Networked expansion PID (Proportion Integration Differentiation) controller design method under event triggering condition and computer system

Abstract

The invention discloses a networked expansion PID controller design method under an event triggering condition, which comprises the following steps: determining a relative order m of a system, and designing an expansion PID controller; designing an event triggering expansion PID controller; designing event triggering conditions; and designing control parameters of the event-triggered expansion PID controller. The method has the advantages that the method is suitable for high-order system control, and communication resources and computing resources are saved.

Description

Technical Field

[0001] The invention relates to the field of affine nonlinear control, and in particular to a networked extended PID controller design method under event triggering conditions and a computer system. Background Art

[0002] As a classic representative, the proportional-integral-derivative (PID) control algorithm is still the earliest and most common control method. Currently, more than 90% of industrial control applications use the PID control strategy.

[0003] Compared with traditional control systems, network control systems have significant advantages such as easy installation, low cost and easy maintenance. However, limited network bandwidth inevitably weakens network performance, accompanied by packet loss, communication delays and channel congestion. The most common solution is to adopt an event trigger mechanism. Unlike the traditional time trigger mechanism, the update of network signals under the event trigger mechanism depends on whether the trigger condition is met, which can significantly reduce the update frequency of the signal.

[0004] Exploring network PID control under an event-triggered framework is of great value, not only in alleviating the network burden, but also in promoting the development of PID control theory. This approach has the potential to optimize system performance while minimizing unnecessary data transmission, thereby broadening the applicability of PID controllers in network control environments.

[0005] Currently, event-triggered PID controllers are only suitable for second-order nonlinear system control, but there is no relevant design method for event-triggered PID control of high-order nonlinear systems. Therefore, the present invention proposes an event-triggered extended PID controller design method for affine nonlinear single-input single-output system to adapt to high-order nonlinear system control. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a design method for a networked extended PID controller under event triggering conditions, which is suitable for high-order system control, reduces the amount of calculation and communication in networked control, and achieves a control effect similar to that of an extended PID.

[0007] In order to solve the above technical problems, the present invention provides a networked extended PID controller design method under event triggering conditions, comprising the following steps:

[0008] Step S1, determine the relative order m of the system and design an extended PID controller;

[0009] For the following m-dimensional affine nonlinear system,

[0010]

[0011] in, is a smooth mapping, f and g are composed of independent function components f i and g i , i = {1, ..., m}, u(t) represents the input control signal;

[0012] Assume that the expected signal and Thus, the control error e(t)=y is defined * -y(t)=y * -h(x(t));

[0013] definition is the derivative of the function h along the vector field f;

[0014] definition is the derivative of function h along function f, and then the obtained function is differentiated again along function g;

[0015] definition The function h is derived k times along the function f, where

[0016] Defining a new coordinate system is a global diffeomorphism;

[0017] definition

[0018] For i = {1, ..., m-1}, let the derivative of the error e(t) be e (m) (t)=-ρ(x(t))-γ(x(x))u(t);

[0019] set up x0(0)=0;

[0020] The expanded PID controller is designed as:

[0021]

[0022] Step S2, designing an event-triggered extended PID controller;

[0023] Defining the error variable

[0024]

[0025] Where: t k represents the specific sampling time of the event triggering moment, k represents the cumulative number of event triggering, t∈[t k , t k+1 ];

[0026] The event-triggered extended PID outputs a new control signal u(t) only when an event is triggered;

[0027] The control signal u(t) of the closed-loop system dynamics is defined as u(t) = κ(t k ), where t∈[t k , t k+1 ], we get the following m-dimensional affine nonlinear system:

[0028]

[0029] in: Step S3, designing event triggering conditions;

[0030] set up

[0031] Where: i = {2, ..., m};

[0032] The event trigger condition r(t) is a switch used to control whether to transmit the signal, and has the following expression:

[0033]

[0034] Among them: A and B are constants greater than zero;

[0035] Step S4, designing control parameters of the event-triggered expanded PID controller;

[0036] set up

[0037] Define Ξ1={ψ|2<ψ i -2iψ3,ψ m >2m+2, i=0,…,m-1};

[0038] Defining the Matrix

[0039] Let [θ0,…,θ m ]=O -1 [0, ..., 0, 1] T Indicates O -1 The last column of the matrix;

[0040] definition

[0041] Define R>0 and

[0042] Based on this, define:

[0043]

[0044] Where: h is a constant greater than zero;

[0045] For the control parameters [σ0,…,σ m ]The following conditions are met:

[0046]

[0047] Get the control parameters of the event-triggered extended PID controller and set the above control parameters in the simulation system.

[0048] The design event triggers the expansion PID controller, including:

[0049] Event generation module: The sensor continuously monitors the measurement status of the controlled object; the control signal is triggered only when a certain performance indicator exceeds the threshold; the controller samples the data and sends the control signal to the zero-order holder; control update module: the control update occurs at the event triggering moment, and the zero-order holder retains and sends the latest control signal to the controlled object;

[0050] Between the event triggering time and the next event triggering time, the zero-order hold generates a continuous-time input signal using the event-triggered extended PID controller.

[0051] The present invention also provides a computer system, including a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of a networked extended PID controller design method under event triggering conditions.

[0052] The beneficial effects of the present invention are:

[0053] (1) Save communication resources: The event trigger mechanism sends control signals only when specific conditions are met, which significantly reduces unnecessary data transmission and reduces network bandwidth usage;

[0054] (2) Save computing resources: By reducing the frequency of control signal updates, the computing burden is reduced and the overall efficiency of the system is improved;

[0055] (3) Applicable to high-order system control: The event-triggered extended PID controller can effectively control high-order single-input and single-output nonlinear systems, overcoming the limitation that the traditional PID controller is only applicable to second-order systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The drawings constituting a part of the present application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0057] Figure 1This is the event-triggered expanded PID principle diagram proposed by the present invention;

[0058] Figure 2 is a flow chart of a specific embodiment of the present invention;

[0059] Figure 3 It is a comparison diagram of the effects of event-triggered extended PID control and extended PID control when the relative order m=3 in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] It should be understood that the step numbers used in this article are only for the convenience of description and are not intended to limit the order in which the steps are executed.

[0062] It should be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0063] The terms “include” and “comprising” indicate the presence of described features, integers, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0064] The term "and / or" means and includes any and all possible combinations of one or more of the associated listed items.

[0065] like Figure 1 As shown in the schematic diagram of the event-triggered expanded PID in the specific embodiment of the present invention, the design of the event-triggered control mainly includes three parts:

[0066] (1) Event generator: The sensor continuously monitors the measurement state y(t) of the controlled object;

[0067] The control signal is triggered only when a certain performance indicator exceeds the threshold, that is, at the event triggering time t k , r(t) = 1, where k represents the total number of triggers that have occurred; at this time, the controller samples the data and controls the signal κ(t k ) is sent to the zero-order holder ZOH;

[0068] (2) Control update: Control update occurs at the event trigger time t k ;

[0069] The zero-order holder retains and sends the latest control signal to the controlled object;

[0070] (3) Continuous input signal generation: At t k and t k+1 The zero-order holder uses κ(t k ) generates a continuous-time input signal u(t), where t∈[t k , t k+1 ].

[0071] Figure 1 In which ∫ represents integrator, D represents differentiator, ZOH represents zero-order holder, Plant represents actual physical system, and Sensor represents sensor.

[0072] The specific embodiment of the present invention takes the electro-hydraulic servo system as an example. The electro-hydraulic servo system has the characteristics of high power-to-weight ratio, large load stiffness, strong effective load capacity and fast response speed. It is widely used in aerospace, weapon equipment, energy metallurgy, marine equipment and mining machinery. It is a typical third-order nonlinear uncertain system, which makes it difficult to achieve a good control effect for the dynamic and steady-state characteristics of the electro-hydraulic servo control system. The present invention provides an event-triggered extended PID controller design method to adapt to the control of third-order nonlinear systems, such as Figure 2 As shown,

[0073] For the electro-hydraulic servo third-order nonlinear system, it is as follows:

[0074]

[0075] Where: x1 represents the valve core displacement of the servo valve, and u(t) represents the rotation angle of the hydraulic motor.

[0076] The present invention provides an event-triggered extended PID controller design method, comprising the following steps:

[0077] Step S1: The electro-hydraulic servo system of the embodiment of the present invention is a nonlinear system with m=3, and the expanded PID controller is designed as follows:

[0078]

[0079] Step S2, designing an event-triggered extended PID controller;

[0080]

[0081] Step S3, designing event triggering conditions;

[0082]

[0083] Where: A = 0.2, B = 6;

[0084] Step S4, designing control parameters of the event-triggered expanded PID controller;

[0085] because R=0.1, So ψ3>8; therefore, let ψ0=2.5, ψ1=4.4, ψ2=6.4, ψ3=8.1;

[0086] Therefore, the designed event-triggered extended PID controller parameters are σ0=570.24, σ1=517.196, σ2=162.89, and σ3=21.4.

[0087] In the simulation system, the above parameters are set to obtain Figure 3 , Figure 3 The y(t) in the figure is the tracking control effect of the square wave under the event-triggered extended PID control method in Example 1. u(t) is the control input of the event-triggered extended PID, and r(t) is the event triggering time. From the graph of r(t), it can be seen that the method proposed by the present invention significantly reduces the number of control signals, reduces the network bandwidth occupation, and also enables the control system to track the square wave signal.

[0088] The present invention also provides a computer system, including a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of a networked extended PID controller design method under event triggering conditions.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for designing a networked extended PID controller under event triggering conditions, comprising the following steps: Step S1, determine the relative order m of the system and design an extended PID controller; For the following m-dimensional affine nonlinear system, in, is a smooth mapping, f and g are composed of independent function components f i and g i , i = {1, ..., m}, u(t) represents the input control signal; Assume that the expected signal and Thus, the control error e(t)=y is defined * -y(t)=y * -h(x(t)); definition is the derivative of the function h along the vector field f; definition is the derivative of function h along function f, and then the obtained function is differentiated again along function g; definition The function h is derived k times along the function f, where Defining a new coordinate system is a global diffeomorphism; definition For i = {1, ..., m-1}, let the derivative of the error e(t) be e (m) (t)=-ρ(x(t))-γ(x(x))u(t); set up x0(0)=0; The expanded PID controller is designed as: Step S2, designing an event-triggered extended PID controller; Defining the error variable Where: t k represents the specific sampling time of the event triggering moment, k represents the cumulative number of event triggering, t∈[t k , t k+1 ]; The event-triggered extended PID outputs a new control signal u(t) only when an event is triggered; The control signal u(t) of the closed-loop system dynamics is defined as u(t) = κ(t k ), where t∈[t k , t k+1 ], we get the following m-dimensional affine nonlinear system: in: Step S3, designing event triggering conditions; set up Where: i = {2, ..., m}; The event trigger condition r(t) is a switch used to control whether to transmit the signal, as shown in the following expression: Where: A and B are constants greater than zero; Step S4, designing control parameters of the event-triggered expanded PID controller; set up Definition: Ξ1={ψ|2<ψ i -2i<3,ψ m >2 m +2, i=0,…, m-1}; Defining the Matrix Let [θ0,…,θ m ] = O-1[0, ..., 0, 1] T Indicates O -1 The last column of the matrix; definition Define R>0 and Based on this, define: Where: h is a constant greater than zero; For the control parameters [σ0,…,σ m ]The following conditions are met:

2. The networked extended PID controller design method under event triggering conditions according to claim 1 is characterized in that: The design event triggers the expansion PID controller, including: Event generation module: The sensor continuously monitors the measurement status of the controlled object; the control signal is triggered only when a certain performance indicator exceeds the threshold; the controller samples the data and sends the control signal to the zero-order holder; control update module: the control update occurs at the event triggering moment, and the zero-order holder retains and sends the latest control signal to the controlled object; Between the event triggering time and the next event triggering time, the zero-order hold generates a continuous-time input signal using the event-triggered extended PID controller.

3. A computer system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the design method according to any one of claims 1 to 2.

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