Robust PID (Proportion Integration Differentiation) control method suitable for urban trolley inverted pendulum first-order control system

Abstract

The invention discloses a robust PID (Proportion Integration Differentiation) control method and system suitable for a first-order control system of an inverted pendulum of a city trolley. The method comprises the following steps: establishing a first-order control system model for controlling the freedom degree of the inverted pendulum of the trolley; determining an H-infinity controller based on the first-order control system model; inputting an output signal of the H infinity controller to a PID (Proportion Integration Differentiation) controller to establish an initial H infinity-PID series control model; and performing parameter setting on the PID series control model to obtain a final H (infinity)-PID series control model, and performing PID control based on the final H (infinity)-PID series control model. According to the method, a dynamic model of the inverted pendulum of the trolley is modeled by taking the friction force as an uncertain factor, and a dynamic differential motion equation of the system under the uncertain factor is deduced. Through the feasibility of the control mode provided by simulation verification, the inverted pendulum system of the trolley under the control strategy can be kept stable, and the armature voltage of the trolley meets the stability requirement.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of PID control, and more particularly, to a robust PID control method and system suitable for an urban trolley inverted pendulum first-order control system. BACKGROUND

[0002] As a typical nonlinear dynamic system, the single-stage inverted pendulum occupies a classic position in control theory research. Its high instability and nonlinear characteristics make it an ideal platform for verifying advanced control algorithms. The dynamic behavior of this system needs to be described through accurate modeling, which is usually based on Newtonian mechanics or Lagrange method to derive the differential motion equation, in order to accurately capture the dynamic response of the trolley inverted pendulum near the equilibrium point, laying the foundation for subsequent control design. At present, there is a great demand for research on the control ability of urban trolley inverted pendulum to improve the level of robust control in nonlinear control environment. With the large-scale increase of trolley as a representative of the first-order control system, it is increasingly important in the fields of urban trolley multi-degree-of-freedom control, nonlinear power system stability control, etc.

[0003] The nonlinear control theory of inverted pendulum model is highly related to the stability challenges of power electronicized power grid. With the large-scale grid connection of high-proportion renewable energy, the system equivalent inertia level continues to decline, leading to prominent frequency response lag and dynamic stability problems, and similar uncertain disturbances of inverted pendulum need robust control strategies to cope with. Drawing on the PID-H∞ method of inverted pendulum, power systems are exploring virtual inertia control, fast frequency modulation and "control instead of cutting" technology to improve the coordination ability of source-grid-load and ensure the frequency stability and system resilience under extreme conditions.

[0004] In engineering applications, the trolley inverted pendulum system is often disturbed by uncertain factors such as friction, which can significantly reduce the robustness and control accuracy of the model, thus exacerbating the risk of system instability. Therefore, it is crucial to develop an efficient control strategy, and a robust PID control method suitable for urban trolley inverted pendulum first-order control system is needed. SUMMARY

[0005] The present application proposes a robust PID control method and system suitable for an urban trolley inverted pendulum first-order control system to solve the problem of how to perform PID control suitable for an urban trolley inverted pendulum first-order control system.

[0006] To solve the above problems, according to one aspect of the present application, a robust PID control method suitable for an urban trolley inverted pendulum first-order control system is provided, the method comprising:

[0007] establishing a first-order control system model of trolley inverted pendulum degree-of-freedom control;

[0008] determining an H∞ controller based on the first-order control system model;

[0009] The output signal of the H∞ controller is input to the PID controller to establish the initial H∞-PID cascade control model;

[0010] Parameters of the PID series control model are tuned to obtain a final H∞-PID series control model, so as to perform PID control based on the final H∞-PID series control model.

[0011] Preferably, the first-order control system model comprises:

[0012]

[0013] Among them, x is the state variable, is the derivative of the state variable, u is the input variable, y is the output variable, A and B are the state space parameter control matrices, and C and D are the output matrices. The control parameter elements in the A and B matrices are derived from the first-order control system and are expressed as partial derivative matrices of the state variables after linearization.

[0014] Let [x1, x2, x3, x4] T =[f1, f2, f3, f4] T ,but

[0015] D=[0 0] T .

[0016] Preferably, determining the H∞ controller based on the first-order control system model includes:

[0017] In the H∞ controller, ω, z, u, and y are set as the external input signal, controlled output, control signal, and measurement output, respectively. They are all vector-valued signals, so the mathematical model is:

[0018]

[0019] The H∞ controller model satisfies the constraints: min||F l (G,K)|| ∞ , that is, H ∞ The goal is to make the transfer matrix F l H of (G,K) ∞ The norm is extremely small; or ||F l (G,K)|| ∞ <ζ,0<ζ∈R, that is, all calculated matrices K can make G stable;

[0020] Where G is the system structure represented by the transfer function; G 11 , G 12, G 21 , G 22 is the system transfer function after block, K is the state feedback control optimal matrix.

[0021] Preferably, the output of the final H∞-PID series control model is:

[0022] OUT = U in · (U outH∞ -ref) · U outPID

[0023] Wherein, U in is the variable input, U outH∞ is the output of the H∞ controller, ref is the feedback, and U outPID is the output of the PID controller.

[0024] According to another aspect of the present application, a robust PID control system suitable for a city trolley inverted pendulum first-order control system is provided, the system comprising:

[0025] A first-order control system model establishment unit for establishing a first-order control system model for trolley inverted pendulum degree of freedom control;

[0026] An H∞ controller determination unit for determining an H∞ controller based on the first-order control system model;

[0027] A series control model establishment unit for inputting the output signal of the H∞ controller to a PID controller to establish an initial H∞-PID series control model;

[0028] A parameter tuning unit for parameter tuning of the PID series control model to obtain a final H∞-PID series control model, and performing PID control based on the final H∞-PID series control model.

[0029] Preferably, the first-order control system model comprises:

[0030]

[0031] Wherein, x is a state variable, is the derivative of the state variable, u is the input variable, y is the output variable, A and B are state space parameter control matrices, and C and D are output matrices; wherein the control parameter elements in the A and B matrices are derived from a first-order control system and are expressed as the partial derivative matrix of the state variable after linearization processing.

[0032] Let [x1, x2, x3, x4] T = [f1, f2, f3, f4] T , then

[0033] D=

[00] T .

[0034] Preferably, the H∞ controller determining unit determines an H∞ controller based on the first-order control system model, comprising:

[0035] In the H∞ controller, ω, z, u, y are respectively external input signal, controlled output, control signal, measured output, all of which are vector value signals, and the mathematical model is:

[0036]

[0037] The model of the H∞ controller satisfies the constraint condition: min||F l (G,K)| ∞ , that is, the H ∞ norm of the transfer matrix F l (G,K) is minimum; or ||F ∞ (G,K)| l <ζ, 0<ζ∈R, that is, all the matrix K calculated can make G stable. ∞

[0038] Wherein, G is a system structure represented by a transfer function; G 11 , G 12 , G 21 , G 22 are system transfer functions after being divided into blocks, and K is an optimal matrix of state feedback control.

[0039] Preferably, the parameter setting unit, the output of the final H∞-PID series control model is:

[0040] OUT=U in ·(U outH∞ -ref)·U outPID

[0041] Wherein, U in is a variable input, U outH∞ is the output of the H∞ controller, ref is a feedback, and U outPID is the output of the PID controller.

[0042] Based on another aspect of the present application, the present application provides a computer readable storage medium, which has a computer program stored thereon, the program being executed by a processor to implement the steps of any one of the robust PID control methods suitable for the urban trolley inverted pendulum first-order control system.

[0043] Based on another aspect of the present application, the present application provides an electronic device, comprising: ​

[0044] the computer readable storage medium; and

[0045] one or more processors for executing the program in the computer readable storage medium.

[0046] The application provides a robust PID control method and system suitable for a city trolley inverted pendulum first-order control system, and the method comprises the following steps: establishing a first-order control system model of trolley inverted pendulum freedom control; determining an H∞ controller based on the first-order control system model; inputting an output signal of the H∞ controller into a PID controller to establish an initial H∞-PID series control model; performing parameter setting on the PID series control model to obtain a final H∞-PID series control model, and performing PID control based on the final H∞-PID series control model. The application models a dynamic model of the trolley inverted pendulum by taking friction as an uncertain factor, and deduces a system dynamic differential motion equation under the uncertain factor. The feasibility of the proposed control mode is verified through simulation, the trolley inverted pendulum system under the control strategy can be kept stable, and the trolley armature voltage meets the stability requirement. BRIEF DESCRIPTION OF DRAWINGS

[0047] The exemplary embodiments of the application can be more completely understood in reference to the following drawings:

[0048] Figure 1 A flowchart of the robust PID control method 100 suitable for the city trolley inverted pendulum first-order control system according to the embodiments of the application;

[0049] Figure 2 A force analysis diagram of the trolley single-stage inverted pendulum system according to the embodiments of the application;

[0050] Figure 3 A control mode diagram of the trolley inverted pendulum system according to the embodiments of the application;

[0051] Figure 4 A trolley inverted pendulum first-order system parameter simulation curve diagram under the PID-H∞ control mode according to the embodiments of the application;

[0052] Figure 5 A structure schematic diagram of the robust PID control method system 500 suitable for the city trolley inverted pendulum first-order control system according to the embodiments of the application. DETAILED DESCRIPTION

[0053] Reference will now be made to the drawings to describe the exemplary embodiments of the present application in greater detail. The present application can be variously embodied and is not limited to the embodiments described herein. These embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the application to those skilled in the art. The terminology used in the description of the exemplary embodiments herein is not intended to be limiting of the present application. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure, and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0054] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure, and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0055] Figure 1 A flow chart of a robust PID control method 100 for a city trolley inverted pendulum first-order control system according to an embodiment of the present application. As shown in the figure, the robust PID control method for the city trolley inverted pendulum first-order control system provided by the embodiment of the present application models the dynamic model of the trolley inverted pendulum with friction as an uncertain factor, and derives the system dynamic differential motion equation under the uncertain factor. The feasibility of the control method proposed by the simulation verification is verified. The trolley inverted pendulum system under the control strategy can be kept stable, and the trolley armature voltage meets the stability requirement. The robust PID control method 100 for the city trolley inverted pendulum first-order control system provided by the embodiment of the present application starts from step 101. In step 101, a first-order control system model of the trolley inverted pendulum freedom control is established. Figure 1

[0056] Preferably, the first-order control system model comprises:

[0057]

[0058] wherein x is a state variable, is a derivative of the state variable, u is an input variable, y is an output variable, A and B are state space parameter control matrices, C and D are output matrices; wherein the control parameter elements in the A and B matrices are derived from the first-order control system, and are expressed as the partial derivative matrix of the state variable after linearization processing;

[0059] Let [x1, x2, x3, x4] T = [f1, f2, f3, f4] T , then

[0060] D =

[00] T . ​

[0061] Single inverted pendulum is a nonlinear and unstable system, which includes a cart and a pendulum rod as controlled object, and a servo motor and a transmission device as actuator. In modeling of the control, air friction is considered as 0, and the system is identified as a cart and a homogeneous lever.

[0062] In the present application, the original active kinetic energy of the trolley is set as the kinetic energy provided by the servo motor. The mathematical model of the motor is:

[0063]

[0064] τ = K T i a

[0065] Wherein, u, i a , R a , L a are the voltage, current, resistance and inductance of the armature respectively; K E is the back EMF coefficient, K T is the torque coefficient, ω is the angular velocity of the motor, and τ is the output torque of the motor.

[0066] The back EMF coefficient and the torque coefficient generally satisfy:

[0067] K E = K T

[0068] Wherein, K E is the back EMF coefficient, and K T is the torque coefficient.

[0069] The angular displacement of the drive wheel of the small trolley is:

[0070]

[0071] Wherein, θ, θ c , K g are the angular displacement of the motor rotor, the angular displacement of the drive wheel and the gear ratio of the drive wheel respectively.

[0072] If the radius of the drive wheel is r, and the displacement of the trolley is x, then the displacement of the trolley satisfies:

[0073]

[0074] The transverse displacement speed of the trolley satisfies:

[0075]

[0076] Wherein, ω, x, r, v c , θ, θ c , K gω, r, x, v, x, φ, i, i

[0077] Since the trolley is powered by the motor, the horizontal force is related to the motor. The horizontal force analysis can be obtained:

[0078]

[0079] wherein f, f F are the motor driving force and the horizontal force of the swing rod on the trolley, respectively; M is the mass of the trolley. The motor driving force and the motor output torque satisfy:

[0080]

[0081] wherein f, K g , r, τ are the motor driving force, the driving wheel gear ratio, the driving wheel radius and the motor output torque.

[0082] Taking the connection point of the trolley and the swing rod as the origin of coordinates, the motion direction of the swing rod is analyzed as horizontal, vertical and rotational directions. The displacement of the swing rod mass center along each direction is:

[0083]

[0084] wherein x H , x v , x φ are the displacements of the swing rod mass center along the horizontal, vertical and rotational directions, respectively; L is the distance from the trolley and the swing rod connection point to the swing rod mass center; φ is the swing rod displacement angle.

[0085] The corresponding motion equation is:

[0086]

[0087] wherein m is the mass of the swing rod; f H , f v are the horizontal and vertical reaction forces of the trolley and the swing rod connection point, respectively; J is the moment of inertia; c is the friction coefficient. The moment of inertia satisfies: Substituting the horizontal and vertical equations into the rotational equation, we can obtain:

[0088]

[0089] wherein J, m, L, φ, x, c, g are the moment of inertia, the mass of the swing rod, the distance from the trolley and the swing rod connection point to the swing rod mass center, the swing rod displacement angle, the trolley displacement, the friction coefficient and the acceleration of gravity, respectively.

[0090] Since f H = f vThe motion equation of the trolley is:

[0091]

[0092] Wherein, M, m, L, φ, x, g, f, f H , f v are the mass of the trolley, the mass of the pendulum, the distance between the mass center of the pendulum and the connecting point of the trolley and the pendulum, the displacement angle of the pendulum, the displacement of the trolley, the gravity acceleration, the driving force of the motor, the horizontal and vertical reaction force of the connecting point of the trolley and the pendulum.

[0093] Neglecting the inductance of the armature loop, there is:

[0094]

[0095]

[0096] Wherein, f, K T , K g , r, u, i a , R a , τ, ω are the driving force of the motor, the torque coefficient, the gear ratio of the driving wheel, the radius of the driving wheel, the voltage of the armature, the current, the resistance, the output torque of the motor and the angular velocity of the motor.

[0097] The dynamic differential equation set of the trolley single-stage inverted pendulum control system is:

[0098]

[0099] Wherein, J, m, L, φ, c, x, g, u, R a , K T , K g are the moment of inertia, the mass of the pendulum, the distance between the mass center of the pendulum and the connecting point of the trolley and the pendulum, the displacement angle of the pendulum, the friction coefficient, the displacement of the trolley, the gravity acceleration, the voltage of the armature, the resistance, the torque coefficient and the gear ratio of the driving wheel.

[0100] The system equilibrium point The system state equation is:

[0101]

[0102] Wherein, x is the state variable, is the derivative of the state variable, u is the input variable, y is the output variable, A, B, C, D are control matrices.

[0103] Let The state space equation is:

[0104]

[0105] M, r, J, m, L, φ, c, x, g, u, R a , K T , K g are the mass of the trolley, the radius of the drive wheel, the moment of inertia, the mass of the swing bar, the distance from the mass center of the swing bar to the connection point of the swing bar and the trolley, the displacement angle of the swing bar, the friction coefficient, the displacement of the trolley, the acceleration of gravity, the voltage of the armature, the resistance, the torque coefficient and the gear ratio of the drive wheel, respectively.

[0106] Linearize it, let [x1, x2, x3, x4] T = [f1, f2, f3, f4] T , the Jacobi matrix J is:

[0107]

[0108] wherein, is the partial derivative of the state variable x, indicating the sensitivity.

[0109] Wherein, the coefficient matrix P1 of u is:

[0110]

[0111] wherein, is the partial derivative of the input variable u, indicating the sensitivity.

[0112] The system state space expression is:

[0113]

[0114] wherein, is the partial derivative of the state variable x, is the partial derivative of the state variable x, indicating the sensitivity.

[0115] Substitute and simplify:

[0116]

[0117] wherein M, r, J, m, L, φ, c, x, g, u, R a , K T , K g are the mass of the trolley, the radius of the drive wheel, the moment of inertia, the mass of the swing bar, the distance from the mass center of the swing bar to the connection point of the swing bar and the trolley, the displacement angle of the swing bar, the friction coefficient, the displacement of the trolley, the acceleration of gravity, the voltage of the armature, the resistance, the torque coefficient and the gear ratio of the drive wheel, respectively.

[0118] Substitute the equilibrium point condition into it, then the coefficient matrix J, P1 is:

[0119]

[0120] wherein M, m, c, J, L, r, R a , K T , K g , K l are the mass of the trolley, the mass of the pendulum, the friction coefficient, the moment of inertia, the distance between the mass center of the pendulum and the connection point of the trolley and the pendulum, the radius of the driving wheel, the resistance of the armature, the torque coefficient and the gear ratio of the driving wheel, respectively.

[0121] In step 102, an H∞ controller is determined based on the first-order control system model.

[0122] Preferably, wherein the H∞ controller is determined based on the first-order control system model, comprising:

[0123] In the H∞ controller, ω, z, u, y are set as external input signal, controlled output, control signal, measured output, respectively, all of which are vector value signals, and the mathematical model is:

[0124]

[0125] The model of the H∞ controller satisfies the constraint condition: min||F l (G,K)| ∞ , i.e. the H ∞ norm of the transfer matrix F l (G,K) is minimum; or ||F ∞ (G,K)| l < ζ, 0 < ζ ∈ R, i.e. all the matrices K calculated can make G stable. ∞

[0126] wherein G is a system structure represented by a transfer function; G 11 , G 12 , G 21 , G 22 are the system transfer functions after being divided into blocks, and K is an optimal matrix of state feedback control.

[0127] In the present application, in the H∞ controller, ω, z, u, y are set as external input signal, controlled output, control signal, measured output, respectively, all of which are vector value signals.

[0128] According to the dimension of the input vector, the system transfer function is converted into:

[0129]

[0130] wherein G is a system structure represented by a transfer function; G 11 , G 12 , G 21 , G 22 are the system transfer functions after being divided into blocks.

[0131] The corresponding mathematical model is:

[0132]

[0133] If K is a reversible rational matrix, there exists:

[0134] z = (G 11 + G 12 K(I-G 22 K)-G 21 )

[0135] Where G 11 , G 12 , G 21 , G 22 are the system transfer functions after block; I is the unit matrix.

[0136] The transfer function matrix T zω from ω to y is:

[0137] T zω = F l (G, K) = (G 11 + G 12 K(I-G 22 K)-G 21 )

[0138] Where G 11 , G 12 , G 21 , G 22 are the system transfer functions after block; I is the unit matrix; K is a reversible rational matrix.

[0139] H ∞ The target makes the H l norm of the transfer matrix F ∞ (G, K) minimum, that is, it can be expressed as:

[0140] min||F l (G, K)| ∞

[0141] It can also be expressed as finding all matrices K that make G stable and satisfy:

[0142] ||F l (G, K)| ∞ < ζ, 0 < ζ ∈ R

[0143] For a four-degree-of-freedom first-order control system, the state space expression of the generalized linear time-invariant system is:

[0144]

[0145] where K is a non-singular rational matrix, A is a control matrix, B1, B2, C1, C2, D 11 , D 12 , D 21 , D 22 are the block matrices of the control matrix. ω, z, u, y are the external input signal, the controlled output, the control signal, the measured output, respectively, all of which are vector-valued signals.

[0146] Using the static feedback controller u = Kx, the closed-loop system is:

[0147]

[0148] where x is the state variable, is the derivative of the state variable, A is a control matrix, B1, B2, C1, C2, D 11 , D 12 , D 21 , D 22 are the block matrices of the control matrix. ω, z, u, y are the external input signal, the controlled output, the control signal, the measured output, respectively, all of which are vector-valued signals.

[0149] The above corresponding closed-loop system is stable, and its infinity norm satisfies:

[0150] ||T zω || ∞ = || (C1+D 12 K) [sI-(A+B2K)]-B1+D 11 || < 1

[0151] where T zω is the transfer function matrix from ω to y; I is the identity matrix; K is a non-singular rational matrix;

[0152] B1, B2, C1, D 11 , D 12 , are the block matrices of the control matrix.

[0153] Substituting the above, we have:

[0154]

[0155] where A is a control matrix, B1, B2, C1, D 11 , D 12 are the block matrices of the control matrix, W is the state feedback gain matrix, and I is the identity matrix.

[0156] For a given scalar ζ > 0, to find the state feedback matrix controller of the system, consider Therefore, through ζ -1 C1, ζ-1 D 11 and ζ -1 D 12 Instead of the matrix C1, D 11 and D 12 .

[0157] Therefore, the above expression can be converted to:

[0158]

[0159] Left and right multiplication of the matrix diag{I, I, ζI} respectively, can be converted to:

[0160]

[0161] Wherein, A is a control matrix, B1, B2, C1, D 11 , D 12 are the block matrix of the control matrix, W is the state feedback gain matrix, I is the unit matrix, and ξ is a given scalar.

[0162] The K matrix obtained is:

[0163] K = WX -1 .

[0164] The control equation of the PID controller of the application is as follows:

[0165]

[0166] Wherein, K P , K I , K D are the proportional, integral and derivative coefficients of the PID control respectively; e(t) is the error signal.

[0167] e(t) = y ref (t) - y(t)

[0168] Wherein, y ref (t) is the output signal reference value, and y ref (t) is generally 0.

[0169] In step 103, the output signal of the H∞ controller is input to the PID controller to establish an initial H∞-PID series control model.

[0170] In step 104, the parameters of the PID series control model are tuned to obtain a final H∞-PID series control model, and PID control is performed based on the final H∞-PID series control model.

[0171] Preferably, the output of the final H∞-PID series control model is:

[0172] OUT = U in · (U outH∞ -ref) · U outPID

[0173] wherein, U in is a variable input, U outH∞ is an output of the H∞ controller, ref is a feedback, and U outPID is an output of the PID controller.

[0174] The present application linearizes uncertain factors in engineering applications, adopts a PID series structure to eliminate dynamic deviation, and the rest still adopts an H∞ feedback control structure. The H∞ controller and the PID series control model are combined, and the expression is as follows:

[0175] An uncertain factor input ω is added to the system, and the system equilibrium point is The system state equation is:

[0176]

[0177] wherein, A is a control matrix, B1 and B2 are sub-matrices of the control matrix, x is a state variable, is a derivative of the state variable, u is a measurement output, and ω is an input uncertain factor.

[0178] Let After arrangement, the state space equation is:

[0179]

[0180] wherein, x is a state variable, is a derivative of the state variable; M, r, J, m, L, φ, c, g, u, R a , K T , K g are the mass of the trolley, the driving wheel radius, the moment of inertia, the pendulum mass, the distance between the pendulum mass center and the connecting point of the trolley and the pendulum, the pendulum displacement angle, the friction coefficient, the gravitational acceleration, the armature voltage, the resistance, the torque coefficient, and the driving wheel gear ratio, respectively.

[0181] Linearization is performed on it, and [x1, x2, x3, x4] T = [f1', f2', f3', f4'] T The Jacobi matrix J is:

[0182]

[0183] is a partial derivative of the state variable x, and represents the sensitivity.

[0184] wherein the coefficient matrix B1 of ω is:

[0185]

[0186] is the partial derivative of the external input signal ω, and represents the sensitivity.

[0187] wherein the coefficient matrix B2 of u is:

[0188]

[0189] is the partial derivative of the measurement output u, and represents the sensitivity.

[0190] The system state space expression is:

[0191]

[0192] is the partial derivative of the state variable x, is the partial derivative of the external input signal ω,

[0193] is the partial derivative of the measurement output u, and represents the sensitivity.

[0194] The state space equation is specifically:

[0195]

[0196] wherein x is the state variable, is the derivative of the state variable; M, r, J, m, L, c, g, R a , K T , K g are the mass of the trolley, the driving wheel radius, the moment of inertia, the pendulum mass, the distance from the mass center of the pendulum to the connecting point of the trolley and the pendulum, the displacement angle of the pendulum, the friction coefficient, the gravitational acceleration, the voltage of the armature, the resistance, the torque coefficient, and the driving wheel gear ratio, respectively.

[0197] Substituting the equilibrium point into the system state space coefficient matrix is:

[0198]

[0199] wherein M, r, J, m, L, c, g, R a , K T , K g are the mass of the trolley, the driving wheel radius, the moment of inertia, the pendulum mass, the distance from the mass center of the pendulum to the connecting point of the trolley and the pendulum, the friction coefficient, the gravitational acceleration, the resistance of the armature, the torque coefficient, and the driving wheel gear ratio, respectively.

[0200] The output OUT of the H∞ controller and PID series control model of the present invention is:

[0201] OUT=U in ·(U outH∞ -ref)·U outPID

[0202] Among them, U in is the variable input, U outH∞ is the output of the H∞ controller, ref is the feedback, U outPID is the output of the PID controller.

[0203] Figure 2 Figure 1 is a force analysis diagram of a single-stage inverted pendulum system on a trolley according to an embodiment of the present invention. Figure 2 As shown in the figure, the controlled object includes the car and the pendulum, and the execution part includes the servo motor and the transmission device. In the control modeling, the air friction is considered to be 0, and the system is considered to be composed of the car and the uniform lever. Figure 3 As shown in the figure, the control mode diagram of the trolley inverted pendulum system is shown, in which the thinking control elements of the LQR feedback control matrix correspond to the four-dimensional control variables of the trolley inverted pendulum first-order system. The parameter simulation curve of the trolley inverted pendulum first-order system under the PID-H∞ control mode is shown in the figure. Figure 4 As shown, the simulation parameters are shown in Table 1 below.

[0204] Table 1 Simulation parameters

[0205]

[0206]

[0207] Among them, three control methods are simulated and compared. Figure 4 It can be seen that under the three methods, the swing arm and the trolley eventually tend to a stable state.

[0208] Among them, H ∞ The C1 matrix in control is:

[0209]

[0210] Among them, the pole configuration is [-7,-5,-11,-10], PID-H ∞ The parameters of the series PID module are P=7, I=2, D=0.025, and the B1 matrix is ​​set to: B1=[0,0,0.2,0] T When t=6s, the pole placement method has Dissatisfied When t=7s, H ∞ Control, PID-H∞ In the control mode, the displacement of the trolley is -0.05925 m and -0.06127 m, respectively.

[0211] Figure 5 A structure diagram of a robust PID control method system 500 suitable for a city trolley inverted pendulum first-order control system according to an embodiment of the present application is shown. As shown in the figure, the PID control system suitable for the city trolley inverted pendulum first-order control system provided by the embodiment of the present application comprises a first-order control system model establishing unit 501, an H∞ controller determining unit 502, a series control model establishing unit 503, and a parameter setting unit 504. Figure 5

[0212] Preferably, the first-order control system model establishing unit 501 is configured to establish a first-order control system model for the freedom control of the trolley inverted pendulum.

[0213] Preferably, the first-order control system model comprises:

[0214]

[0215] wherein x is a state variable, is a derivative of the state variable, u is an input variable, y is an output variable, A and B are state space parameter control matrices, C and D are output matrices; wherein the control parameter elements in the A and B matrices are derived from the first-order control system and are expressed as the partial derivative matrix of the state variable after linearization processing;

[0216] Let [x1, x2, x3, x4] T = [f1, f2, f3, f4] T , then

[0217] D =

[00] T .

[0218] Preferably, the H∞ controller determining unit 502 is configured to determine an H∞ controller based on the first-order control system model.

[0219] Preferably, the H∞ controller determining unit 502 determines the H∞ controller based on the first-order control system model, and comprises:

[0220] In the H∞ controller, ω, z, u, and y are respectively set as external input signals, controlled outputs, control signals, and measured outputs, all of which are vector value signals, and the mathematical model is:

[0221]

[0222] The model of the H∞ controller satisfies the constraint condition: min||F l ​(G,K)| ∞ i.e.H ∞ targeting transfer matrix F l H of (G,K) ∞ norm minimum; or ||F l (G,K)| ∞ <ζ,0<ζ∈R, i.e. all matrices K calculated can make G stable;

[0223] wherein G is a system structure represented by a transfer function; G 11 , G 12 , G 21 , G 22 is a system transfer function after block, and K is an optimal matrix of state feedback control.

[0224] Preferably, the series control model establishing unit 503 is configured to input an output signal of the H∞ controller into a PID controller to establish an initial H∞-PID series control model.

[0225] Preferably, the parameter setting unit 504 is configured to perform parameter setting on the PID series control model to obtain a final H∞-PID series control model, and perform PID control based on the final H∞-PID series control model.

[0226] Preferably, in the parameter setting unit 504, an output of the final H∞-PID series control model is:

[0227] OUT=U in ·(U outH∞ -ref)·U outPID

[0228] wherein U in is a variable input, U outH∞ is an output of the H∞ controller, ref is a feedback, and U outPID is an output of the PID controller.

[0229] The robust PID control method system 500 of the embodiment of the present application corresponding to the robust PID control method 100 of another embodiment of the present application suitable for a city trolley inverted pendulum first-order control system, which will not be described here.

[0230] According to another aspect of the present application, a computer readable storage medium is provided, which stores a computer program, and the program is executed by a processor to implement the steps of any one of the robust PID control method.

[0231] According to another aspect of the present invention, the present invention provides an electronic device, including:

[0232] The computer-readable storage medium described above; and

[0233] One or more processors are configured to execute the program in the computer-readable storage medium.

[0234] The present invention has been described with reference to a few embodiments. However, it is apparent to those skilled in the art that other embodiments than the ones disclosed above are equally within the scope of the present invention.

[0235] Generally, all terms used in this disclosure are to be interpreted according to their ordinary meaning in the art, unless explicitly defined otherwise herein. All references to "a / the / the [device, component, etc.]" are to be interpreted openly as referring to at least one instance of the device, component, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not necessarily need to be performed in the exact order disclosed, unless explicitly stated otherwise.

[0236] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0237] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0238] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxesFigure 1 the function specified in the one or more blocks.

[0239] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operation steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, thus the instructions executed on the computer or other programmable data processing devices provide processes for implementing the flows Figure 1 the flows or the plurality of flows and / or blocks Figure 1 the steps of the function specified in the one or more blocks.

[0240] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit it, although the present application has been described in detail with reference to the above examples, those skilled in the art should understand: the specific embodiments of the present application can still be modified or replaced by the equivalent, without departing from the spirit and scope of the present application, any modification or equivalent replacement, which should be covered within the protection scope of the present application.

Claims

1. A robust PID control method for the first-order control system of an inverted pendulum in an urban trolley, characterized in that: The method comprises: Establish a first-order control system model for the degree of freedom control of the trolley inverted pendulum; determining an H∞ controller based on the first-order control system model; The output signal of the H∞ controller is input to the PID controller to establish the initial H∞-PID cascade control model; Parameters of the PID series control model are tuned to obtain a final H∞-PID series control model, so as to perform PID control based on the final H∞-PID series control model.

2. The method according to claim 1, characterized in that The first-order control system model comprises: Among them, x is the state variable, is the derivative of the state variable, u is the input variable, y is the output variable, A and B are the state space parameter control matrices, and C and D are the output matrices. The control parameter elements in the A and B matrices are derived from the first-order control system and are expressed as partial derivative matrices of the state variables after linearization. Let [x1, x2, x3, x4] T =[f1, f2, f3, f4] T ,but 3. The method according to claim 1, characterized in that Determining an H∞ controller based on the first-order control system model includes: In the H∞ controller, ω, z, u, and y are set as the external input signal, controlled output, control signal, and measurement output, respectively. They are all vector-valued signals, so the mathematical model is: The H∞ controller model satisfies the constraints: min||F l (G,K)|| ∞ , that is, H ∞ The goal is to make the transfer matrix F l H of (G,K) ∞ The norm is extremely small; or ||F l (G,K)|| ∞ <ζ,0<ζ∈R, that is, all calculated matrices K can make G stable; Where G is the system structure represented by the transfer function; G 11 , G 12 , G 21 , G 22 is the system transfer function after block division, and K is the optimal matrix of state feedback control.

4. The method according to claim 1, wherein The output of the final H∞-PID cascade control model is: OUT=U in ·(U outH∞ -ref)·U outPID Among them, U in is the variable input, U outH∞ is the output of the H∞ controller, ref is the feedback, U outPID is the output of the PID controller.

5. A robust PID control system suitable for the first-order control system of an inverted pendulum in an urban trolley, characterized in that: The system comprises: A first-order control system model building unit is used to build a first-order control system model for the trolley inverted pendulum degree of freedom control; An H∞ controller determination unit, configured to determine an H∞ controller based on the first-order control system model; A series control model building unit is used to input the output signal of the H∞ controller into the PID controller to build an initial H∞-PID series control model; A parameter tuning unit is used to tune the parameters of the PID series control model to obtain a final H∞-PID series control model, so as to perform PID control based on the final H∞-PID series control model.

6. The system according to claim 5, characterized in that The first-order control system model comprises: Among them, x is the state variable, is the derivative of the state variable, u is the input variable, y is the output variable, A and B are the state space parameter control matrices, and C and D are the output matrices. The control parameter elements in the A and B matrices are derived from the first-order control system and are expressed as partial derivative matrices of the state variables after linearization. Let [x1, x2, x3, x4] T =[f1, f2, f3, f4] T ,but 7. The system according to claim 5, characterized in that The H∞ controller determination unit determines the H∞ controller based on the first-order control system model, including: In the H∞ controller, ω, z, u, and y are set as the external input signal, controlled output, control signal, and measurement output, respectively. They are all vector-valued signals, so the mathematical model is: The H∞ controller model satisfies the constraints: min||F l (G,K)|| ∞ , that is, H ∞ The goal is to make the transfer matrix F l H of (G,K) ∞ The norm is extremely small; or ||F l (G,K)|| ∞ <ζ,0<ζ∈R, that is, all calculated matrices K can make G stable; Where G is the system structure represented by the transfer function; G 11 , G 12 , G 21 , G 22 is the system transfer function after block division, and K is the optimal matrix of state feedback control.

8. The system according to claim 5, wherein: The output of the parameter tuning unit and the final H∞-PID series control model is: OUT=U in ·(U outH∞ -ref)·U outPID Among them, U in is the variable input, U outH∞ is the output of the H∞ controller, ref is the feedback, U outPID is the output of the PID controller.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

10. An electronic device, characterized in that: include: The computer-readable storage medium of claim 9; as well as One or more processors are configured to execute the program in the computer-readable storage medium.

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