Self-adaptive sliding mode control method for forcible entry robot based on disturbance observer

Abstract

The invention relates to a self-adaptive sliding mode control method for a forcible entry robot based on a disturbance observer, and the method comprises the steps: S1, carrying out the kinematics modeling of the forcible entry robot, and obtaining the expected stroke of each hydraulic cylinder in the forcible entry robot through the kinematics modeling; s2, a nonlinear model of a hydraulic cylinder is established, and a state space expression of a hydraulic system is obtained; s3, designing a non-linear interference observer based on an extended state observer, wherein the non-linear interference observer is used for estimating external interference and compensating system input; s4, designing a continuous adaptive sliding mode controller based on the disturbance observer, eliminating system buffeting and improving control precision; and S5, according to the expected stroke of each hydraulic cylinder, the hydraulic cylinders are driven according to the steps, and accurate adjustment of the tail end pose of the forcible entry robot is achieved. Through joint simulation of AMESim and Matlab, it is verified that the method has high control precision and good robustness under the condition of external interference.

Description

Technical Field:

[0001] The present invention relates to the technical field of anti-interference control of demolition robots, and specifically relates to an adaptive sliding mode control method for demolition robots based on a disturbance observer. Background Art:

[0002] The autonomous and precise motion control of demolition robots is a very challenging topic because its hydraulic system has characteristics such as strong nonlinearity, parameter uncertainty, and load time-variation, which seriously affect the tracking accuracy of the end of the demolition hammer. At present, the trajectory tracking control methods of hydraulic manipulators mainly include PID control, adaptive control, fuzzy control, and other intelligent control methods, etc. However, PID control is difficult to handle the parameter uncertainty and nonlinear problems existing in the system model. Although the adaptive control method has a certain adaptive adjustment ability for hydraulic systems with parameter uncertainty, too large a change in the system structure may lead to a deterioration of the system stability. In addition, intelligent methods such as fuzzy control and neural network control can, to a certain extent, achieve position control of nonlinear uncertain hydraulic systems, but they strictly rely on the operator's experience and relevant professional knowledge.

[0003] Sliding mode control has the advantages of being insensitive to parameter changes and disturbances and having a simple physical implementation, and is widely used in the position control of hydraulic systems. Dang et al. proposed an improved adaptive backstepping integral sliding mode control based on incomplete differentiation to achieve position control of a hydraulic servo system based on friction compensation. Zhang et al. designed a sliding mode control strategy based on an observer, and used the observer's ability to observe external disturbances to ensure that the actuator can achieve the desired control effect even under the action of disturbances. Jiang et al. proposed a global fast terminal sliding mode active disturbance rejection control to solve the problem that it is difficult for a single-structure controller to achieve precise and stable control due to the coupling of multiple nonlinear factors in a double-closed-loop digital hydraulic cylinder position control system. However, the disadvantage of this algorithm is that it is easy to cause the system state trajectory to cross back and forth on both sides of the sliding mode surface, resulting in an undesired chattering phenomenon.

[0004] In order to achieve fast tracking and eliminate the chattering of the system, Shen et al. used an estimation method to feedback the total integral disturbance to the sliding mode control law, and used a fuzzy system to approximately minimize the sliding mode gain by taking the system error as the input, so as to ensure that the system has a fast tracking speed while minimizing chattering. Ji et al. proposed a new smooth and continuous sliding mode control law, which reduces the chattering generated by the system compared with the traditional sliding mode control law, and proved the stability of the algorithm based on Lyapunov theory.

[0005] Although the above-mentioned sliding mode control method improves the accuracy of trajectory tracking to a certain extent, it cannot meet the requirements of precise tracking when facing problems such as strong nonlinearity, parameter uncertainty, and time-varying load of the hydraulic manipulator system during operation. Therefore, aiming at the strong nonlinearity, parameter uncertainty, and time-varying load problems of the hydraulic manipulator of the demolition robot during unmanned operation, it is necessary to develop a new adaptive sliding mode control method based on a disturbance observer, in order to achieve precise tracking of the manipulator for the desired trajectory and improve the accuracy of trajectory tracking.

[0006] It should be noted that the above content belongs to the technical cognition scope of the inventor and does not necessarily constitute the prior art. Summary of the Invention:

[0007] The purpose of the present invention is to solve the problems existing in the prior art, and provide an adaptive sliding mode control method for a demolition robot based on a disturbance observer. A nonlinear disturbance observer is designed to estimate external disturbances and compensate for system inputs; combined with the disturbance observer, a continuous adaptive sliding mode control method based on the disturbance observer is designed to eliminate system chattering and improve control accuracy; the stability of the closed-loop system of this method is proved by the Lyapunov method; through the joint simulation of AMESim and Matlab, it is verified that this method has high control accuracy and good robustness under external disturbances.

[0008] The present invention realizes the above purpose by adopting the following technical solutions:

[0009] The adaptive sliding mode control method for a demolition robot based on a disturbance observer includes the following steps:

[0010] S1. Conduct kinematic modeling on the demolition robot

[0011] Construct a kinematic mechanism schematic diagram of the demolition robot, and conduct kinematic modeling to obtain the mutual conversion relationship between the pose space and the joint space of the end of the demolition robot, as well as the mutual conversion relationship between the drive space and the joint space; obtain the expected stroke of each hydraulic cylinder in the demolition robot through kinematic modeling, and the hydraulic cylinder is a valve-controlled asymmetric hydraulic cylinder.

[0012] S2. Establish a nonlinear model of the hydraulic cylinder

[0013] When the asymmetric hydraulic cylinder directly drives the inertial load, establish the dynamic model of the load:

[0014]

[0015] In the formula, A1 and A2 are respectively the effective working areas of the rodless cavity and the rod cavity of the hydraulic cylinder, p1 and p2 are respectively the pressures of the rodless cavity and the rod cavity of the hydraulic cylinder, m is the equivalent mass of the load, x p is the load displacement. is the second derivative of the load displacement, B is the viscous damping coefficient of the piston, the first derivative of the load displacement, F L represents the external load force on the hydraulic cylinder, and f represents other unmodeled disturbances;

[0016] The dynamic equation of the pressure in the hydraulic cylinder is:

[0017]

[0018]

[0019] where V1 and V2 are the initial volumes of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, and β e is the bulk modulus of the oil, q1 is the oil supply flow rate to the rodless chamber of the hydraulic cylinder; q2 is the oil return flow rate from the rod chamber of the hydraulic cylinder, and C i is the internal leakage coefficient of the hydraulic cylinder, and C e is the external leakage coefficient of the hydraulic cylinder;

[0020] Assuming that the oil return pressure of the hydraulic system is 0, and the volume changes of the rodless chamber and the rod chamber are much smaller than the original effective volume, then and these two terms can be omitted, and the dynamic equation of the pressure in the hydraulic cylinder becomes:

[0021]

[0022] q1 and q2 are functions of the spool displacement x v of the servo valve:

[0023]

[0024]

[0025] where C d is the flow coefficient of the servo valve, w1 and w2 are the area gradients of the servo valve, ρ is the density of the hydraulic oil, and p s is the supply pressure;

[0026] The relationship expression between the spool displacement x v of the servo valve and the control input voltage u:

[0027] x v = k v u

[0028] k v > 0

[0029] where k v is the electrical gain coefficient of the servo valve;

[0030] The expressions of q1 and q2 are transformed into:

[0031]

[0032]

[0033] Set: n = A2 / A1, w1 = w2;

[0034] From the above formula, we can get:

[0035]

[0036] In the hydraulic servo system, ignoring the leakage flow rate, subtracting the two dynamic equations of the pressure in the hydraulic cylinder gives:

[0037]

[0038] In the formula:

[0039]

[0040]

[0041]

[0042] Define variables:

[0043]

[0044] The state - space representation form of the hydraulic system is:

[0045]

[0046] In the formula:

[0047]

[0048]

[0049] S3. Design a nonlinear disturbance observer

[0050] Use d to represent the external disturbance, and its expression is:

[0051]

[0052] Set the viscous damping coefficient B of the piston to 0. The selected nonlinear disturbance observer based on the state variable x2 can be written in the following form:

[0053]

[0054] Since:

[0055]

[0056] Then:

[0057]

[0058] Where ω1 and ω2 are observer parameters, represents the estimated value of the external disturbance d, is the error of the external disturbance;

[0059] S4. Design an adaptive sliding mode variable structure controller

[0060] From the above equation, the state space of the hydraulic system can be redefined as:

[0061]

[0062] Where G1(x) and G2(x) respectively refer to the constant values of g1(x) and g2(x) under the initial state;

[0063] f = Δg2(x)u + Δg1(x)x2

[0064] Let x d x d be the expected stroke of the hydraulic cylinder, then the deviation between the actual stroke of the hydraulic cylinder and it is:

[0065]

[0066] Select the sliding mode switching function as:

[0067] s = c1e1 + c2e2 + e3

[0068] Adopt the exponential reaching law By adjusting k1 and k2, improve the reaching speed when far from the sliding mode surface and eliminate high-frequency chattering.

[0069] Taking the derivative of both sides of the above sliding mode switching function and arranging, we can get:

[0070]

[0071] Combining the above equation with the reaching law, the control law of the hydraulic system can be described as

[0072]

[0073] The adaptive law is taken as:

[0074]

[0075] Where λ is the adaptive law parameter;

[0076] S5. According to the expected strokes of the respective hydraulic cylinders, drive each hydraulic cylinder separately according to the above steps to achieve precise adjustment of the end pose of the demolition robot.

[0077] In step S3, verify the stability of the disturbance observer, specifically including:

[0078] Set the external disturbance d as a slow time-varying signal, then

[0079]

[0080] Define the Lyapunov equation as:

[0081]

[0082] In the formula, Then:

[0083]

[0084] According to the Lyapunov theory, the designed disturbance observer is stable; input the observed disturbance term into the controller for compensation by the controller.

[0085] In step S5, conduct a stability analysis on the entire hydraulic closed-loop system, specifically including:

[0086] Take the Lyapunov function:

[0087]

[0088] In the formula, Set z as a slowly time-varying internal disturbance of the system, then

[0089]

[0090] Take the derivative of the above formula and substitute the control law and adaptive law:

[0091]

[0092] It is known that when k1 > 0 and k2 > 0, It always holds, so the hydraulic closed-loop system is stable.

[0093] The present invention adopts the above structure and can bring the following beneficial effects:

[0094] (1) By considering the external disturbances of the electro-hydraulic system, a non-linear disturbance observer based on the extended state observer was designed to estimate the external disturbances and compensate for the system input. (2) Combining with the non-linear disturbance observer, a continuous adaptive sliding mode control method based on the disturbance observer was proposed to eliminate the system chattering and improve the control accuracy. The stability of the closed-loop system of this algorithm was proved by the Lyapunov method. (3) Through the co-simulation of AMESim and Matlab, it was verified that in the presence of external disturbances, this algorithm has high control accuracy and good robustness. Description of the Drawings:

[0095] Figure 1 It is a structural schematic diagram of the kinematic mechanism of the working device of the wall-breaking robot of the present invention;

[0096] Figure 2 It is a flow chart of the kinematic modeling of the working device of the wall-breaking robot of the present invention;

[0097] Figure 3 It is the D-H method coordinate system of the working device of the wall-breaking robot of the present invention;

[0098] Figure 4 It is the working principle diagram of the hydraulic cylinder for driving the robotic arm of the present invention;

[0099] Figure 5 It is the control block diagram of the hydraulic-driven robotic arm of the present invention;

[0100] Figure 6 It is the co-simulation model of the electro-hydraulic system of the demolition robot of the present invention;

[0101] Figure 7 It is the robotic arm control system of the demolition robot of the present invention;

[0102] Figure 8 It is the model of the pilot servo valve-controlled asymmetric hydraulic cylinder of the present invention;

[0103] Figure 9 It is the observation result of the external load force of the disturbance observer of the present invention;

[0104] Figure 10 It is the observation result of the error of the disturbance observer of the present invention;

[0105] Figure 11 It is the schematic diagram of the robotic arm model of the mechanical library of the present invention;

[0106] Figure 12 It is the schematic diagram of the working state a of the present invention;

[0107] Figure 13 It is the schematic diagram of the working state b of the present invention;

[0108] Figure 14Schematic diagram of the working state of the present invention;

[0109] Figure 15 Simulation result diagram of the end tracking of the breaker at the working state a of the present invention;

[0110] Figure 16 Error result diagram of the end tracking of the breaker at the working state a of the present invention;

[0111] Figure 17 Simulation result diagram of the tracking situation of each hydraulic cylinder at the working state a of the present invention;

[0112] Figure 18 Simulation result of the end error of the breaker hydraulic cylinder at the working state b of the present invention;

[0113] Figure 19 Schematic diagram of the load forces on the breaker at the working states b and c of the present invention;

[0114] Figure 20 Simulation result diagram of the end tracking situation of the breaking device at the working state c of the present invention;

[0115] Figure 21 Simulation result diagram of the end tracking error of the breaking device at the working state c of the present invention;

[0116] In the figure, 1. Pilot valve; 2. Servo valve; 3. Hydraulic station; 4. Pressure sensor; 5. Driving hydraulic cylinder; 6. Displacement and velocity sensor. Specific implementation method:

[0117] In order to more clearly explain the overall concept of the present invention, the following is an illustration by way of example in combination with the drawings in the specification.

[0118] The adaptive sliding mode control method for a breaking robot based on a disturbance observer includes the following steps:

[0119] S1. Kinematic modeling of the breaking robot

[0120] Before control, it is necessary to establish the kinematic model of the working device of the breaking robot. As Figure 1 shown is the kinematic mechanism schematic diagram of the working device of the breaking robot. Kinematic analysis is crucial for the motion trajectory planning of the working device, and the motion trajectory planning provides a basis for the motion control of the working device. The kinematic modeling process of the working device (i.e., the breaking robot) is as Figure 2 shown; according to the conversion of different spaces, the kinematic modeling of the working device can be divided into the following two parts:

[0121] a. The mutual conversion between the joint space and the pose space, that is, the forward and inverse solutions of kinematics;

[0122] b. Mutual conversion between the driving space and the joint space;

[0123] (1) Pose space [x, y, z, γ] T ; x, y, and z are the coordinates of the end of the demolition device in the original coordinate system, and γ is the angle between the end of the demolition device and the horizontal direction.

[0124] (2) Joint space [θ1, θ2, θ3, θ4] T ; θ1, θ2, θ3, and θ4 represent the joint angles of the upper arm, middle arm, lower arm, and rocker respectively.

[0125] (3) Driving space [l1, l2, l3, l4] T ; l1, l2, l3, and l4 represent the lengths (i.e., expected strokes) of the hydraulic cylinders of the upper arm, middle arm, lower arm, and rocker respectively.

[0126] Kinematic modeling includes forward and inverse kinematic solutions, involving the mutual conversion between the joint space [θ1, θ2, θ3, θ4] T and the pose space [x, y, z, γ] T where θ i corresponds to the i-th joint angle in the figure; x, y, and z represent the spatial position of the end of the breaker; γ is the attitude angle of the breaker.

[0127] The forward kinematic solution uses the D-H method. A D-H coordinate system is established at each joint of the working device, as Figure 3 shown in the D-H method coordinate system of the working device. Among them, the coordinate system at the i-th joint is O i X i Y i Z i ; all connecting rods are represented by four D-H parameters: the link distance a i , the joint rotation angle θ i , the link twist angle α i , and the joint distance d i . a i represents the distance from the positive direction of the Z i-1 axis along the X i axis to the Z i axis; θ i represents the rotation angle of the X i-1 axis around the positive direction of the Z i-1 axis to the X i axis direction; α i represents the rotation angle of the Z i-1 axis around the positive direction of the X i axis to the Z i axis direction; d i represents the distance from the positive direction of the X i-1 axis along the Z i-1 axis to the X iDistance from the axis. Adjacent joint coordinate system O i-1 X i-1 Y i-1 Z i-1 and O i X i Y i Z i transformation matrix can be calculated according to the following formula:

[0128]

[0129] Establish a D-H coordinate system. The fuselage coordinate system is O0X0Y0Z0, and the D-H coordinate systems of the boom, mid-arm, forearm, and breaker are O1X1Y1Z1, O2X2Y2Z2, O3X3Y3Z3, and O4X4Y4Z4 respectively. The D-H parameters of the working device are shown in Table Ⅰ.

[0130] Table Ⅰ D-H parameters of the working device of the breaker robot

[0131]

[0132] According to the aforementioned D-H method, the transformation matrix between adjacent joints can be calculated:

[0133]

[0134] Then the transformation matrix between the end of the hydraulic breaker and the fuselage of the breaker robot is:

[0135]

[0136] where c1 = cos(θ1); s1 = sin(θ1); c 1234 = cos(θ1 + θ2 + θ3 + θ4); s 1234 = sin(θ1 + θ2 + θ3 + θ4)

[0137] From this, the pose [x, y, z, γ] of the breaker can be obtained T is:

[0138]

[0139] The inverse kinematics solution uses the geometric method. From Figure 3 it can be known the coordinates of points K, G, D and L DK L DK :

[0140]

[0141]

[0142] It can be obtained from this that:

[0143]

[0144] In order to reduce the total stroke of the hydraulic cylinder during the demolition process, the sum of the squares of the joint angle changes is used as the optimization objective function in this paper:

[0145]

[0146] The mapping relationship from the driving space to the joint space is to solve the mapping relationship between the moving changes l1~l4 of the hydraulic cylinders and the joint variables θ1~θ4. The relationship between the driving lengths of each hydraulic cylinder and the joint angles can be obtained by the geometric method:

[0147]

[0148] This formula is the mapping relationship between the hydraulic cylinder l1 and the joint angle θ1;

[0149]

[0150] This formula is the mapping relationship between the hydraulic cylinder l2 and the joint angle θ2;

[0151]

[0152] This formula is the mapping relationship between the hydraulic cylinder l3 and the joint angle θ3;

[0153]

[0154] This formula is the mapping relationship between the hydraulic cylinder l4 and the joint angle θ4; S2. Establish the nonlinear model of the hydraulic cylinder

[0155] The hydraulic manipulator is mainly composed of an execution mechanism (manipulator) and a drive system (hydraulic actuator, control valve, power source, etc.). The object studied in this paper is a four-degree-of-freedom hydraulic manipulator, and each degree of freedom corresponds to a driving hydraulic cylinder, but there are only differences in the cylinder body sizes among the four hydraulic cylinders. Therefore, in the process of modeling the hydraulic system, we take the hydraulic cylinder driving the breaker as an example, and the modeling methods of the other hydraulic cylinders are the same as it.

[0156] The working principle of the breaker driving hydraulic cylinder is as Figure 4 shown. During the working process of the hydraulic cylinder, it is necessary to control the flow of hydraulic oil through a hydraulic control valve (servo valve) to achieve precise motion control of the manipulator. At the same time, the power source (such as a hydraulic pump) provides the required pressure and flow for the hydraulic system. In the modeling process, we will consider the dynamic characteristics, fluid mechanics characteristics of the hydraulic cylinder and the feedback control strategy of the control system to achieve the motion control of the hydraulic manipulator.

[0157] The hydraulic actuator of this hydraulic manipulator selects a valve-controlled asymmetric hydraulic cylinder. However, the valve-controlled asymmetric hydraulic cylinder system has serious nonlinear problems and modeling uncertainties. Therefore, in order to study the nonlinear characteristics of the system and adopt appropriate control strategies, a nonlinear model of the hydraulic system is established.

[0158] When considering the direct drive of an inertial load by an asymmetric hydraulic cylinder, we can describe the dynamic model of the load as:

[0159]

[0160] where, A1 and A2 are the effective working areas of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, p1 and p2 are the pressures of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, m is the equivalent mass of the load, x p is the load displacement, is the second derivative of the load displacement, B is the viscous damping coefficient of the piston, the first derivative of the load displacement, F L represents the external load force on the hydraulic cylinder, and f represents other unmodeled disturbances;

[0161] The dynamic equation of the pressure in the hydraulic cylinder is:

[0162]

[0163]

[0164] where, V1 and V2 are the initial volumes of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, β e is the bulk modulus of the oil, q1 is the oil supply flow rate of the rodless chamber of the hydraulic cylinder; q2 is the oil return flow rate of the rod chamber of the hydraulic cylinder, C i is the internal leakage coefficient of the hydraulic cylinder, C e is the external leakage coefficient of the hydraulic cylinder;

[0165] Assuming that the oil return pressure of the hydraulic system is 0, and the volume changes of the rodless chamber and the rod chamber are much smaller than the original effective volume, then and These two terms can be omitted, and the dynamic equation of the pressure in the hydraulic cylinder becomes:

[0166]

[0167] q1 and q2 are functions of the servo valve spool displacement x v :

[0168]

[0169]

[0170] where, C dis the flow coefficient of the servo valve, w1 and w2 are the area gradients of the servo valve, ρ is the density of the hydraulic oil, p s is the supply pressure;

[0171] The spool displacement x of the servo valve v and the relationship expression with the control input voltage u:

[0172] x v = k v u; k v > 0

[0173] In the formula, k v is the electrical gain coefficient of the servo valve;

[0174] The expressions of q1 and q2 are transformed into:

[0175]

[0176]

[0177] Set: n = A2 / A1, w1 = w2;

[0178] From the above formula, it can be obtained:

[0179]

[0180] In the hydraulic servo system, ignoring the leakage flow, subtracting the two dynamic equations of the pressure in the hydraulic cylinder gives:

[0181]

[0182] In the formula:

[0183]

[0184]

[0185]

[0186] Define variables:

[0187]

[0188] The state - space expression form of the hydraulic system is:

[0189]

[0190] In the formula:

[0191]

[0192]

[0193] S3. Design a non - linear disturbance observer

[0194] Based on sliding - mode control and introducing a non - linear disturbance observer, an adaptive sliding - mode control based on the non - linear disturbance observer is designed, which can effectively alleviate the chattering phenomenon and improve the trajectory tracking accuracy of the manipulator system. The control system structure is as Figure 5 .

[0195] During the operation of the demolition robot, the dynamic equation parameters of the working device (manipulator) will change with the change of the manipulator posture, which causes the external load force on the driving component (hydraulic cylinder) to fluctuate during the operation. In addition, there are other unmodeled disturbance terms f, which belong to unknown states. To comprehensively consider these two kinds of disturbances, they are collectively referred to as external disturbance d, and the expression of d is:

[0196]

[0197] Set the viscous damping coefficient B of the piston to 0, and the disturbance observer can be written in the following form based on the state variable x2:

[0198]

[0199] Since:

[0200]

[0201] Then:

[0202]

[0203] In the formula, ω1 and ω2 are observer parameters, represents the estimated value of the external disturbance d, is the error of the external disturbance;

[0204] Set the external disturbance d as a slow - time - varying signal, then

[0205] Define the Lyapunov equation as:

[0206]

[0207] In the formula, Then:

[0208]

[0209] According to the Lyapunov theory, the designed disturbance observer is stable; the observed disturbance term is input into the controller for compensation through the controller.

[0210] S4. Design an adaptive sliding - mode variable - structure controller

[0211] By using the sliding mode variable structure control method, we can overcome the uncertainties of the nonlinear hydraulic position servo system, achieve robust control of system disturbances and unmodeled dynamics, and at the same time meet the requirements of the system for fast response. On the other hand, through the adaptive control strategy, we can estimate the uncertainties of the controlled object, solve the problems of inaccurate system models and time-varying parameters, and thus effectively reduce the system chattering problem caused by parameter perturbations. This combined method can maintain the stability of the system to a certain extent and achieve the optimal or approximate optimal system performance index.

[0212] From the above equation, the state space of the hydraulic system can be redefined as:

[0213]

[0214] In the formula, G1(x) and G2(x) respectively refer to the constant values of g1(x) and g2(x) under the initial state;

[0215] f = Δg2(x)u + Δg1(x)x2

[0216] Let x d x d be the expected stroke of the hydraulic cylinder, then the deviation between the actual stroke of the hydraulic cylinder and it is:

[0217]

[0218] Select the sliding mode switching function as:

[0219] s = c1e1 + c2e2 + e3

[0220] Adopt the exponential reaching law By adjusting k1 and k2, the reaching speed away from the sliding mode surface is increased and the high-frequency chattering is eliminated; differentiating both sides of the above sliding mode switching function and arranging, we can get:

[0221]

[0222] Combining the above formula with the reaching law, the control law of the hydraulic system can be described as

[0223]

[0224] The adaptive law is taken as:

[0225]

[0226] In the formula, λ is the adaptive law parameter;

[0227] Define for the entire closed-loop system, take the Lyapunov function:

[0228]

[0229] In the formula,

[0230] Assume that z is a slowly time-varying internal disturbance of the system, then

[0231] Take the derivative of the above formula and substitute the control law and adaptive law:

[0232]

[0233] When k1 > 0 and k2 > 0, always holds, so the hydraulic closed-loop system is stable.

[0234] S5. According to the expected stroke of each hydraulic cylinder, drive each hydraulic cylinder respectively according to the above steps to achieve precise adjustment of the end pose of the demolition robot.

[0235] Simulation analysis

[0236] The co-simulation of AMESim and MATLAB is adopted. The S-Function function in MATLAB / Simulink is mainly used to combine the two. By modifying the file name and setting the system parameters, the simulation of the hydraulic system in the combined environment is completed. According to the physical model of the hydraulic manipulator, it can be divided into two parts: the hydraulic system model and the control system model. The hydraulic model is constructed in the AMESim environment, while the control model part is completed in MATLAB.

[0237] The system model of the manipulator hydraulic system in the AMESim environment is as Figure 6 shown; the simulation model includes a pilot valve 1, a servo valve 2, a hydraulic station 3, a pressure sensor 4, a drive hydraulic cylinder 5, and a displacement and velocity sensor 6. The hydraulic system parameters are shown in Table II.

[0238] Table II Hydraulic system parameters

[0239]

[0240] The control system model is completed in MATLAB / Simulink. The S function generated by AMESim is added to the Simulink model through the S-Function module in Simulink. At the same time, the control algorithm model in Simulink is also connected to the control module in AMESim, thus completing the modeling of the entire hydraulic manipulator control system. The system of the adopted hydraulic manipulator control system in the MATLAB / Simulink environment is as Figure 7 shown.

[0241] (1) Analysis of the simulation results of the disturbance observer

[0242] To verify the accuracy of the observer estimates, a single-driven hydraulic cylinder system was designed using AMESim software, with the same parameters as in Table II and the structure as Figure 8 . A periodically fluctuating external load force was added to the external load of the hydraulic cylinder, and its observation results were compared with those of the observer. The disturbance observer parameters were ω1 = 10000 and ω2 = 5. The simulation results are as Figure 9 and 10 .

[0243] Through the analysis of the simulation results, it can be seen that the designed nonlinear disturbance observer can accurately observe the fluctuations of the external load force. It can compensate for the changes in the dynamic parameters of the manipulator, better control the performance and stability of the manipulator during movement, and provide an effective compensation control strategy for the changes in the dynamic parameters of the demolition robot during movement.

[0244] (2) Analysis of the simulation results of the adaptive sliding mode controller

[0245] According to the adaptive sliding mode control algorithm based on the disturbance observer, the controller and the hydraulic drive system of the manipulator were built in MATLAB / Simulink and AMESim respectively, and a 1:1 scale model was established, as Figure 11 shown.

[0246] The specific parameters of the hydraulic system refer to Table II. A PID controller, a traditional sliding mode controller, and an adaptive sliding mode controller based on the disturbance observer were established in MATLAB respectively. The simulation parameters are shown in Table III.

[0247] Table III Simulation parameters

[0248]

[0249] Based on the relationship among the end pose of the demolition hammer, the joint angles of the manipulator, and the telescopic length of the driving hydraulic cylinder above, the expected length corresponding to each hydraulic cylinder when facing different target points can be obtained. The obtained expectations were input into different controllers in the form of curves. AMESim simulated three working states of the demolition robot during operation:

[0250] a: As Figure 12 shown, the demolition hammer advances to the given target point, and there is no need to ensure the pose angle and movement trajectory of the demolition hammer during the feeding process. Four cases were assumed: namely, target point 1 is 0.5 meters in front of the initial point, target point 2 is 0.5 meters above the initial point, target point 3 is 0.5 meters behind the initial point, and target point 4 is 0.5 meters below the initial point.

[0251] b: As Figure 13As shown, through the planar design library of AMESim, a sinusoidal load force with an amplitude of 10,000 N, a frequency of 180 bpm, and a direction that periodically changes between positive and negative along the horizontal direction can be applied to the end node of the established model to simulate the vibration and impact conditions in actual work. The robotic arm needs to have sufficient stiffness and stability to maintain the accurate position and posture of the end node during the demolition process.

[0252] c: As Figure 14 shown, during the actual working process of the demolition robot, the demolition operation is carried out during the horizontal feeding of the demolition device, which is common in slag cleaning. Assume that the target point is 0.5 m horizontally in front of the current initial point, and it is required that the feeding process be straight and the posture angle of the demolition hammer always be horizontal; a sinusoidal load force with an amplitude of 10,000 N, a frequency of 180 bpm, and a direction that periodically changes between positive and negative along the horizontal direction is applied during the feeding process.

[0253] It should be noted that Figure 13 and Figure 14 the demolition hammer in Figure 12 is shown in red, which means that the demolition hammer is in the working state and applies a demolition force to external objects; while

[0254] the demolition hammer in

[0255] As Figures 15 - 21 Figure 12 is shown in blue, which is the working state without applying a demolition force.

[0254] To verify the performance of the adaptive control algorithm based on the disturbance observer under different working conditions, PID control and traditional sliding mode control are added in the simulation process for comparison. Through co-simulation, the adaptability and stability of each control algorithm under different working conditions are objectively evaluated. During the simulation process, the end posture trajectory of the demolition hammer will be converted into the angle changes of each hydraulic drive joint according to the inverse kinematics model, and further the angle changes of the joints will be converted into the changes in the stroke of the drive hydraulic cylinder to generate the expected stroke trajectory required for the corresponding working conditions. According to the description of working condition a, the inverse-solved hydraulic cylinder stroke trajectory presents step signals of different heights. The obtained expected signals are respectively input into the traditional sliding mode controller and the adaptive sliding mode controller, and co-simulation is carried out. Through co-simulation, the tracking situation and error of the distance between the end of the demolition hammer and the target point during the feeding process for the three control algorithms can be observed.

[0255] As Figures 15 - 21The tracking situation and error of the distance between the end of the demolition hammer and the target point during the feeding process are respectively shown for three control algorithms. According to the simulation results, the end of the demolition hammer can reach the preset target point by all three control algorithms within a short time. However, there are differences in the approaching speed and stability. Compared with the PID algorithm, the traditional sliding mode algorithm and the adaptive algorithm based on the disturbance observer are superior in terms of approaching speed. This can be attributed to the fact that the traditional sliding mode algorithm and the adaptive algorithm can better cancel out the interference and improve the dynamic response of the system. In addition, due to the influence of its own reaching law in traditional sliding mode control and when dealing with models with time-varying parameters, it may be difficult to maintain stability after reaching the target point. In contrast, the adaptive sliding mode control based on the disturbance observer can maintain the stability of the motion trajectory faster under the action of the adaptive law. This shows that the adaptive sliding mode control has advantages in canceling out external interference and maintaining stability.

[0256] During the working process of the demolition robot, the demolition force generated by the demolition hammer is an important factor for the precise position control of the hydraulic cylinder. To simulate this situation, the mechanical library in AMESim can be used to input a periodically varying force at the end of the established model to represent the demolition force generated by the demolition hammer during the working process. The output forces of different models of demolition robots are also different. In this paper, the demolition force has an amplitude of 10,000 N and a frequency of 180 bpm (i.e., a period of 1 / 3 s), as Figure 19 shown.

[0257] The simulation results show that in the case where the demolition hammer generates a reciprocating load force on the hydraulic cylinder, both the adaptive sliding mode control based on the disturbance observer and the traditional sliding mode control exhibit the robustness of sliding mode control, while the PID control has poor anti-interference ability.

[0258] In the application scenario of the demolition robot, slag cleaning is relatively common. During the slag cleaning process by the robot, it is required that the hydraulic manipulator keep the horizontal attitude angle of the demolition hammer while feeding linearly to the target point. Similarly, the expected stroke curves of each driving hydraulic cylinder are inversely solved and input into the three controllers, Figure 20 and Figure 21 are the trajectory tracking situation and tracking error of the end of the demolition hammer.

[0259] It can be seen from the simulation results that the tracking curve of PID control fluctuates significantly in the presence of external disturbances. However, due to the lack of compensation of the disturbance observer, traditional sliding mode control generates vibrations when the pressures in the two chambers of the hydraulic cylinder do not reach the working pressure. When the sliding mode controller based on the disturbance observer is working, the disturbance observer observes the external load force of the hydraulic cylinder in real time. During the movement of the hydraulic cylinder piston, the adaptive law compensates for the time-varying parameters in the control system, enabling the designed controller to not only exhibit good robustness but also eliminate the chattering of the traditional sliding mode to a certain extent during the simulation process. When facing different demolition operations, it can well maintain the pose of the manipulator.

[0260] The above specific implementation manners shall not be used to limit the protection scope of the present invention. For those skilled in the art of this technology, any alternative improvement or transformation made to the implementation manners of the present invention falls within the protection scope of the present invention.

[0261] Those not elaborated in the present invention are all well-known technologies to those skilled in the art of this technology.

Claims

1. The adaptive sliding mode control method of the demolition robot based on the disturbance observer is characterized by: The following steps are involved: S1. Kinematic modeling of the demolition robot Construct a kinematic diagram of the demolition robot and perform kinematic modeling to obtain the mutual transformation relationship between the posture space and joint space of the end of the demolition robot and the mutual transformation relationship between the drive space and joint space; obtain the expected stroke of each hydraulic cylinder in the demolition robot through kinematic modeling, and the hydraulic cylinder is a valve-controlled asymmetric hydraulic cylinder; S2. Establish a nonlinear model of the hydraulic cylinder When an asymmetric hydraulic cylinder directly drives an inertial load, the dynamic model of the load is established: Where A1 and A2 are the effective working areas of the rodless and rod-end chambers of the hydraulic cylinder, p1 and p2 are the pressures of the rodless and rod-end chambers of the hydraulic cylinder, m is the equivalent mass of the load, and x is the equivalent mass of the load. p is the load displacement, is the second-order derivative of the load displacement, B is the viscous damping coefficient of the piston, First derivative of load displacement, F L represents the external load force on the hydraulic cylinder, and f represents other unmodeled disturbances; The dynamic equation of pressure in the hydraulic cylinder is: Where V1 and V2 are the initial volumes of the rodless and rod-bearing chambers of the hydraulic cylinder, respectively, and β e is the bulk modulus of the oil, q1 is the oil supply flow rate of the hydraulic cylinder rodless chamber; q2 is the oil return flow rate of the hydraulic cylinder rod chamber, C i is the leakage coefficient in the hydraulic cylinder, C e is the external leakage coefficient of the hydraulic cylinder; Assume that the return oil pressure of the hydraulic system is 0, and the volume change of the rodless chamber and the rod chamber is much smaller than the original effective volume, then and The two terms can be omitted, and the dynamic equation of pressure in the hydraulic cylinder becomes: q1 and q2 are the servo valve core displacement x v Function: In the formula, C d is the servo valve flow coefficient, w1 and w2 are the area gradients of the servo valve, ρ is the hydraulic oil density, p s is the oil supply pressure; Servo valve spool displacement x v The relationship expression with the control input voltage u is: x v =k v u k v ＞0 In the formula, k v is the electrical gain coefficient of the servo valve; The expressions of q1 and q2 are transformed into: Setting: n = A2 / A1, w1=w2; From the above formula, we can get: In the hydraulic servo system, ignoring the leakage flow, the two dynamic equations of the pressure in the hydraulic cylinder are subtracted to obtain: Where: Define variables: The state space expression of the hydraulic system is: Where: S3. Design of nonlinear disturbance observer Use d to represent external interference, and its expression is: The viscous damping coefficient B of the piston is set to 0, and the selected nonlinear disturbance observer can be written as follows based on the state variable x2: because: but: Where ω1 and ω2 are observer parameters, represents the estimated value of the external disturbance d, is the error caused by external interference; S4. Design of adaptive sliding mode variable structure controller The state space of the hydraulic system can be redefined by the above formula: In the formula, G1(x) and G2(x) refer to the constant values ​​of g1(x) and g2(x) respectively in the initial state; f=Δg2(x)u+Δg1(x)x2 Let x d x d is the expected stroke of the hydraulic cylinder, and the deviation between the actual stroke of the hydraulic cylinder and it is: Select the sliding mode switching function as: s=c1e1+c2e2+e3 Exponential Reaching Law By adjusting k1 and k2, the approach speed when moving away from the sliding surface can be increased and high-frequency chattering can be eliminated; By taking the derivatives on both sides of the above sliding mode switching function, we can get: Combining the above equation with the reaching law, the control law of the hydraulic system can be described as Adaptive law: Where λ is the adaptive law parameter; S5. According to the expected stroke of each hydraulic cylinder, drive each hydraulic cylinder according to the above steps to achieve precise adjustment of the terminal posture of the demolition robot.

2. The adaptive sliding mode control method for a demolition robot based on a disturbance observer according to claim 1 is characterized in that: In step S3, the stability of the disturbance observer is verified, which specifically includes: Assuming the external interference d is a slow time-varying signal, then Define the Lyapunov equation as: In the formula, but: According to Lyapunov theory, the designed disturbance observer is stable; the observed disturbance term is input into the controller and compensated by the controller.

3. The adaptive sliding mode control method for a demolition robot based on a disturbance observer according to claim 2 is characterized in that: In step S5, a stability analysis is performed on the entire hydraulic closed-loop system, specifically including: Take the Lyapunov function: In the formula, Assuming z is a slowly time-varying internal disturbance of the system, then Derivative the above equation and bring it into the control law and adaptive law: It is known that when k1>0 and k2>0, The hydraulic closed-loop system is stable.

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