Hydraulic mechanical transmission device control method based on optimal trajectory optimization

Abstract

The invention discloses a hydraulic mechanical transmission device control method based on optimal trajectory optimization, and relates to the technical field of equipment intelligent auxiliary operation and control, and the method comprises the following steps: S1, building a physical model of a hydraulic mechanical transmission device; s2, taking the shortest motion time, the most smooth trajectory and the minimum energy consumption as optimization objectives, and obtaining an optimal trajectory based on a trajectory planning algorithm combining an improved sparrow algorithm and a quintic non-uniform B-spline curve; s3, oil return control is optimized; and S4, oil inlet control is optimized, specifically, an oil inlet flow controller is optimized based on a time-varying secant obstacle Lyapunov function and an RBF neural network. According to the trajectory planning algorithm, the trajectory of the hydraulic transmission device can be optimized, oil return and oil inlet are optimized based on the optimal trajectory, and working trajectory planning and high-precision control over the hydraulic equipment executing mechanism are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent auxiliary operation and control of equipment, and specifically relates to a hydraulic mechanical transmission device control method based on optimal trajectory optimization. Background Art

[0002] With the update and iteration of complex equipment, it is gradually developing in the direction of green, intelligent and unmanned, so that the equipment has the necessary self-perception, self-planning and self-execution systemized intelligent operation capabilities, thereby reducing the dependence on driver experience, which puts higher requirements on the motion planning and control of the equipment. Therefore, it is of great significance to improve the autonomous execution capability of the equipment and perform high-precision trajectory tracking control based on the generated optimal equipment operation trajectory for the development of intelligent equipment.

[0003] That is, while achieving the optimal trajectory planning, it is also necessary to overcome the problems of low control accuracy, poor stability, and long stable tracking time caused by factors such as high nonlinearity and unknown external disturbances in the control system, so as to achieve high-precision progressive tracking of the trajectory after posture solution by each actuator.

[0004] Optimal trajectory planning is the premise and foundation of intelligent assisted operation of equipment. Generally speaking, optimal trajectory planning of equipment refers to constructing a trajectory that can optimize single or multiple performance indicators and meet relevant constraints. Current research mainly considers the impact of movement time and energy consumption on trajectory planning optimization, and few studies consider the impact of joint pulsation on trajectory smoothness, resulting in poor performance, obvious vibration and low service life of equipment during operation. Therefore, when planning the optimal trajectory, it is necessary to consider the optimization of the comprehensive performance of time, energy and joint pulsation.

[0005] In order to enable the equipment actuator to accurately execute the planned optimal trajectory, the corresponding actuator hydraulic cylinder must be controlled with high precision. At present, the research mainly focuses on the nonlinear compensation of the system and the improvement of steady-state tracking performance, and many advanced trajectory tracking control methods such as PID control, fuzzy variable structure control, adaptive robust control and intelligent control have been proposed. These studies have overcome the problems of low equipment control accuracy, poor stability, and long time to reach stable tracking caused by factors such as high nonlinearity and unknown external disturbances in the equipment control system to a certain extent, but rarely involve the transient performance of the control system and the energy efficiency of the system. How to select a high-precision asymptotic tracking control strategy with low parameter dependence, simple structure, and suitable for equipment of such complex heavy hydraulic manipulators, which takes into account energy-saving characteristics while ensuring high precision and effectively improves the energy efficiency of the system, is a problem worthy of in-depth study. Summary of the invention

[0006] In order to solve the deficiencies of the above-mentioned prior art, the present invention proposes a control method for a hydraulic mechanical transmission device based on optimal trajectory optimization. Aiming at the working trajectory planning and high-precision control of the hydraulic equipment actuator, an algorithm combining the improved sparrow algorithm and the quintic non-uniform B-spline curve is established for trajectory planning to obtain an optimal motion trajectory. At the same time, in order to ensure that the equipment actuator can accurately execute the generated optimal trajectory, an oil inlet flow controller based on the time-varying secant barrier Lyapunov function and the RBF neural network and an oil return pressure controller based on direct parameter adaptive robust control are established in combination with the load port independent hydraulic system to achieve high-precision and high-efficiency trajectory tracking control.

[0007] Specifically, the present invention proposes a control method for a hydraulic mechanical transmission device based on optimal trajectory optimization, which comprises the following steps:

[0008] S1. Establish a physical model of the hydraulic mechanical transmission device taking into account unmodeled errors and external disturbances;

[0009] S2. Taking the shortest motion time, the smoothest trajectory and the lowest energy consumption as the optimization goals, and taking the actual kinematic and dynamic constraints of the equipment as constraints, the trajectory planning algorithm based on the improved sparrow algorithm combined with the quintic non-uniform B-spline curve is used to obtain the optimal trajectory; specifically, it includes the following sub-steps:

[0010] S21, using a quintic non-uniform B-spline algorithm to perform trajectory planning to obtain a target trajectory;

[0011] S22, using the improved sparrow algorithm to optimize the target trajectory based on the optimization function, specifically including the following sub-steps:

[0012] S221. In order to improve the randomness and ergodicity of individual sparrows, the population is initialized by firstly using the cat mapping chaotic sequence and combining it with the reverse solution. The cat mapping expression is:

[0013]

[0014] Where a and b are arbitrary real numbers; mod is the decimal part of a; X s+1 and W s+1 is a sequence;

[0015] Randomly generate a feasible solution for the current population, recorded as:

[0016]

[0017] Among them, X', X s ' d is a feasible solution, q is a uniformly distributed real number on the interval [0,1]; X min and X maxis the boundary of feasible solutions, d and D both represent the number of feasible solutions;

[0018] S222. To avoid the population being too concentrated or dispersed, Tent chaotic perturbation and Cauchy mutation are introduced to adjust the individuals, and random variables are introduced into the original Tent mapping expression. The Tent mapping expression is:

[0019]

[0020] Among them, z is the Tent map, N T is the number of particles in the chaotic sequence; rand(0,1) is a random number between [0,1]; i is the number of populations;

[0021] S223, construct an optimization objective function with the shortest motion time, the smoothest trajectory and the lowest energy consumption as the optimization goals:

[0022]

[0023] Among them, h i is the time for the mechanical transmission device to move along each section; n is the number of interpolation points; T is the total time for the mechanical transmission device to move; a is the joint acceleration; j is the joint pulsation; T is the movement time, F1 is the movement efficiency of the mechanical transmission device; F2 is the average acceleration of the joint, representing the energy consumption of the mechanical transmission device; F3 is the joint pulsation, representing the smoothness of the trajectory; M is the number of key points of the trajectory;

[0024] The constraints for optimizing the objective function are:

[0025]

[0026] in, a i 、j i are the angular velocity, angular acceleration and angular jerk of the joint respectively; V imax , A imax , R imax are the maximum angular velocity, maximum angular acceleration and maximum angular jerk allowed by the joint respectively;

[0027] S224, using the improved sparrow algorithm of step S221 and step S222, optimizing the target trajectory based on the optimization function of step S223 to obtain the optimal trajectory;

[0028] S3. Optimize the oil return control: Use the load port independent hydraulic system to control the pressure flow of the high pressure chamber and the back pressure chamber of the control actuator respectively, and optimize the oil return pressure controller based on direct parameter adaptive robustness;

[0029] S4. Optimize the oil inlet control: Establish a Lyapunov function based on time-varying secant barrier and RBF neural network to jointly optimize the oil inlet flow controller.

[0030] Preferably, step S1 specifically includes the following sub-steps:

[0031] S11. The dynamic equation of the hydraulic mechanical transmission device is described as:

[0032]

[0033] Among them, q i , i=1,2,3, respectively joint angle, velocity and acceleration vector; M i represents the inertia matrix of the robot; C i G represents the Coriolis force / centrifugal force matrix of the robot arm; i is the gravity vector matrix of the manipulator; B i is the node viscous friction coefficient matrix; J iha (q i )(P i1 A i1 -P i2 A i2 ) represents the torque vector acting on the joint, where x iha is the displacement of the cylinder; d i1 Total disturbance vector; ΔG i Unmodeled parts for joint coupling dynamics;

[0034] S12. The pressure of the rod chamber and the rodless chamber of the hydraulic cylinder is:

[0035]

[0036] Among them, β e is the bulk elastic modulus of the oil, V i1 =V i01 +A i1 x iha , V i2 =V i02 -A i2 x iha V is the volume of the rodless and rod-bearing chambers of the cylinder; i01 and V i02 A is the initial volume of the rodless and rod-bearing chambers of the cylinder, i1 and A i2 Q is the piston area of ​​the rodless and rod-end chambers of the oil cylinder; i1 and Q i2 is the oil inlet flow rate and the oil return flow rate; D i1 and D i2is the unmodeled error; Δ i1 and Δ i2 is an external unknown disturbance;

[0037] S13. Define x1 = q i , x3=P i1 A i1 -P i2 A i2 , establish the state space equation of the hydraulic mechanical transmission device:

[0038]

[0039] Among them are:

[0040]

[0041]

[0042] Preferably, step S3 is specifically as follows: first set the back pressure chamber pressure, control the output of the return oil flow through the rod chamber return oil pressure controller, so that the pressure of the rod chamber is constant during operation, and based on the given back pressure chamber pressure, calculate the flow required for accurately tracking the optimal trajectory through the rodless chamber oil inlet flow controller, thereby optimizing the return oil pressure controller.

[0043] Preferably, step S4 specifically includes the following sub-steps:

[0044] S41. Construct an RBF neural network. The RBF neural network consists of an input layer, a hidden layer and an output layer. The transformation from the input layer to the hidden layer is nonlinear, and the transformation from the hidden layer to the output layer is linear. The neuron excitation function of the hidden layer is a radial basis function. The expression of the RBF neural network function F(X) is:

[0045] F(X)=W *T φ(X)+ε

[0046] in, is the weight vector, c and v are the number of outputs and the number of neurons in the hidden layer respectively; is the input of the neural network, z is the number of inputs; ε is the approximation error of the neural network. is a positive constant; φ(X)=[φ1(X),φ2(X),…,φ l (X)], is the activation function, and its specific expression is:

[0047]

[0048] Among them, μ i and σ iare the center and width of the Gaussian function of the i-th neuron, X1 is the first layer input of the neural network, and l is the total number of neurons;

[0049] S42. Establish Lyapunov function based on time-varying secant barrier;

[0050] S43, updating the RBF neural network using a Lyapunov function based on a time-varying secant barrier;

[0051] S44. Optimize the oil inlet flow controller.

[0052] Preferably, step S42 specifically includes the following sub-steps:

[0053] S421. Design the Lyapunov function V of the secant barrier as:

[0054]

[0055] Where F(t) is the time-varying boundary where the function value is greater than zero; e is the system tracking error variable;

[0056] When the error variable crosses the time-varying boundary, the value of the time-varying secant barrier Lyapunov function will approach infinity. The controller is set to be bounded to ensure that the system error is always constrained within the time-varying boundary.

[0057]

[0058] Among them, F i0 , F i∞ , n i are all constants greater than zero and satisfy 0 <F i∞ <F i0 ,||e1(0)|| <F i0 , e1(0) is the initial value of e1;

[0059] S422. Suppose that a continuous function V(t) is positive definite and satisfies the following differential equation:

[0060]

[0061] Among them, β, ξ are constants, β>0, 0<ξ<1, at this time V(t) satisfies uniform final bounded convergence;

[0062] Assume that there exists a Lyapunov function V(x), constants α>0, β>0, 0<η0<∞, 0<γ1<1 and γ2>1, if the following holds:

[0063]

[0064] Then V(x) can converge to a neighborhood near the equilibrium point within a fixed time, and the neighborhood is expressed as:

[0065]

[0066] Where θ is a constant and satisfies the inequality 0<θ<1;

[0067] Among them, the time T required for the system variables to converge to the neighborhood satisfies the inequality:

[0068]

[0069] S423. Define the first Lyapunov function V1 and derive it to obtain:

[0070]

[0071] Among them, e2=x2-α1, α1 is the virtual control quantity, is the derivative of the planned trajectory;

[0072] The designed virtual control law is:

[0073]

[0074] Among them, γ1, γ2, k 11 , k 12 is a constant greater than zero and satisfies 0<γ1<1,γ2>1;

[0075] As long as e2 is bounded, V1 is uniformly ultimately bounded, that is, the first subsystem is stable;

[0076] S424. Define the second Lyapunov function and take its derivative.

[0077] Preferably, step S43 specifically includes the following sub-steps:

[0078] S431, according to step S424, the neural network weight update rate is obtained, and the error variable is further defined and derived;

[0079] S432. Define the third Lyapunov function and take its derivative.

[0080] Preferably, step S44 specifically includes the following sub-steps:

[0081] S441, optimize the oil inlet flow controller:

[0082]

[0083] make Substitutions are:

[0084]

[0085] S442, the update rate of the neural network weights is:

[0086]

[0087] Scaling gives:

[0088]

[0089] Where ρ = min{k 12 ,k 22 ,k 32 ,σ w1 ,σ w2 ,σ ε1 ,σ ε2}, The integrals on both sides are:

[0090]

[0091] When t tends to infinity, we have:

[0092] From the boundedness of V3, it can be inferred that the tracking error of the system is always constrained within the time-varying boundary (-F i (t),F i (t))

[0093] Since V3 is bounded, the error signal e i , and are bounded, that is, there is a constant greater than zero and satisfy and Therefore the following inequality holds:

[0094]

[0095] Substitutions are:

[0096]

[0097] Since 0≤sec(·) i -1<sec(·) i ,get Further zooming in:

[0098]

[0099] in,

[0100]

[0101] Among them, α, β and η0 are expressed as:

[0102]

[0103] Preferably, the oil return pressure controller is optimized in step S3 as follows:

[0104] To determine the only reference pressure for both chambers under a given load force, the back pressure side will be set to a low constant pressure P i2d Keep overall stress levels low;

[0105] The purpose of the return oil pressure controller is to calculate the output flow Q of the rod chamber i2M Make the pressure P i2 Track P with a certain accuracy i2d , define the parameter vector θ p2 =[θ β ,θ Q ]=[β e ,β e D i2 ], define the pressure tracking error and take its derivative:

[0106] z p =P i2 -P i2d

[0107]

[0108] Q i2M As the control input, according to the DCARC theory, the return oil pressure control law is obtained as follows:

[0109]

[0110] Among them, the control law includes the adaptive model compensation term Q i2Ma and the robust feedback term Q i2Ms Two parts, θ βmin Denotes the parameter θ β The lower bound of θ β >0, the selection conditions of feedback gain k1 will be given later, and the selection of k2 needs to ensure the nonlinear robust feedback term Q i2Ms2 The following conditions are met:

[0111]

[0112] Among them, ε p For any small design parameter, the regression vector

[0113] For the parameter vector θ p2 The estimated value is updated online by the following adaptive law:

[0114]

[0115] Among them, Γ p >0 is the adaptive rate diagonal matrix, the adaptive function τ p =ω p φ p z p .

[0116] Compared with the prior art, the present invention has the following beneficial effects:

[0117] (1) On the one hand, in order to solve the problems of long planning time, high energy consumption, and unstable motion in the current intelligent assisted operation of equipment, the present invention designs a trajectory planning algorithm based on the combination of quintic non-uniform B-spline curve and sparrow algorithm, optimizes the trajectory of the hydraulic transmission device, obtains the optimal motion trajectory, and realizes the working trajectory planning and high-precision control of the hydraulic equipment actuator.

[0118] (2) At the same time, based on the optimized trajectory, the method of the present invention designs an oil inlet flow controller based on the time-varying secant barrier Lyapunov function (TSBLF) to solve the problems of nonlinear dynamics and modeling uncertainty in the hydraulic and mechanical systems when the hydraulic equipment tracks the planned trajectory, so as to ensure that the system error converges to a predefined boundary within a finite time.

[0119] (3) The method of the present invention uses RBF neural network to approximate the derivative of unknown nonlinear function and system virtual control quantity, and designs the return oil pressure controller considering the system energy efficiency to ensure that the return oil back pressure is at a low level. The designed controller can ensure the transient tracking performance of the system while ensuring the asymptotic stability of the system, and can also achieve the purpose of energy saving of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0121] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0122] Figure 2 It is a schematic diagram of the specific method flow of the present invention;

[0123] Figure 3a It is a schematic diagram of the structure of a hydraulic mechanical transmission device in an embodiment of the present invention. Figure 3b It is a schematic diagram of the principle of hydraulic mechanical transmission device;

[0124] Figure 4 It is a flow chart of trajectory planning in an embodiment of the present invention;

[0125] Figure 5 It is a flow chart of improving the sparrow algorithm in the embodiment of the present invention;

[0126] Figure 6 Schematic diagram of a load port independent system controller in an embodiment of the present invention;

[0127] Figure 7 This is a diagram showing the tracking effect of the controller on the boom arm and the bucket in an embodiment of the present invention;

[0128] Figure 8 4 is a comparison chart of tracking errors of three different controllers in an embodiment of the present invention. DETAILED DESCRIPTION

[0129] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings. It should be understood that the specific examples described here are only used to explain the present invention and are not used to limit the present invention.

[0130] The present invention proposes a control method for a hydraulic mechanical transmission device based on optimal trajectory optimization, such as Figure 1 and Figure 2 As shown, it includes the following steps:

[0131] S1. Establishing a physical model of the hydraulic mechanical transmission device in consideration of unmodeled errors and external disturbances; Step S1 specifically includes the following sub-steps:

[0132] S11. The dynamic equation of the hydraulic mechanical transmission device is described as:

[0133]

[0134] Among them, q i , i=1,2,3, respectively joint angle, velocity and acceleration vector; M i represents the inertia matrix of the robot; C i G represents the Coriolis force / centrifugal force matrix of the robot arm; i is the gravity vector matrix of the manipulator; B i is the node viscous friction coefficient matrix; J iha (q i )(P i1 A i1 -P i2 A i2 ) represents the torque vector acting on the joint, where x iha is the displacement of the cylinder; d i1 Total disturbance vector; ΔG iUnmodeled part of the joint coupling dynamics.

[0135] S12. The pressure of the rod chamber and the rodless chamber of the hydraulic cylinder is:

[0136]

[0137] Among them, β e is the bulk elastic modulus of the oil, V i1 =V i01 +A i1 x iha , V i2 =V i02 -A i2 x iha V is the volume of the rodless and rod-bearing chambers of the cylinder; i01 and V i02 A is the initial volume of the rodless and rod-bearing chambers of the cylinder, i1 and A i2 Q is the piston area of ​​the rodless and rod-end chambers of the oil cylinder; i1 and Q i2 is the oil inlet flow rate and the oil return flow rate; D i1 and D i2 is the unmodeled error; Δ i1 and Δ i2 is an external unknown disturbance.

[0138] S13. Define x1 = q i , x3=P i1 A i1 -P i2 A i2 , establish the state space equation of the hydraulic mechanical transmission device:

[0139]

[0140] Among them are:

[0141]

[0142] S2. Taking the shortest motion time, the smoothest trajectory and the lowest energy consumption as the optimization goals, and taking the actual kinematic and dynamic constraints of the equipment as constraints, the trajectory planning algorithm based on the improved sparrow algorithm combined with the quintic non-uniform B-spline curve is used to obtain the optimal trajectory; specifically, it includes the following sub-steps:

[0143] S21. Use the quintic non-uniform B-spline algorithm to perform trajectory planning to obtain the target trajectory.

[0144] S22, using the improved sparrow algorithm to optimize the target trajectory based on the optimization function, specifically including the following sub-steps:

[0145] S221. In order to improve the randomness and ergodicity of individual sparrows, the population is initialized by firstly using the cat mapping chaotic sequence and combining it with the reverse solution. The cat mapping expression is:

[0146]

[0147] Where a and b are arbitrary real numbers; mod is the decimal part of a; X s+1 and W s+1 For sequence.

[0148] Randomly generate a feasible solution for the current population, recorded as:

[0149]

[0150] Among them, X', X' sd is a feasible solution, q is a uniformly distributed real number on the interval [0,1]; X min and X max is the boundary of feasible solutions, and d and D represent the number of feasible solutions.

[0151] S222. To avoid the population being too concentrated or dispersed, Tent chaotic perturbation and Cauchy mutation are introduced to adjust the individuals, and random variables are introduced into the original Tent mapping expression. The Tent mapping expression is:

[0152]

[0153] Among them, z is the Tent map, N T is the number of particles in the chaotic sequence; rand(0,1) is a random number between [0,1]; i is the number of populations.

[0154] S223, construct an optimization objective function with the shortest motion time, the smoothest trajectory and the lowest energy consumption as the optimization goals:

[0155]

[0156] Among them, h i is the time for the mechanical transmission device to move along each section; n is the number of interpolation points; T is the total time for the mechanical transmission device to move; a is the joint acceleration; j is the joint pulsation; T is the movement time, F1 is the movement efficiency of the mechanical transmission device; F2 is the average acceleration of the joint, representing the energy consumption of the mechanical transmission device; F3 is the joint pulsation, representing the smoothness of the trajectory; M is the number of key points in the trajectory.

[0157] The constraints for optimizing the objective function are:

[0158]

[0159] in, a i 、j i are the angular velocity, angular acceleration and angular jerk of the joint respectively; V imax , A imax , R imax They are the maximum angular velocity, maximum angular acceleration and maximum angular jerk allowed by the joint respectively.

[0160] S224, using the improved sparrow algorithm of step S221 and step S222, based on the optimization function of step S223, the target trajectory is optimized to obtain the optimal trajectory.

[0161] S3. Optimize the return oil control: use a load-port independent hydraulic system to control the pressure flow of the high-pressure chamber and the back-pressure chamber of the control actuator respectively, and optimize the return oil pressure controller based on direct parameter adaptive robustness; step S3 is specifically as follows: first set the back-pressure chamber pressure, and control the output of the return oil flow through the rod chamber return oil pressure controller to make the pressure of the rod chamber constant during operation, and on the basis of the given back-pressure chamber pressure, calculate the flow required for accurately tracking the optimal trajectory through the rodless chamber oil inlet flow controller, thereby optimizing the return oil pressure controller.

[0162] S4, optimize the oil inlet control: establish a Lyapunov function based on time-varying secant barrier and RBF neural network to jointly optimize the oil inlet flow controller. Step S4 specifically includes the following sub-steps:

[0163] S41. Construct an RBF neural network. The RBF neural network consists of an input layer, a hidden layer and an output layer. The transformation from the input layer to the hidden layer is nonlinear, and the transformation from the hidden layer to the output layer is linear. The neuron excitation function of the hidden layer is a radial basis function. The expression of the RBF neural network function F(X) is:

[0164] F(X)=W *T φ(X)+ε

[0165] in, is the weight vector, c and v are the number of outputs and the number of neurons in the hidden layer respectively; is the input of the neural network, z is the number of inputs; ε is the approximation error of the neural network. is a positive constant; φ(X)=[φ1(X),φ2(X),…,φ l (X)], is the activation function, and its specific expression is:

[0166]

[0167] Among them, μ i and σ iare the center and width of the Gaussian function of the i-th neuron, X1 is the first layer input of the neural network, and l is the total number of neurons.

[0168] S42, establishing a Lyapunov function based on a time-varying secant barrier; specifically comprising the following sub-steps:

[0169] S421. Design the Lyapunov function V of the secant barrier as:

[0170]

[0171] Where F(t) is the time-varying boundary where the function value is greater than zero; e is the system tracking error variable.

[0172] When the error variable crosses the time-varying boundary, the value of the time-varying secant barrier Lyapunov function will approach infinity. Setting the controller to be bounded ensures that the system error is always constrained within the time-varying boundary.

[0173]

[0174] Among them, F i0 , F i∞ , n i are all constants greater than zero and satisfy 0 <F i∞ <F i0 ,||e1(0)|| <F i0 , e1(0) is the initial value of e1.

[0175] S422. Suppose that a continuous function V(t) is positive definite and satisfies the following differential equation:

[0176]

[0177] Among them, β, ξ are constants, β>0, 0<ξ<1, at this time V(t) satisfies uniform final bounded convergence.

[0178] Assume that there exists a Lyapunov function V(x), constants α>0, β>0, 0<η0<∞, 0<γ1<1 and γ2>1, if the following holds:

[0179]

[0180] Then V(x) can converge to a neighborhood near the equilibrium point within a fixed time, and the neighborhood is expressed as:

[0181]

[0182] Where θ is a constant and satisfies the inequality 0<θ<1;

[0183] Among them, the time T required for the system variables to converge to the neighborhood satisfies the inequality:

[0184]

[0185] S423. Define the first Lyapunov function V1 and derive it to obtain:

[0186]

[0187] Among them, e2=x2-α1, α1 is the virtual control quantity, is the derivative of the planned trajectory.

[0188] The designed virtual control law is:

[0189]

[0190] Among them, γ1, γ2, k 11 , k 12 is a constant greater than zero and satisfies 0<γ1<1,γ2>1.

[0191] As long as e2 is bounded, V1 is uniformly eventually bounded, that is, the first subsystem is stable.

[0192] S424. Define the second Lyapunov function and take its derivative.

[0193] S43, using the time-varying secant barrier Lyapunov function to update the RBF neural network; specifically including the following sub-steps:

[0194] S431. Obtain the neural network weight update rate according to step S424, further define the error variable and derive it.

[0195] S432. Define the third Lyapunov function and take its derivative.

[0196] S44, optimizing the oil inlet flow controller. Specifically including the following sub-steps:

[0197] S441, optimize the oil inlet flow controller:

[0198]

[0199] make Substitutions are:

[0200]

[0201] S442, the update rate of the neural network weights is:

[0202]

[0203] Scaling gives:

[0204]

[0205] Where ρ = min{k 12 ,k 22 ,k 32 ,σ w1 ,σ w2 ,σ ε1 ,σ ε2}, The integrals on both sides are:

[0206]

[0207] When t tends to infinity, we have:

[0208] From the boundedness of V3, it can be inferred that the tracking error of the system is always constrained within the time-varying boundary (-F i (t),F i (t))

[0209] Since V3 is bounded, the error signal e i , and are bounded, that is, there is a constant greater than zero and satisfy and Therefore the following inequality holds:

[0210]

[0211] Substitutions are:

[0212]

[0213] Since 0≤sec(·) i -1<sec(·) i ,get Further zooming in:

[0214]

[0215] in,

[0216]

[0217] Among them, α, β and η0 are expressed as:

[0218]

[0219]

[0220] The optimized oil return pressure controller in step S3 is:

[0221] To determine the only reference pressure for both chambers under a given load force, the back pressure side will be set to a low constant pressure P i2d Keep overall stress levels low.

[0222] The purpose of the return oil pressure controller is to calculate the output flow Q of the rod chamber i2M Make the pressure P i2 Track P with a certain accuracy i2d , define the parameter vector θ p2 =[θ β ,θ Q ]=[β e ,β e D i2 ], define the pressure tracking error and take its derivative:

[0223] z p =P i2 -P i2d

[0224]

[0225] Q i2M As the control input, according to the DCARC theory, the return oil pressure control law is obtained as follows:

[0226]

[0227] Among them, the control law includes the adaptive model compensation term Q i2Ma and the robust feedback term Q i2Ms Two parts, θ βmin Denotes the parameter θ β The lower bound of θ β >0, the selection conditions of feedback gain k1 will be given later, and the selection of k2 needs to ensure the nonlinear robust feedback term Q i2Ms2 The following conditions are met:

[0228]

[0229] Among them, ε p For any small design parameter, the regression vector

[0230] For the parameter vector θ p2 The estimated value is updated online by the following adaptive law:

[0231]

[0232] Among them, Γ p>0 is the adaptive rate diagonal matrix, the adaptive function τ p =ω p φ p z p . Specific embodiments

[0234] The equipment structure of this embodiment is as follows Figure 3a and Figure 3b The overall workflow is as shown in Figure 4 As shown, L1 is the length of the boom; l1 is the length of the boom cylinder; L2 is the length of the dipper arm; l2 is the length of the dipper arm cylinder; L3 is the length of the bucket; l3 is the length of the dipper cylinder. The driving cylinder is connected to the working device in an articulated form, and the cylinder is used to control the compound movement of each joint so that the hydraulic equipment can complete the specified work task. The trajectory planning of this embodiment does not consider the rotation of the slewing joint, but only considers the combined movement of the boom, dipper arm and bucket joints in one plane. Figure 3a The mechanical arm shown in the figure is studied, and its dynamic equation is described as:

[0235]

[0236] The pressure of the rod chamber and the rodless chamber of the hydraulic cylinder is:

[0237]

[0238] Establish the state space equation of the hydraulic mechanical transmission:

[0239]

[0240] Aiming at the problems of long trajectory time, high energy consumption and unstable movement in the current intelligent assisted operation planning of equipment, a trajectory planning algorithm combining an improved sparrow algorithm with a quintic non-uniform B-spline curve is designed. The cat mapping chaotic sequence is used for population initialization of the improved sparrow algorithm to improve the randomness and global distribution ability of the initial group. The individuals are adjusted through Cauchy mutation and Tent chaotic perturbation to avoid the population being too "concentrated" or "dispersed". Finally, an adaptive explorer-follower number adjustment formula is introduced to balance the ability to find the global and local optimality, making the planned trajectory smoother and more stable, with shorter time and better energy. Figure 5 The flowchart of the improved sparrow algorithm is shown.

[0241] The foraging process of sparrows can be abstracted into a discoverer-joiner-warner model. The discoverer has high fitness and a wide search range, which guides the population to search and forage. Joiners follow the discoverer with the highest fitness to forage. At the same time, in order to increase their own predation rate, some joiners will monitor the discoverer in order to compete for food or forage around it. When the warner perceives a threat to the population, it will perform anti-predation behavior. If the alarm value is greater than the safety threshold, the discoverer will take all joiners away from the dangerous area.

[0242] In order to improve the randomness and ergodicity of individual sparrows, the population is initialized by firstly using the cat mapping chaotic sequence and combining it with the reverse solution. The cat mapping expression is:

[0243]

[0244] Randomly generate a feasible solution for the current population, recorded as:

[0245]

[0246] In order to avoid the population being too "concentrated" or "dispersed", Tent chaotic perturbation and Cauchy mutation are introduced to adjust the individuals. At the same time, in order to avoid the characteristics of the Tent mapping itself causing the population to fall into a small period point or an unstable period point, and not to destroy the three characteristics of chaotic variables, random variables are introduced into the original Tent mapping expression. The Tent mapping expression is:

[0247]

[0248] In order to improve the operating efficiency of hydraulic equipment and reduce energy consumption, it is generally expected that the hydraulic equipment has the shortest movement time, the smoothest trajectory and the lowest energy consumption, so the following optimization objective function is defined:

[0249]

[0250] The constraints are:

[0251]

[0252] Traditional hydraulic equipment often uses proportional multi-way valves to control actuators, which results in pressure-flow coupling between the two chambers of the actuator, making it impossible to achieve independent throttling control, and resulting in high energy consumption and other problems. Figure 5As shown, the present invention adopts an independent load port system to control the pressure and flow of the two chambers of the actuator respectively. The hydraulic equipment has higher efficiency, higher control accuracy, higher design flexibility and is more energy-efficient. The two sides of the oil cylinder in the equipment are independently controlled by the independent load port hydraulic system to realize the independent control of the oil inlet and return. First, the back pressure chamber pressure is set, and the output of the return oil flow is controlled by the rod chamber return oil pressure controller to make the rod chamber pressure constant during operation, so that the system return oil pressure is kept within a reasonable range, thereby reducing the energy loss of the hydraulic system. Under a given back pressure chamber pressure, the rodless chamber oil inlet flow controller is used to calculate the flow required for accurate trajectory tracking, and the trajectory tracking function of the cylinder is realized under the condition of composite control of flow and pressure.

[0253] The embodiment of the present invention proposes an oil inlet flow controller based on a time-varying secant barrier Lyapunov function, and uses a neural network to estimate the derivative of the system uncertainty part and the virtual control quantity, so as to enhance the robust performance of the system and simplify the controller.

[0254] The RBF neural network consists of an input layer, a hidden layer and an output layer.

[0255] F(X)=W *T φ(X)+ε (11).

[0256] Design the secant barrier Lyapunov function as:

[0257]

[0258] It can be seen that when the error variable crosses the time-varying boundary, the value of the time-varying secant barrier Lyapunov function will approach infinity. Therefore, as long as the controller is designed to be bounded, the system error can be always constrained within the time-varying boundary.

[0259]

[0260] Suppose that the continuous function V(t) is positive definite and satisfies the following differential equation:

[0261]

[0262] Assume that there exists a Lyapunov function V(x), constants α>0, β>0, 0<η0<∞, 0<γ1<1 and γ2>1, if the following holds:

[0263]

[0264] Then V(x) can converge to a neighborhood near the equilibrium point in a fixed time, which can be expressed as:

[0265]

[0266] Among them, the time required for the system variables to converge to the neighborhood satisfies the inequality:

[0267]

[0268] Define the first Lyapunov function and take its derivative:

[0269]

[0270] The designed virtual control law is:

[0271]

[0272] As long as e2 is bounded, V1 is uniformly bounded, that is, the first subsystem is stable. The boundedness of e2 is proved below. Define the error variable and take the derivative:

[0273]

[0274] Define the second Lyapunov function and take its derivative:

[0275]

[0276] The designed virtual control quantity is:

[0277]

[0278] According to formula (22), the update rate of the neural network weights is

[0279]

[0280] According to Young's inequality, we have:

[0281]

[0282] It can be seen that as long as e3 converges, V2 can be guaranteed to be uniformly bounded. The boundedness of e3 is proved below. Define the error variable and take the derivative:

[0283]

[0284] According to formula (19), the oil inlet flow controller is designed as follows:

[0285]

[0286] The update rate of the neural network weights is obtained as follows:

[0287]

[0288] Due to sec(·) iThe inequality sec(·)2≥1 is satisfied, so further scaling equation (64) yields:

[0289]

[0290] To determine the only reference pressure for both chambers under a given load force, the back pressure side will be set to a lower constant pressure P i2d Maintain overall pressure at a low level to save energy.

[0291] The purpose of the return oil pressure controller is to calculate the output flow Q of the rod chamber i2M Make the pressure P i2 Track P with a certain accuracy i2d . Define the parameter vector θ p2 =[θ β ,θ Q ]=[β e ,β e D i2 ], define the pressure tracking error and take its derivative:

[0292]

[0293] For the parameter vector θ p2 The estimated value is updated online by the following adaptive law:

[0294]

[0295] In order to verify the effectiveness of the proposed trajectory tracking control algorithm, the following three control algorithms are used for comparative simulation.

[0296] Controller C1: This is a direct adaptive neural network control (PD controller) for a class of strict feedback affine nonlinear systems with unknown nonlinearities.

[0297] Controller C2: This is an adaptive neural network controller based on the traditional time-varying barrier Lyapunov function for error constraints (TLBLF controller).

[0298] Controller C3: This is an adaptive neural network controller based on time-varying secant barrier Lyapunov function (TSBLF controller) designed by this application.

[0299] The tracking effect of the TSBLF controller on the boom arm and bucket mentioned in this application is as follows: Figure 7 The tracking errors of the joint angles of the three controllers are shown in Figure 8As shown in the figure, both TSBLF and TLBLF controllers can limit the transient and steady-state tracking errors within the specified boundary constraints under the constraints of boundary conditions. However, since the TLBLF controller is not designed to stably track the trajectory within a limited time, it takes a long time to stabilize the tracking. Figure 8 , the controller designed in this application has better error dynamic response stage than TSBLF and TLBLF controllers, and PD controller is the worst. Among them, TSBLF controller reduces the error overshoot of boom, dipper arm and bucket by 28.6%, 93.8% and 85.7% respectively, and the time to reach stability is reduced by 28.3%, 39.4% and 85.5% compared with TLBLF controller. The error dynamic characteristics are better than TLBLF controller. Figure 8 The control accuracy of the TSBLF controller in the stable stage is ±1×10 -3 The control accuracy of the TLBLF controller in the stable stage is ±1×10 -2 The control accuracy of the PD controller in the stable stage is ±4×10 -2 The range of fluctuations proves that the TSBLF controller proposed in this application is superior to the TLBLF and PD controllers in control accuracy. In summary, the TSBLF controller proposed in this application can ensure better control accuracy while also allowing the system error to converge to a predefined boundary within a limited time. That is, the proposed controller has higher tracking accuracy and better dynamic characteristics.

[0300] The present invention studies the trajectory planning of hydraulic equipment and the high-precision asymptotic tracking control of the planned trajectory. The equipment trajectory planning part designs a trajectory planning algorithm based on a combination of a quintic non-uniform B-spline curve and an improved sparrow algorithm to solve the problems of long planning time, high energy consumption, and unstable movement of the current equipment intelligent auxiliary operation. The trajectory tracking part designs the controller based on the load port independent system, in which the oil inlet flow controller is designed based on the time-varying secant barrier Lyapunov function to ensure that the system error converges to the predefined boundary within a limited time, and at the same time uses the RBF neural network to approximate the unknown nonlinear function and the derivative of the system virtual control quantity. The return oil pressure controller is designed based on adaptive robustness to ensure that the return oil back pressure is at a low level.

[0301] The above embodiments are only descriptions of the preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A control method for a hydraulic mechanical transmission device based on optimal trajectory optimization, characterized in that: It includes the following steps: S1. Establish a physical model of the hydraulic mechanical transmission device taking into account unmodeled errors and external disturbances; S2, taking the shortest movement time, the smoothest trajectory and the lowest energy consumption as the optimization goals, and taking the actual kinematic and dynamic constraints of the equipment as constraints, the trajectory planning algorithm based on the improved sparrow algorithm combined with the quintic non-uniform B-spline curve is used to obtain the optimal trajectory; It includes the following sub-steps: S21, using a quintic non-uniform B-spline algorithm to perform trajectory planning to obtain a target trajectory; S22, using the improved sparrow algorithm to optimize the target trajectory based on the optimization function, specifically including the following sub-steps: S221. In order to improve the randomness and ergodicity of individual sparrows, the population is initialized by firstly using the cat mapping chaotic sequence and combining it with the reverse solution. The cat mapping expression is: Where a and b are arbitrary real numbers; mod is the decimal part of a; X s+1 and W s+1 is a sequence; Randomly generate a feasible solution for the current population, recorded as: Among them, X', X' sd is a feasible solution, q is a uniformly distributed real number on the interval [0,1]; X min and X max is the boundary of feasible solutions, d and D both represent the number of feasible solutions; S222. To avoid the population being too concentrated or dispersed, Tent chaotic perturbation and Cauchy mutation are introduced to adjust the individuals, and random variables are introduced into the original Tent mapping expression. The Tent mapping expression is: Among them, z is the Tent map, N T is the number of particles in the chaotic sequence; rand(0,1) is a random number between [0,1]; i is the number of populations; S223, construct an optimization objective function with the shortest motion time, the smoothest trajectory and the lowest energy consumption as the optimization goals: Among them, h i is the time for the mechanical transmission device to move along each section; n is the number of interpolation points; T is the total time for the mechanical transmission device to move; a is the joint acceleration; j is the joint pulsation; T is the movement time, F1 is the movement efficiency of the mechanical transmission device; F2 is the average acceleration of the joint, representing the energy consumption of the mechanical transmission device; F3 is the joint pulsation, representing the smoothness of the trajectory; M is the number of key points of the trajectory; The constraints for optimizing the objective function are: in, a i 、j i are the angular velocity, angular acceleration and angular jerk of the joint respectively; V imax , A imax , R imax are the maximum angular velocity, maximum angular acceleration and maximum angular jerk allowed by the joint respectively; S224, using the improved sparrow algorithm of step S221 and step S222, optimizing the target trajectory based on the optimization function of step S223 to obtain the optimal trajectory; S3. Optimize the oil return control: Use the load port independent hydraulic system to control the pressure flow of the high pressure chamber and the back pressure chamber of the control actuator respectively, and optimize the oil return pressure controller based on direct parameter adaptive robustness; S4. Optimize the oil inlet control: Establish a Lyapunov function based on time-varying secant barrier and RBF neural network to jointly optimize the oil inlet flow controller.

2. The control method of a hydraulic mechanical transmission device based on optimal trajectory optimization according to claim 1, characterized in that: Step S1 specifically includes the following sub-steps: S11. The dynamic equation of the hydraulic mechanical transmission device is described as: Among them, q i , i=1,2,3, respectively joint angle, velocity and acceleration vector; M i represents the inertia matrix of the robot; C i G represents the Coriolis force / centrifugal force matrix of the robot arm; i is the gravity vector matrix of the manipulator; B i is the node viscous friction coefficient matrix; J iha (q i )(P i1 A i1 -P i2 A i2 ) represents the torque vector acting on the joint, where x iha is the displacement of the cylinder; d i1 Total disturbance vector; ΔG i Unmodeled parts for joint coupling dynamics; S12. The pressure of the rod chamber and the rodless chamber of the hydraulic cylinder is: Among them, β e is the bulk elastic modulus of the oil, V i1 =V i01 +A i1 x iha , V i2 =V i02 -A i2 x iha V is the volume of the cylinder without rod chamber and with rod chamber; i01 and V i02 A is the initial volume of the rodless and rod-bearing chambers of the cylinder, i1 and A i2 Q is the piston area of ​​the rodless and rod-end chambers of the oil cylinder; i1 and Q i2 is the oil inlet flow rate and the oil return flow rate; D i1 and D i2 is the unmodeled error; Δ i1 and Δ i2 is an external unknown disturbance; S13. Define x1 = q i , x3=P i1 A i1 -P i2 A i2 , establish the state space equation of the hydraulic mechanical transmission device: Among them are:

3. The control method of a hydraulic mechanical transmission device based on optimal trajectory optimization according to claim 2, characterized in that: Step S3 is specifically as follows: first, set the back pressure chamber pressure, and control the output of the return oil flow rate through the rod chamber return oil pressure controller to make the pressure of the rod chamber constant during operation; based on the given back pressure chamber pressure, calculate the flow rate required to accurately track the optimal trajectory through the rodless chamber oil inlet flow controller, thereby optimizing the return oil pressure controller.

4. The control method of a hydraulic mechanical transmission device based on optimal trajectory optimization according to claim 2, characterized in that: Step S4 specifically includes the following sub-steps: S41. Construct an RBF neural network. The RBF neural network consists of an input layer, a hidden layer and an output layer. The transformation from the input layer to the hidden layer is nonlinear, and the transformation from the hidden layer to the output layer is linear. The neuron excitation function of the hidden layer is a radial basis function. The expression of the RBF neural network function F(X) is: F(X)=W *T φ(X)+ε in, is the weight vector, c and v are the number of outputs and the number of neurons in the hidden layer respectively; is the input of the neural network, z is the number of inputs; ε is the approximation error of the neural network. is a positive constant; φ(X)=[φ1(X),φ2(X),…,φ l (X)], is the activation function, and its specific expression is: Among them, μ i and σ i are the center and width of the Gaussian function of the i-th neuron, X1 is the first layer input of the neural network, and l is the total number of neurons; S42. Establish Lyapunov function based on time-varying secant barrier; S43, updating the RBF neural network using a Lyapunov function based on a time-varying secant barrier; S44. Optimize the oil inlet flow controller.

5. The control method of a hydraulic mechanical transmission device based on optimal trajectory optimization according to claim 4, characterized in that: Step S42 specifically includes the following sub-steps: S421. Design the Lyapunov function V of the secant barrier as: Where F(t) is the time-varying boundary where the function value is greater than zero; e is the system tracking error variable; When the error variable crosses the time-varying boundary, the value of the time-varying secant barrier Lyapunov function will approach infinity. The controller is set to be bounded to ensure that the system error is always constrained within the time-varying boundary. Among them, F i0 , F i∞ , n i are all constants greater than zero and satisfy 0 <F i∞ <F i0 ,||e1(0)|| <F i0 , e1(0) is the initial value of e1; S422. Suppose that a continuous function V(t) is positive definite and satisfies the following differential equation: Among them, β, ξ are constants, β>0, 0<ξ<1, at this time V(t) satisfies uniform final bounded convergence; Assume that there exists a Lyapunov function V(x), constants α>0, β>0, 0<η0<∞, 0<γ1<1 and γ2>1, if the following holds: Then V(x) can converge to a neighborhood near the equilibrium point within a fixed time, and the neighborhood is expressed as: Where θ is a constant and satisfies the inequality 0<θ<1; Among them, the time T required for the system variables to converge to the neighborhood satisfies the inequality: S423. Define the first Lyapunov function V1 and derive it to obtain: Among them, e2=x2-α1, α1 is the virtual control quantity, is the derivative of the planned trajectory; The designed virtual control law is: Among them, γ1, γ2, k 11 , k 12 is a constant greater than zero and satisfies 0<γ1<1,γ2>1; As long as e2 is bounded, V1 is uniformly ultimately bounded, that is, the first subsystem is stable; S424. Define the second Lyapunov function and take its derivative.

6. The control method of a hydraulic mechanical transmission device based on optimal trajectory optimization according to claim 5, characterized in that: Step S43 specifically includes the following sub-steps: S431, according to step S424, the neural network weight update rate is obtained, and the error variable is further defined and derived; S432. Define the third Lyapunov function and take its derivative.

7. The control method of a hydraulic mechanical transmission device based on optimal trajectory optimization according to claim 4, characterized in that: Step S44 specifically includes the following sub-steps: S441, optimize the oil inlet flow controller: make Substitutions are: S442, the update rate of the neural network weights is: Scaling gives: Where ρ = min{k 12 ,k 22 ,k 32 ,σ w1 ,σ w2 ,σ ε1 ,σ ε2 }, The integrals on both sides are: When t tends to infinity, we have: From the boundedness of V3, it can be inferred that the tracking error of the system is always constrained within the time-varying boundary (-F i (t),F i (t)) Since V3 is bounded, the error signal e i , and are bounded, that is, there is a constant greater than zero and satisfy and Therefore the following inequality holds: Substitutions are: Since 0≤sec(·) i -1<sec(·) i ,get Further zooming in: in, Among them, α, β and η0 are expressed as:

8. The control method of a hydraulic mechanical transmission device based on optimal trajectory optimization according to claim 3, characterized in that: The optimized oil return pressure controller in step S3 is: To determine the only reference pressure for both chambers under a given load force, the back pressure side will be set to a low constant pressure P i2d Keep overall stress levels low; The purpose of the return oil pressure controller is to calculate the output flow Q of the rod chamber i2M Make the pressure P i2 Track P with a certain accuracy i2d , define the parameter vector θ p2 =[θ β ,θ Q ]=[β e ,β e D i2 ], define the pressure tracking error and take its derivative: z p =P i2 -P i2d Q i2M As the control input, according to the DCARC theory, the return oil pressure control law is obtained as follows: Among them, the control law includes the adaptive model compensation term Q i2Ma and the robust feedback term Q i2Ms Two parts, θ βmin Denotes the parameter θ β The lower bound of θ β >0, the selection conditions of feedback gain k1 will be given later, and the selection of k2 needs to ensure the nonlinear robust feedback term Q i2Ms2 The following conditions are met: Among them, ε p For any small design parameter, the regression vector For the parameter vector θ p2 The estimated value is updated online by the following adaptive law: Among them, Γ p >0 is the adaptive rate diagonal matrix, the adaptive function τ p =ω p φ p z p .

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