and abroad have received little attention to T_iHow to adjust. Therefore, how to adjust T_i？T_iIs it related to the controlled object? These two problems are also key scientific issues that the present invention needs to solve.

3)z_cExternal connection with controlled object

Considering that the dynamic change speed of the controlled object is closely related to the time scale tau, the smaller tau is, the faster the dynamic change speed of the controlled object is, otherwise, the reverse is true. Therefore, the inventors consider that: provided that the minimum central speed factor z of the MCPI cooperative controller_cm＝2/T_iIf the dynamic change speed is greater than 2/tau of the controlled object, the controlled object can be effectively controlled, namely: z is a radical of_cm>2/tau. Accordingly, the minimum center speed factor of the MCPI cooperative controller may be defined as:

z_cm＝2α/τ (22)

wherein 1< α ≦ 10, and τ is the time scale of the controlled object.

Since τ is an abstract time scale concept, the size of τ is difficult to obtain for a nonlinear system, and therefore, z is adjusted using the time scale τ_cTheoretical and practical difficulties are encountered. However, the dynamic change speed of the controlled object can be predicted or measured, and the transient process time of the controlled object from the dynamic state to the steady state is assumed to be T_rAnd is provided with T _r10 τ, the minimum center speed factor of the MCPI cooperative controller is, according to equation (22):

z_cm＝20α/T_r(23)

wherein 1 is<α≤10，T_rIs the transition process time of the controlled object.

From the equation (23), z of the MCPI cooperative controller_cmCan be composed of T_rTo set, for example: t is_r1 second, z_cm＝20α；T_r0.1 second, z_cm＝200α；T_r100 seconds, z_cm0.2 α, and so on.

Obviously, by testing the dynamic characteristics (unit step response characteristics) of the unknown controlled system, T can be determined_rSo that z can be set according to equation (23)_cmThe value range of (A) is convenient for practical operation. Due to 1<α ≦ 10, therefore, z_cmMinimum value z of_cm＝20/T_rAnd a maximum value z_cm＝200/T_rThe difference is 10 times, has great setting elasticity and is usually taken as the middle value, namely z_cm＝100/T_r。

4) Adaptive speed factor model

Taking into account tracking errors e during dynamics₁And its integral e₀＝∫e₁dt is large, requirement z_cShould not be too large, otherwise, the control force will be integrated

Too large causing overshoot and ringing. Considering that the absolute error during the dynamic period is large, the invention defines an adaptive speed factor model:

z_c＝z_cmexp(-β|e₁|) (24)

wherein z is_cm＝20α/T_r，1<α≤10，β＝1+0.1α。

The formula (24) is the central velocity factor z_cTime T of transition process with controlled object_rThe external connection between them. Obviously, as long as T is determined_rCan adjust z_cmAnd z_c. And T can be easily obtained because the dynamic characteristics of any known or unknown controlled object can be obtained through testing_rTo obtain the minimum velocity factor z_cm＝20α/T_rAnd is self-adaptingResponsive to velocity factor z_c＝z_cmexp(-β|e₁And | to facilitate zero-distance connection between the MCPI cooperative control theory and the actual control engineering, and to provide scientific theoretical basis for evaluation and upgrade of the existing PI control technology.

5) MCPI cooperative control force amplitude limiting

Since integral saturation easily causes overshoot and oscillation phenomena and considers the limited input condition of the practical physical system, the integral control force u of the MCPI is required_iAnd clipping in cooperation with the control force u. Setting the maximum amplitude of the MCPI cooperative control force as u_mThe clipping conditions are as follows:

|u_i|≤0.8u_m，|u|≤u_m(25)

and 4, a block diagram of an MCPI control system, as shown in figure 1.

6, testing and analyzing the performance of the MCPI cooperative control system

In order to verify the effectiveness of the novel MCPI cooperative control theory method, the following simulation experiment is carried out aiming at the control problem of an unknown non-affine nonlinear object.

Let a certain unknown non-affine nonlinear system be:

wherein the content of the first and second substances,

is an unknown system model function, u and y are the control input and the actual output of the system, respectively, and d is the external disturbance.

Obviously, the system (26) is a typical first order non-affine nonlinear system.

1) Unknown non-affine non-linear system dynamic characteristic test

Setting the sampling frequency f_s1000Hz, initial state: y is₁(0) When u is 1, the dynamic characteristics are as shown in fig. 2. As can be seen from FIG. 2, the state of the unknown object has mutated at 1.106 seconds, indicating that the unknown system (26) is not only a fast system, but is also a very fast systemUnstable systems.

As can be seen from the dynamics test information of FIG. 2, a transient time T is required for effective control of the unknown system (26)_rLess than or equal to 1.1 seconds. If T is taken_rAt 1 second, the minimum center velocity is, according to equation (23): z is a radical of_cm＝20α/T _r20 α, therefore, the adaptive center velocity factor model for MCPI is, according to equation (24):

z_c＝20α exp(-β|e₁|) (27)

wherein, 1< α is less than or equal to 10, β is 1+0.1 α.

2) Related parameters of MCPI cooperative controller

When the unknown non-affine nonlinear system (26) is controlled, α is 5, β is 1+0.1 α is 1.5, and according to the formula (27), the adaptive center speed factor is:

z_c＝100exp(-1.5|e₁|) (28)

according to equation (19), the control force u is integrated_iProportional control force u_pAnd the MCPI cooperative control force u is respectively as follows:

due to 0.5u³+u＝(1+0.5u²) u and b is 1+0.5u²>1, if b is taken₀1, then 0.5u³May act as an internal perturbation. To reduce the effect of the integral control force, σ may be 0.5.

In all the following simulation experiments, the initial state of the controlled object is as follows: y is₁(0) At 0.0, the relevant parameters of the MCPI are identical, and the control force limiting conditions are also identical, namely: | u_i|≤4，|u|≤5。

In order to verify the disturbance rejection capability of the MCPI cooperative control system, the same external disturbance is used in the following simulation experiments, namely, a square wave disturbance with the amplitude of +/-1 exists in the period of (9 s-11 s), as shown in FIG. 3.

Simulation experiment 1: cosine trajectory tracking control experiment

In order to verify the sine tracking control performance of the novel MCPI cooperative control theory method, a cosine trajectory tracking control experiment is carried out aiming at an unknown controlled system (26).

Given a desired output trajectory of y_dUsing the control method of the present invention, the tracking control result is shown in fig. 4. FIG. 4 shows that the MCPI cooperative control system not only has fast response speed (can enter a stable state within 1 second) but also has higher control precision (the maximum absolute error is less than 1.5 multiplied by 10)^-4) And has good disturbance robustness, thus being an effective control method. In addition, it was found in the experiment that: at b₀Any value in the range of 0.5-5.0 can obtain a good control effect, which indicates that the estimated value of the control channel gain is not required to be accurate, any value in the range of 1- α -10 can obtain effective control, the larger the α is, the higher the steady-state precision is and the stronger the disturbance resistance is, however, the transient oscillation phenomenon occurs in the control input, and therefore, the α -5 (intermediate value) is usually suitable.

Simulation experiment 2: step tracking control experiment

In order to verify the step tracking control capability of the novel MCPI cooperative control theory method, a step tracking control experiment is carried out on an unknown controlled system (26).

Since the output trace is expected to be a unit step signal, a state abrupt change exists, and a reasonable transition process needs to be arranged for the state abrupt change. Due to the transient time setting to T for the unknown system (26)_r1 second, therefore, the desired output transition should be: y is_d(t) 1-exp (-10t), and

the simulation results are shown in fig. 5 by using the control method of the present invention. FIG. 5 shows that the MCPI cooperative control system of the present invention not only has a fast response speed (entering a steady state within about 1 second) but also has a high control accuracy (the maximum absolute error is less than 1.0 × 10)^-261) Theoretically, zero-error tracking control can be realized, and the method has good disturbance resistance robustness, and further shows that the method has the advantages of high accuracy, high reliability and low costThe MCPI cooperative control theory new method is a globally stable strong disturbance rejection control method. In addition, it was found in the experiment that: b₀The same control effect can be obtained by any value within the range of 0.5-5.0, further showing that the estimated value of the control channel gain is not required to be accurate, effective control can be obtained by any value within the range of 1- α -10, the larger the α is, the higher the steady state precision is, the stronger the disturbance resistance is, however, the transient oscillation phenomenon can occur in the control input, and therefore, the more suitable the α -5 (intermediate value) is usually adopted.

7. Conclusion

In the control field of a first-order system or an MIMO system, although a PI controller based on a control theory strategy is a mainstream controller widely used in the field of actual control engineering at present, PI and various improved PI thereof have the limitations of poor gain robustness and poor disturbance rejection robustness. Compared with various PI controllers, the novel MCPI cooperative control theory method can effectively solve the problem of setting the PI, and for any unknown controlled object, the dynamic speed characteristic of a controlled system can be easily known only by testing the unit step response of the unknown controlled object, so that the transition process time, the minimum central speed factor and the self-adaptive central speed factor can be easily determined, and an effective setting method is provided for the central speed factor of the MCPI cooperative controller. In addition, the effect of integral control force can be effectively reduced by increasing the central speed deviation ratio 0 to be less than or equal to sigma <1, and overshoot and oscillation phenomena caused by integral saturation are avoided. Therefore, the emergence of the theory of cooperative control of the MCPI with the central velocity factor as the core coupling factor reveals not only the objective physical attributes of the controller, but also reflects the external association characteristics established between the controller and the controlled object through the minimum central velocity factor model, and will certainly become a subversive revolution of the existing control theory system.

The invention not only has wide application prospect in the control field of any first-order system and MIMO system, but also can provide scientific theoretical basis for the evaluation and upgrade of the current PI control technology, promotes the zero-distance rail connection of the MCPI cooperative control theory and the actual control engineering, and has great scientific significance.

Claims

1. A mutual coupling PI cooperative control theory new method is characterized in that a minimum speed factor model comprises the following specific steps: