A dual-drive H∞ robust control method for synchronous opening and closing mechanisms

Abstract

The present invention discloses a dual-drive H∞ robust control method for a synchronous opening and closing mechanism. Based on the H∞ control theory, the problem that the classical control theory and the modern control theory are limited by the accurate mathematical model of the controlled object is solved. In view of the uncertainties such as external disturbances and parameter perturbations, a controller combining state feedback and force compensation is designed, so that the synchronous opening and closing mechanism meets the synchronous drive accuracy requirements. The H∞ robust design index is used to design constraints on the controller in the initial state of the system and in the state under interference, and the designed controller has better robustness.

Description

Technical Field

[0001] The invention belongs to the technical field of servo control, and in particular to a dual-drive H∞ robust control method for a synchronous opening and closing mechanism. Background Art

[0002] At present, synchronous control is mainly divided into mechanical synchronous control and electromechanical synchronous control. The traditional mechanical method has a simple control system, but a complex mechanical structure. It is limited by its own transmission range and spatial dimensions, and the control accuracy is low. It is difficult to meet the requirements of modern industrial manufacturing. The synchronous control of the electronic control method is flexible and convenient, and basically does not need to consider structural limitations. It has been widely used in modern industrial applications and has made great progress in control technology. The core of the application of electrical coordinated motion control is the design of the motion controller, which controls each servo unit to achieve the predetermined motion trajectory.

[0003] Controllers designed by classical control theory and modern control theory must obtain accurate mathematical models of the controlled objects and meet specific indicators and requirements. However, there are often many uncertain factors in practical applications. In order to ensure reliable opening and closing actions, the synchronous opening and closing mechanism adopts a dual electric cylinder parallel drive mode, but due to the influence of external uncertain disturbances, process and other factors, it is difficult to achieve high-precision synchronous drive. Since the synchronous opening and closing mechanism system has parameter uncertainty, its model is an uncertain control object. Summary of the invention

[0004] The object of the present invention is to provide a dual-drive H∞ robust control method for a synchronous switching mechanism, so that the synchronous switching mechanism meets the synchronous drive requirements and has good robustness to parameter changes and load disturbances.

[0005] The technical solution to achieve the purpose of the present invention is:

[0006] A dual-drive H∞ robust control method for a synchronous opening and closing mechanism adopts the following controller:

[0007] u=K1x(t)+K2f d (t)

[0008] Where x(t) is the state variable, f d (t) is the disturbance force of the main electric cylinder, K1 and K2 are state feedback and force compensation respectively; the controller needs to meet the following requirements:

[0009] When f d When (t) = 0, there exist arbitrary constants α>0, β>0 such that ||x(t)||<β||x(0)||e -αt ,

[0010] When x(0) = 0, for any given value T a >0, holds true, where ε is a given constant;

[0011] There is a positive solution H>0:

[0012]

[0013] in, I is the unit matrix, Q is the positive definite matrix;

[0014] Among them A k =A1+B2K1,B k =B1+B2K2,C k =C1+D2K1,D k =D1+D2K2;

[0015]

[0016]

[0017]

[0018] Among them, q1, q2, q3, q4 are weighted coefficients, m1 and m2 represent the mass of the master and slave electric cylinders, μ1 and μ2 are the friction coefficients of the master and slave electric cylinders and are fixed constants, and c e and k e are the equivalent damping parameter and elastic coefficient respectively; and there is a constant σ c >0,σ k >0 makes |Δc e |≤σ c , |Δc k |≤σ k , Δc e , Δk e are the uncertain perturbation parameters of the damping parameter and elastic coefficient respectively.

[0019] Compared with the prior art, the present invention has the following significant advantages:

[0020] (1) The present invention takes into account the parameter uncertainty of the synchronous opening and closing mechanism system and adopts the H∞ control theory to design the controller. Compared with the traditional algorithm when the accurate mathematical model cannot be determined, the controller designed by the present invention has higher accuracy.

[0021] (2) The controller designed by the present invention includes a force compensator to address the uncertainty issues such as external disturbances and parameter perturbations of the synchronous opening and closing system, so it has stronger anti-interference ability.

[0022] (3) The present invention adopts the H∞ robust design index to design constraints on the controller in the initial state and the disturbed state of the system, which has better robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a schematic diagram of the composition of the synchronous opening and closing mechanism system.

[0024] Figure 2 It is a structural diagram of the control method of the synchronous opening and closing mechanism system.

[0025] Figure 3 It is a curve chart of the position tracking of the master and slave electric cylinders. DETAILED DESCRIPTION

[0026] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0027] The present invention proposes a dual-drive H∞ robust control method for a synchronous opening and closing mechanism. The schematic diagram of the synchronous opening and closing mechanism system is shown in FIG. Figure 1 As shown, the control unit sends the electric cylinder driving force command to the driver through CAN communication, and the electric cylinder executes the command and drives the actuator to open and close through the reducer. The control unit can obtain the electric cylinder position information and driving force information through the encoder and driver feedback. The actuator is driven by two identical electric cylinders on the left and right. The specific steps of this control method are as follows:

[0028] Step 1: Establish the mathematical model of the synchronous opening and closing mechanism system:

[0029] The left electric cylinder is used as the master electric cylinder, and the right electric cylinder is used as the slave electric cylinder. Assume that the disturbance to the master electric cylinder is f d (t), then the compensation force output to the electric cylinder is f c (t), the dynamic characteristics of the synchronous opening and closing mechanism driving model are as follows:

[0030]

[0031] The mass matrix is ​​M = (m1, m2) T , position matrix Y = (y1(t), y2(t)) T , friction coefficient matrix μ = (μ1, μ2) T , disturbance and compensation force matrix f=(-f d (t),f c (t)) T , driving force matrix F = (F1(t), F2(t)) T .

[0032] Among them, y1(t) and y2(t) represent the positions of the master and slave electric cylinders respectively. The positions of the electric cylinders can be obtained through the encoder. m1 and m2 represent the masses of the master and slave driving electric cylinders respectively. F1(t) and F2(t) are the driving forces of the master and slave electric cylinders respectively. μ1 and μ2 are the friction coefficients of the master and slave electric cylinders respectively and are fixed constants.

[0033] Step 2: Obtain the disturbance force f of the electric cylinder based on the nominal parameters of the synchronous opening and closing system actuator and the environment. d (t) is the mechanical equation.

[0034] Assume that the equivalent damping parameter c of the actuator and the environment of the synchronous opening and closing system is e and elastic modulus k e (c e and k e is the nominal parameter), the equivalent damping parameter and elastic coefficient are perturbed within a certain range, assuming Δc e , Δk e are the uncertain perturbation parameters of the damping parameter and elastic coefficient, respectively, and there is a known constant σ c >0,σ k >0 makes |Δc e |≤σ c , |Δc k |≤σ k . From this we can get f d (t) is expressed as follows:

[0035]

[0036] Step 3, obtain the state equation of the synchronous switching system, which is described as follows:

[0037] Let the state variable t is time. According to formula (1) and formula (2), the state equation of the system can be expressed as follows:

[0038]

[0039] The matrix A m , B1, B2 are as follows:

[0040]

[0041]

[0042] Step 4: Design a controller based on the H∞ robust control theory. Obtain the master-slave electric cylinder position tracking error according to the master-slave electric cylinder position deviation. Obtain the compensation force error according to the disturbance force and the compensation force deviation. Design a synchronous opening and closing system controller combining state feedback and force compensator based on the H∞ robust control theory. The specific process is as follows:

[0043] Step 4.1, the position tracking error of the master and slave electric cylinders can be expressed as e y =y1(t)-y2(t), the compensation force error is e f =f d (t)-f c (t).

[0044] Step 4.2, when the system has perturbation changes within a certain range, in order to ensure the system synchronization control accuracy and system state stability, it is necessary to suppress the position tracking error and compensation force error as much as possible and control them within the allowable range. Based on the H∞ robust control theory, the controller combining state feedback K1 and force compensation K2 is designed as follows:

[0045] u=K1x(t)+K2f d (t) (4)

[0046] Step 5, constrain the controller according to the robust design criteria. The robustness constraints include two points. The first is that the synchronous opening and closing system controller should be robustly stable to the uncertain disturbances of the system and the external environment in the initial state. The second is that when the master electric cylinder is disturbed by the disturbance force, the tracking error of the master and slave electric cylinders should be as small as possible. In order to ensure that the system is robustly stable to the uncertain perturbations of the actuator and the environment in the initial state, the controller must meet certain requirements, which are described as follows:

[0047] Step 5.1, under the initial zero position state, the actuator and environmental uncertainty of the synchronous opening and closing system must be robust exponentially stable, so the controller must meet indicator 1:

[0048] When f d When (t) = 0, there exist arbitrary constants α>0, β>0 such that ||x(t)||<β||x(0)||e -αt ,

[0049] Step 5.2: When the controller is subjected to external disturbances, it is necessary to suppress the tracking error caused by the disturbance as much as possible. Therefore, the controller needs to meet indicator 2:

[0050] When x(0) = 0, for any given value T a >0, holds true, where ε is a given constant. The smaller the value, the better the suppression effect.

[0051] Step 6: Use the Riccati equation to solve the controller. The specific description is as follows:

[0052] Step 6.1: Assume that the disturbance suppression performance evaluation signal is Z(t), where q1, q2, q3, and q4 are weighted coefficients. Then the state equation of the system and the disturbance suppression performance evaluation signal can be expressed as follows:

[0053]

[0054] Z(t)=(C1+ΔC)x(t)+D1f d (t)+D2u (5-2)

[0055]

[0056]

[0057]

[0058] Step 6.2, to solve the Riccati equation, assume that the uncertain perturbation matrices ΔA and ΔC can be expressed as:

[0059]

[0060] in

[0061] Step 6.3, express the closed-loop systems (5-1, 5-2) and (4) as follows:

[0062]

[0063] Z(t)=(C k +ΔC)x(t)+D k f d (t) (7-2),

[0064] Among them A k =A1+B2K1,B k =B1+B2K2,C k =C1+D2K1,D k =D1+D2K2.

[0065] Step 6.4, the controller can be solved using the Riccati equation. According to the theorem: if there are appropriate constants λ1>0 and λ2>0 such that the Riccati equation is:

[0066]

[0067] If there is a positive solution H>0, the closed-loop system (7-1, 7-2) can be solved, and the system meets the robustness design index requirements of steps 5.1 and 5.2. (I is the unit matrix), Q is a proper positive definite matrix. According to the above theorem, the positive solution of the Riccati equation can be solved, that is, the controller (4) that meets the robust design index.

[0068] Step 7, take the Lyapunov function V(x(t))=x T (t)Hx(t), let ε=σ min (Q)(σ min is the minimum singular value), it can be proved from Riccati equation (8) that Then the system is robust exponentially stable.

[0069] A synchronous opening and closing mechanism, the system composition is as follows Figure 1 As shown, the controller designed by the above method has a master-slave electric cylinder position tracking curve of the synchronous opening and closing system as shown in Figure 3 As shown, the curve results show that under the condition that the mechanism and external disturbance of the synchronous switching system exist uncertainties, the controller designed based on the H∞ control theory has strong anti-interference and robustness, and has good synchronous control accuracy.

Claims

1. A dual-drive H∞ robust control method for a synchronous opening and closing mechanism, using the following controller: u=K1x(t)+K2f d (t) Where x(t) is the state variable, f d (t) is the disturbance force on the main electric cylinder, K1 and K2 are the state feedback gain matrix and force compensation gain matrix of the controller respectively; it is characterized in that, The controller must meet the following requirements: When f d When (t) = 0, there exist any constants α>0, β>0 such that When x(0) = 0, for any given value T a >0, holds true, where ε is a given constant; There is a positive solution H>0: in, I is the unit matrix, Q is the positive definite matrix; Among them A k =A1+B2K1,B k =B1+B2K2,C k =C1+D2K1,D k =D1+D2K2; Among them, q1, q2, q3, q4 are weighted coefficients, m1 and m2 represent the mass of the master and slave electric cylinders, μ1 and μ2 are the friction coefficients of the master and slave electric cylinders and are fixed constants, and c e and k e are the equivalent damping parameter and elastic coefficient respectively; and there is a constant σ c >0,σ k >0 makes |Δc e |≤σ c , |Δc k |≤σ k , Δc e , Δk e are the uncertain perturbation parameters of damping parameter and elastic coefficient respectively; The controller solution process is as follows: Step 1, establishing a mathematical model of the synchronous opening and closing mechanism system; Step 2, obtaining the mechanical equation of the disturbance force of the master electric cylinder according to the nominal parameters of the synchronous opening and closing system actuator and the environment; Step 3, obtaining the state equation of the synchronous switching system; Step 4, obtaining the master-slave electric cylinder position tracking error according to the master-slave electric cylinder position deviation, obtaining the compensation force error according to the disturbance force and the compensation force deviation, and designing a synchronous opening and closing system controller combining state feedback and force compensator based on H∞ robust control theory; Step 5, constraining the controller according to the robust design criteria; Step 6: Solve the synchronous switching system controller according to the Riccati equation.

2. A dual-drive H∞ robust control method for a synchronous opening and closing mechanism according to claim 1, characterized in that: The mathematical model of the synchronous opening and closing mechanism system is established as follows: The mass matrix is ​​M = (m1, m2) T , position matrix Y = (y1(t), y2(t)) T , friction coefficient matrix μ = (μ1, μ2) T , disturbance and compensation force matrix f=(-f d (t),f c (t)) T , driving force matrix F = (F1(t), F2(t)) T ; Among them, y1(t) and y2(t) represent the positions of the master and slave electric cylinders respectively, and F1(t) and F2(t) are the driving forces of the master and slave electric cylinders respectively.

3. The dual-drive H∞ robust control method for a synchronous opening and closing mechanism according to claim 1, characterized in that: The mechanical equation of the disturbance force of the electric cylinder is obtained as follows: Where y1(t) represents the position of the master electric cylinder.

4. The dual-drive H∞ robust control method for a synchronous opening and closing mechanism according to claim 1, characterized in that: The state equation of the synchronous switching system is obtained as: The matrix A m , B1, B2 are as follows: State variables t is time.

5. The dual-drive H∞ robust control method for a synchronous opening and closing mechanism according to claim 1, characterized in that: It also includes step 7, taking the Lyapunov function V(x(t))=x T (t)Hx(t), and we can conclude that the controller is stable.

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