An active disturbance rejection sliding mode composite control system for a wrist rehabilitation robot

Abstract

This invention proposes an active disturbance rejection sliding mode composite control system for a wrist rehabilitation robot, which relates to the field of rehabilitation robot control technology. The wrist rehabilitation robot uses a folding airbag as a driving element. The control system includes: a tracking differentiator for tracking and differentiating an input target angle signal; an extended state observer for real-time estimation of the system state and total disturbance; a sliding mode controller for designing a nonlinear control rate; a dead-zone nonlinear inverse function control module for compensating for the nonlinear control rate of the sliding mode controller and eliminating the dead-zone nonlinearity of the high-speed switching valve; and an adaptive combination valve, comprising two high-speed switching valves, a control unit, and a pressure sensor, for executing control commands and monitoring the pressure within the folding airbag. This invention overcomes issues such as the compressibility of air within the airbag, the dead-zone nonlinearity of the gas control element, and the nonlinearity of the gas flow rate, achieving high-precision trajectory tracking control of the wrist rehabilitation robot.

Description

Technical Field

[0001] The present invention relates to the technical field of rehabilitation robot control, and in particular to an auto-disturbance rejection sliding mode composite control system of a wrist rehabilitation robot. Background Art

[0002] Wrist dysfunction is a common movement disorder, and repetitive physical training is a common method for restoring wrist function. However, providing long-term, repetitive physical training to a large number of people requires a large number of dedicated technicians, and a lack of medical resources hinders the rehabilitation process. To address this problem, researchers have proposed a solution for robot-assisted rehabilitation, which can provide users with more precise and repetitive training with minimal supervision.

[0003] Over the past few decades, researchers have developed a variety of robotic devices for wrist rehabilitation training. These devices, including single-degree-of-freedom and multi-degree-of-freedom wrist rehabilitation robots, can provide a variety of movements, including palmar flexion / dorsiflexion, abduction / adduction, and more. Most of these devices are motor-driven and rigid exoskeleton structures, offering high control precision, strong rigidity, and minimal misalignment. However, this structure can easily cause wrist injury if the user's maximum tolerance angle is exceeded during exercise.

[0004] To improve the flexibility of rehabilitation devices, some researchers have begun to use pneumatic drives, such as pneumatic artificial muscles. Compared with motor-driven devices, pneumatically driven devices are more compact, lighter, and easier to use. However, due to the compressibility of the air within the pneumatic system, the pressure-angle-force nonlinearity of the airbag itself, the dead zone nonlinearity of the gas control element, and the nonlinearity of the gas flow through the control element, these nonlinear factors are coupled with each other and jointly affect the dynamic characteristics of the pneumatic system. Traditional linear control methods (such as PID control) have difficulty effectively handling these complex nonlinearities and uncertainties, and cannot achieve accurate trajectory tracking control. Summary of the Invention

[0005] In light of this, this paper proposes an active disturbance rejection and sliding mode composite control system for a wrist rehabilitation robot. By combining the advantages of active disturbance rejection and sliding mode control, a control strategy is designed that effectively estimates and compensates for the system's total disturbance. This system aims to overcome issues such as the compressibility of air within the airbag, the nonlinear dead zone of the gas control element, and the nonlinearity of the gas flow rate, thereby achieving high-precision trajectory tracking control of the wrist rehabilitation robot.

[0006] The technical solution of the present invention is achieved as follows: The present invention provides an active disturbance rejection sliding mode composite control system for a wrist rehabilitation robot, wherein the wrist rehabilitation robot uses a folding airbag as a driving element, and the control system includes:

[0007] A tracking differentiator, used to track and differentiate the input target angle signal;

[0008] Extended State Observer for real-time estimation of system state and total disturbance;

[0009] Sliding mode controller for designing nonlinear control rates;

[0010] Dead zone nonlinear inverse function control module, used to compensate for the nonlinear control rate of the sliding mode controller and eliminate the dead zone nonlinearity of the high-speed switching valve;

[0011] The adaptive combination valve includes two high-speed switching valves, a control unit and a pressure sensor, which are used to execute control instructions and monitor the pressure in the folding airbag.

[0012] On the basis of the above technical solution, preferably, the mathematical model of the high-speed switching valve is:

[0013]

[0014] Among them, f(u) is the effective opening area coefficient of the valve, u is the input duty cycle, u s is the dead-band duty cycle.

[0015] Based on the above technical solution, preferably, the energy conservation equation of the folded airbag is:

[0016]

[0017] Where, P q is the internal pressure of the folded airbag, q m1 is the net mass flow rate in the airbag cavity, q m1 =q m2 -q m3 , where q m2 is the mass flow rate of inflating the folded airbag, q m3 is the mass flow rate of the folded airbag deflation, K is the air specific heat ratio, R is the ideal gas constant, V q is the volume of the folded airbag, T u Absolute temperature of the gas source.

[0018] Based on the above technical solution, preferably, the dynamic model of the folding airbag driven wrist rehabilitation robot is:

[0019]

[0020] Where θ f is the rotation angle of the wrist rehabilitation robot, r is the distance from the center of the folded airbag to the wrist joint rotation axis, S is the contact area between the folded airbag and the base plate, K is the air specific heat ratio, R is the ideal gas constant, T is the absolute temperature, q mis the mass flow rate of the gas in the folding airbag, J is the moment of inertia of the joint rotor, f(u) is the effective opening area coefficient of the valve, b v is the joint damping coefficient, m is the mass of the hand support plate, g is the acceleration of gravity, F h is the force exerted on the wrist rehabilitation robot when the wrist interacts with it, b0 is a constant term, a1, a2, and a3 are fitting coefficients used to fit the volume V of the folded airbag q The rotation angle θ of the wrist rehabilitation robot f Functional relationship:

[0021] make and:

[0022]

[0023] Then the state space equation of the control system is obtained as:

[0024]

[0025] Among them, is regarded as an unknown nonlinear term of the control system.

[0026] Based on the above technical solution, preferably, the tracking differentiator is designed as follows:

[0027]

[0028] fHan(θ r1 -θ d ,θ r2 ,r0,h0)The specific expression is as follows:

[0029]

[0030] in:

[0031]

[0032] Where: r0 is the speed factor of the tracking differentiator. The larger r0 is, the faster the tracking speed is. h0 is the filter factor of the differential tracker. θ d is the input target angle signal of the tracking differentiator; θ r1 is the input tracking signal of the tracking differentiator; θ r2 is θ r1 The differential signal.

[0033] On the basis of the above technical solution, preferably, the unknown nonlinear term of the control system is As the state variable of the extended state observer, let The derivative of Right now The third-order extended state observer is designed as follows:

[0034]

[0035] Where ε1 is the angle observation value and output angle The error, and They are and The estimated value of β 01 , β 02 and β 03 are the gain coefficients of the extended state observer; fal(ε i ,a i ,δ) function is defined as follows:

[0036]

[0037] in, i=1,2,3.

[0038] Based on the above technical solution, preferably, the nonlinear control rate of the sliding mode controller is as follows:

[0039]

[0040] Where, f u is the sliding mode control rate; s is the sliding surface; e1 and e2 are the sliding surface generated by the tracking differentiator Signal and the estimate produced by the extended state observer The error between η>0, and 0

[0041]

[0042] Where x represents the system state, which is used to represent the distance from the system state point to the sliding surface, and α is a variable coefficient. is the variable gain term of the approach rate, and c is the control parameter used to control the smooth continuity of sigmoid(s).

[0043] On the basis of the above technical solution, preferably, the dead zone nonlinear inverse function control module takes the effective opening area coefficient f(u) of the inflation and deflation valve output by the sliding mode controller as input, and calculates the effective opening area coefficient f(u) of the inflation and deflation valve through f -1 (f(u)) is used as the input duty cycle command u for the high-speed on-off valve for charging and discharging to eliminate the dead zone nonlinearity of the high-speed on-off valve. The expression of the control rate u is: ​

[0044]

[0045] When f(u)>0, the control rate u1=u is obtained, which serves as the input duty cycle of the high-speed switching valve to control the inflation flow of the folding airbag; when f(u)<0, the control rate u2=-u is obtained, which serves as the input duty cycle of the high-speed switching valve to control the deflation flow of the folding airbag.

[0046] On the basis of the above technical solution, preferably, the control system further includes:

[0047] Sine wave function generation module, used to generate target angle signal:

[0048] θ d =A sin(πft-0.5π)+B

[0049] Among them, θ d is the target angle signal, A=25 is the amplitude of the sine wave, f=0.025Hz is the frequency of the sine wave, and B=35 is the offset of the sine wave angle;

[0050] Minimum acceleration model generation module, used to generate the optimal wrist motion curve:

[0051]

[0052] θ0=10,θ1=10when t∈[nT,1 / 4T+nT)

[0053] θ0=10,θ1=50when t∈[1 / 4T+T,1 / 2T+nT)

[0054] θ0=50,θ1=50when t∈[1 / 2T+nT,3 / 4T+nT)

[0055] θ0=50,θ1=10when t∈[3 / 4T+nT,T+nT)

[0056] Among them, θ0 is the initial position of the joint movement, θ1 is the stop position of the joint movement, T is the period of the optimal control curve of the wrist movement, n is the number of times the wrist movement control curve is repeated, t is the time value, d is the interval time, t1 is the moment when the joint movement stops, and t0 is the moment when the joint movement starts.

[0057] On the basis of the above technical solution, preferably, the operation process of the control system is:

[0058] The S1 tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal;

[0059] The S2 extended state observer estimates the system state and total disturbance based on the system input and output;

[0060] The S3 sliding mode controller designs nonlinear control rates based on state estimation and disturbance estimation;

[0061] The S4 dead zone nonlinear inverse function control module compensates for the nonlinear control rate and eliminates the dead zone nonlinearity of the high-speed switching valve;

[0062] The S5 adaptive combination valve executes the compensated control instructions to adjust the gas flow in the folding airbag;

[0063] The S6 encoder records the wrist joint rotation angle in real time and feeds it back to the control system to form a closed-loop control.

[0064] The present invention has the following beneficial effects compared to the prior art:

[0065] (1) By combining the advantages of ADRC and sliding mode control, the complex nonlinear problems and uncertainties in the wrist rehabilitation robot driven by a folding airbag are effectively overcome. The system can estimate and compensate for the total system disturbance in real time, while using nonlinear sliding mode control to deal with the nonlinear characteristics of the folding airbag, model inaccuracies, and external load disturbances, thereby achieving high-precision trajectory tracking control of the wrist rehabilitation robot.

[0066] (2) A tracking differentiator is used to track and differentiate the input target angle signal to generate a smooth input tracking signal and its differential signal, effectively avoiding the high-frequency noise that may be introduced by the traditional differentiator and improving the system's anti-interference ability and control accuracy;

[0067] (3) The designed extended state observer can estimate the system state and total disturbance in real time, normalize the system's "unmodeled dynamics" and "unknown external disturbances" into the system's total disturbance, and provide real-time estimation and dynamic compensation, thereby improving the system's adaptability to external disturbances and parameter changes.

[0068] (4) The proposed nonlinear sliding mode controller designs a new reaching law and uses the sigmoid function instead of the traditional sign function, which effectively reduces the system chattering phenomenon and improves the system stability and comfort;

[0069] (5) The designed dead zone nonlinear inverse function control module effectively eliminates the dead zone nonlinearity of the high-speed switching valve by compensating the nonlinear control rate output by the sliding mode controller, thereby improving the control accuracy and response speed of the system;

[0070] (6) The adaptive combination valve is used to execute control instructions and monitor the pressure inside the folding airbag, which achieves precise control of the gas flow and improves the dynamic response performance and stability of the system;

[0071] (7) The provided sine wave function generation module and minimum acceleration model generation module can generate target angle signals that conform to the motion characteristics of the human body, making the motion trajectory of the wrist rehabilitation robot closer to natural human motion, thereby improving the effect and comfort of rehabilitation training. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0073] Figure 1 It is a control system framework diagram of the present invention;

[0074] Figure 2 Schematic diagram of the curve of the fitted folding airbag gas and wrist joint rotation angle of the present invention;

[0075] Figure 3 A graph showing the relationship between the input duty cycle and the valve port effective area coefficient of the high-speed switching valve of the present invention;

[0076] Figure 4 Schematic diagram of the structure of the active disturbance rejection sliding mode composite controller of the present invention;

[0077] Figure 5 It is the sigmoid function curve graph of the present invention;

[0078] Figure 6 This is a curve diagram of the control rate u after eliminating the dead zone nonlinearity of the present invention;

[0079] Figure 7 1 is a comparison chart of the experimental results of the sinusoidal wave trajectory tracking control of the control system and the PID controller in Example 1 of the present invention;

[0080] Figure 8 This is a schematic diagram of estimating angular velocity and system disturbance during operation of the control system in Example 1 of the present invention;

[0081] Figure 9 This is a comparison chart of wrist optimal trajectory tracking control experimental results of the control system and the PID controller in Example 2 of the present invention;

[0082] Figure 10 Schematic diagram of the estimation of angular velocity and system disturbance during operation of the control system of Example 2 of the present invention. DETAILED DESCRIPTION

[0083] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0084] like Figure 1 As shown, the present invention provides an active disturbance rejection sliding mode composite control system for a wrist rehabilitation robot, wherein the wrist rehabilitation robot uses a folding airbag as a driving element, and the control system includes:

[0085] A tracking differentiator, used to track and differentiate the input target angle signal;

[0086] Extended State Observer for real-time estimation of system state and total disturbance;

[0087] Sliding mode controller for designing nonlinear control rates;

[0088] Dead zone nonlinear inverse function control module, used to compensate for the nonlinear control rate of the sliding mode controller and eliminate the dead zone nonlinearity of the high-speed switching valve;

[0089] The adaptive combination valve includes two high-speed switching valves, a control unit and a pressure sensor, which are used to execute control instructions and monitor the pressure in the folding airbag.

[0090] Specifically, the present invention proposes an active disturbance rejection sliding mode composite controller ADRSMC, which normalizes the effects of "unmodeled dynamics" and "unknown external disturbances" into the total disturbance of the system, and combines them by an extended state observer to provide real-time estimation and dynamic compensation. At the same time, a nonlinear sliding mode control rate is used to overcome the influence of factors such as strong nonlinearity of the folding airbag, inaccurate model and the existence of external load disturbance on the system.

[0091] Specifically, the wrist rehabilitation robot of the present invention uses a folding airbag as a driving element. The robot body is mainly composed of a hand support, a base, an encoder and a forearm support. When the wrist rehabilitation robot is operating, the forearm of the arm is placed on the forearm support, the wrist is placed on the hand support, and the wrist is fixed with a bandage. The folding airbag is inflated and deflated to drive the wrist to rotate along the axis. The encoder records the angle of rotation. The movable forearm support is designed to adapt to different forearm sizes.

[0092] The control system of the present invention mainly combines an anti-disturbance sliding mode composite controller and an adaptive combination valve to control the inflation and deflation flow of the folding airbag. The combination valve integrates two high-speed switching valves, a control unit, and a pressure sensor. The pressure sensor monitors the internal pressure of the folding airbag. The predefined data and pressure data are communicated to the host computer through the control unit. The air inlet of high-speed switching valve 1 (HSV1) is connected to the air compressor, and the exhaust port is connected to the airbag. When HSV1 is opened, compressed air enters the folding airbag, the volume of the folding airbag chamber increases, and the rotation angle θ f By adjusting the duty cycle of the PWM wave input to HSV1, the gas flow entering the folded airbag can be adjusted, thereby achieving the rotation angle θ f The air inlet of HSV2 is connected to the airbag. When HSV is opened, the gas inside the folded airbag is discharged to the atmosphere, the volume of the folded airbag chamber becomes smaller, and the turning angle θ f Reduce, similarly, to achieve the angle θ f Reduce acceleration control. Use a low-noise air compressor to power the wrist rehabilitation robot.

[0093] As the airbag volume increases, the wrist rotation angle increases; as the volume decreases, the rotation angle decreases, with the two showing a positive proportional relationship. Due to the irregular shape of the folded airbag and the compressibility of air, direct measurement of the airbag volume is difficult, and no relevant theoretical modeling exists. An indirect measurement scheme was proposed and a test platform was constructed to establish a mathematical model of the relationship between the folded airbag chamber volume and the wrist rotation angle. The test platform primarily consists of an air tank, an airbag, shutoff valves 1 and 2, a pressure sensor, an angle sensor, their data acquisition module, and a computer providing a human-computer interface. The test process is as follows: 1) Open stop valve 1, inflate the air tank to the pressure P1, close stop valve 1, and collect the air tank pressure at this time after the temperature stabilizes; 2) Open stop valve 2, and gas with a certain pressure in the air tank enters the airbag. After the temperature stabilizes, record the readings of the pressure sensor and the angle sensor; 3) After the recording is completed, open the air release valve to restore the initial posture of the wrist joint support; 4) Take different values ​​of the inflation pressure P1 in step 1 and repeat processes 1)-3).

[0094] According to the isothermal process: the Boyle-Mars law, when a certain mass of a gas is kept at a constant temperature, the product of pressure and volume is a constant:

[0095] P1V1=P2V2 (1)

[0096] Where P1 is the pressure of the air tank, P2 is the pressure of the air bag, and V1 is the volume of the air tank and the connecting air pipe. Using formula (1), V2 (the total volume of the air bag, air tank, and connecting air pipe) can be calculated, and thus the air bag volume V can be calculated. q .

[0097] Repeat the above test several times, and perform quadratic function fitting on the rotation angle of the wrist rehabilitation device and the calculated airbag volume to obtain the functional relationship:

[0098]

[0099] Among them, a1, a2, a3 are the coefficients of the fitting relationship:

[0100]

[0101] The curve diagram of the fitted airbag volume and wrist joint rotation angle is as follows: Figure 2 As shown, the fitting curve can well characterize V q and θ f The relationship between them.

[0102] High-speed on-off valves are usually controlled by PWM waves. The duty cycle represents the proportion of time that the high level is maintained within a PWM wave cycle. Adjusting the duty cycle can adjust the duration of the high-speed on-off valve opening, thereby adjusting the gas flow through the high-speed on-off valve. When the duration of the PWM wave high-level signal is less than the opening time of the high-speed on-off valve, the high-speed on-off valve switches to closed before it is fully opened, and appears to be closed externally. The valve effective opening area coefficient f(u) = 0. When the input duty cycle is greater than the high-speed on-off valve dead zone duty cycle u s When u=1, the valve is in a fully open state, f(u)=1.

[0103] The control system of the present invention adopts two-way high-speed switch valves to control the inflation and deflation flow respectively. Figure 3 The first quadrant curve is the relationship between the control rate u (input duty cycle) and the effective opening area coefficient of the inflation valve, and the third quadrant curve is the relationship between the control rate u and the effective opening area coefficient f(u) of the deflation valve. The relationship between the control rate u and the effective opening area coefficient f(u) of the system inflation and deflation is as follows:

[0104]

[0105] The Sanville formula is used to approximate the gas mass flow rate through the high-speed switching valve port:

[0106] q m =Q m f(u) (4)

[0107] in:

[0108]

[0109] Where: A vis the maximum effective valve port area; K = 1.4 is the air specific heat ratio, R = 287 N m / kg k is the ideal gas constant, T u is the absolute temperature of the gas source. When the folding airbag is inflated, p u is the upstream pressure of the high-speed switching valve port, that is, the pressure of the gas source, p d is the pressure downstream of the high-speed switching valve port, which is equal to the internal pressure of the folding airbag; when the folding airbag is deflated, p u is the internal pressure of the folded airbag, p d It is the downstream pressure of the high-speed valve port and is equal to atmospheric pressure.

[0110] The inflation and deflation process of the foldable airbag complies with the thermodynamic energy conservation equation, and its pressure change can be expressed as:

[0111]

[0112] Where, P q is the internal pressure of the folded airbag, q m1 is the net mass flow rate in the airbag cavity, q m1 =q m2 -q m3 , where q m2 is the mass flow rate of inflating the folded airbag, q m3 The mass flow rate for deflation of the folded airbag.

[0113] Through relevant mechanical and physical theories, the dynamic model of the airbag-driven wrist joint device can be described as:

[0114]

[0115] Where τ is the driving torque of the wrist joint, S is the contact area between the folding airbag and the base plate, r is the distance from the center point of the folding airbag to the rotation axis of the wrist joint, J is the moment of inertia of the joint wheel, and b is the rotational inertia of the joint wheel. v is the joint damping coefficient, θ f is the rotation angle of the wrist rehabilitation robot, m is the mass of the hand support plate, g is the acceleration of gravity, F h It is the force exerted on the wrist rehabilitation robot when the wrist interacts with the wrist rehabilitation robot.

[0116] Substituting equations (2), (4), and (5) into equation (6), the dynamic model of the folding airbag-driven wrist rehabilitation robot can be obtained as follows:

[0117]

[0118] The transformation of formula (7) is:

[0119]

[0120] Pick and:

[0121]

[0122] Then the state space equation of the control system is obtained as:

[0123]

[0124] Among them, is regarded as an unknown nonlinear term of the control system.

[0125] The structure of the active disturbance rejection sliding mode composite controller provided by the present invention is as follows: Figure 4 As shown, it includes a tracking differentiator, an extended state observer, a sliding mode controller, and a dead zone nonlinear inverse function control module.

[0126] Tracking differentiator TD is a nonlinear dynamic link that reasonably extracts the differential signal. The input signal θ d After the tracking differentiator, an input tracking signal θ can be obtained. r1 and a differential signal θ r2 The tracking differentiator is designed as follows:

[0127]

[0128] fhan(θ r1 -θ d ,θ r2 ,r0,h0)The specific expression is as follows:

[0129]

[0130] in:

[0131]

[0132] Where: r0 is the speed factor of the tracking differentiator. The larger r0 is, the faster the tracking speed is. It is determined by the speed of the transition process and the limit capability of the system. h0 is the filter factor of the differential tracker. The value of h0 needs to comprehensively consider the filtering effect and the limit tracking speed of the system. θ d is the input target angle signal of the tracking differentiator; θ r1 is the input tracking signal of the tracking differentiator; θ r2 is θ r1 The differential signal.

[0133] The extended state observer (ESO) is used to estimate state variables and unknown nonlinear terms. In formula (10), As the state variable of the expansion state machine, The derivative of Right now Then formula (10) is rewritten as:

[0134]

[0135] The third-order ESO design is as follows:

[0136]

[0137] Where ε1 is the angle observation value and output angle The error, and They are and The estimated value of β 01 , β 02 and β 03 are the gain coefficients of the extended state observer; fal(ε i ,a i ,δ) function is defined as follows:

[0138]

[0139] in, i=1,2,3.

[0140] Tracking the θ generated by the differentiator r1 ,θ r2 Signal and ESO generated estimates This results in errors e1 and e2.

[0141]

[0142] In order to achieve rapid convergence of the system state within a limited time, the terminal sliding mode function is selected as follows:

[0143]

[0144] η>0, and 0

[0145] Derivative of the sliding surface s:

[0146]

[0147] The present invention adds a system state variable x to represent the distance from the system state point to the sliding surface, and the proposed convergence rate is as follows:

[0148]

[0149] Where x represents the system state, which is used to represent the distance from the system state point to the sliding surface, and α is a variable coefficient.​

[0150] like Figure 5 As shown in Figure 1, as the system trajectory approaches the sliding mode surface, the variable gain term |x| / |x|+α of the approach rate gradually decreases and eventually converges to zero. In addition, λ1|x| / |x|+α is always less than λ1, which can further suppress sliding mode chattering.

[0151] The traditional exponential reaching law uses the sign(s) function, requiring the controller to have an infinite switching frequency. However, this is not practically achievable, resulting in the actual sliding mode motion state not being able to accurately reach the pre-designed sliding surface, and traversing back and forth on the sliding surface, thus generating chattering. The present invention uses the sigmoid(s) function for the reaching rate, with the parameter c determining the smooth continuity of the sigmoid(s) function. The sliding mode reaching law utilizes the smoothness of the sigmoid(s) function to improve the system chattering caused by the high switching frequency of the traditional exponential reaching law.

[0152] The sliding mode control rate f can be obtained by combining equations (16) and (17) u for:

[0153]

[0154] In order to illustrate the stability of the designed sliding mode controller, the Lyapunov function is selected:

[0155]

[0156] Taking the derivative of formula (19), we can get:

[0157]

[0158] It can be seen from this that the system meets the reachability condition, the controller is stable, and the system can converge to the sliding mode surface (s=0) from any point outside the sliding mode surface (s≠0) within a finite time, that is, the system state tracking error can always converge to zero within a finite time.

[0159] Due to the inherent time characteristics of the high-speed switching valve opening / closing, there are some problems during the charging and discharging process. Figure 3 The typical dead zone nonlinearity is shown, and the dead zone time consistency of different valves is good. The present invention sets a dead zone nonlinear inverse function control module, takes the effective opening area coefficient f(u) of the inflation and deflation valve output by the sliding mode controller as input, and calculates the dead zone nonlinearity of the inverse function control module through f -1 (f(u)) is used as the input duty cycle command u for the high-speed on / off valve control of the gas charging and discharging valve to eliminate the dead zone nonlinearity of the high-speed on / off valve, such as Figure 6 As shown. The expression of control rate u is:

[0160]

[0161] When f(u)>0, the control rate u1=u is obtained, which serves as the input duty cycle of the high-speed switching valve to control the inflation flow of the folding airbag; when f(u)<0, the control rate u2=-u is obtained, which serves as the input duty cycle of the high-speed switching valve to control the deflation flow of the folding airbag.

[0162] Specifically, the control system of the present invention further includes:

[0163] Sine wave function generation module, used to generate target angle signal:

[0164] θ d =A sin(πft-0.5π)+B (22)

[0165] Among them, θ d is the target angle signal, A=25 is the amplitude of the sine wave, f=0.025Hz is the frequency of the sine wave, and B=35 is the offset of the sine wave angle.

[0166] The minimum acceleration model generation module is used to generate the optimal wrist motion curve. The minimum acceleration model satisfies the following mathematical rules:

[0167]

[0168] Where t0 is the start time of joint movement, θ0 is the initial position of joint movement, t1 is the stop time of joint movement, θ1 is the stop position of joint movement, is the joint angular acceleration, which is the third-order derivative of the joint angle with respect to time.

[0169] Combined with the minimum acceleration model, the optimal joint angle curve is obtained through variational transformation:

[0170]

[0171] Maintain a certain delay time of 1 / 4T at the lowest position and the highest position respectively, and finally obtain the optimal wrist motion control curve law as follows:

[0172]

[0173] Among them, θ0 is the initial position of the joint movement, θ1 is the stop position of the joint movement, T is the period of the optimal control curve of the wrist movement, n is the number of times the wrist movement control curve is repeated, t is the time value, d is the interval time, t1 is the moment when the joint movement stops, and t0 is the moment when the joint movement starts.

[0174] The operation process of the control system provided by the present invention is:

[0175] The S1 tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal;

[0176] The S2 extended state observer estimates the system state and total disturbance based on the system input and output;

[0177] The S3 sliding mode controller designs nonlinear control rates based on state estimation and disturbance estimation;

[0178] The S4 dead zone nonlinear inverse function control module compensates for the nonlinear control rate and eliminates the dead zone nonlinearity of the high-speed switching valve;

[0179] The S5 adaptive combination valve executes the compensated control instructions to adjust the gas flow in the folding airbag;

[0180] The S6 encoder records the wrist joint rotation angle in real time and feeds it back to the control system to form a closed-loop control.

[0181] Specifically, in order to verify the effect of the active disturbance rejection sliding mode composite control system proposed in the present invention, a comparative experiment was carried out between the active disturbance rejection sliding mode composite controller ADRSMC of the present invention and the traditional PID controller. A total of two groups of experiments were conducted to form two embodiments. In the two groups of experiments, the parameters of the ADRSMC and PID controllers are shown in Tables 1 and 2.

[0182] Table 1 ADRSMC parameters

[0183]

[0184]

[0185] Table 2 PID parameters

[0186] kp ki kd 0.1 0.5 0.001

[0187] Example 1

[0188] The first set of experiments is the sinusoidal wave trajectory tracking control experiment. The experimental results of ADRSMC and PID control are shown in the following figure. Figure 7 As shown, Figure 7 (a) is the experimental curve of ADRSMC trajectory tracking control when there is no load. Figure 7 (b) is the error between ADRSMC and PID control when there is no load. Figure 7 (c) is the experimental curve of PID trajectory tracking control when there is no load. Figure 7 (d) is the experimental curve of ADRSMC trajectory tracking control when there is load force. Figure 7 (e) is the experimental curve ADRSMC of trajectory tracking control and PID control error, Figure 7 (f) in the figure is the experimental curve of PID trajectory tracking control when there is load force. The results of ESO estimation of angular velocity and disturbance in the experiment are as follows: Figure 8As shown, Figure 8 (a) in the equation is the angular velocity estimation. Figure 8 (b) in the figure is the perturbation estimate.

[0189] Depend on Figure 7 and Figure 8 It can be seen that no matter there is no load or there is a load force, the actual output θf zero load and θf load can quickly and accurately reach the command input θd.

[0190] The output of the tracking differentiator θr1 accurately tracks the given θd, the rotation angle observation value It is almost consistent with θf zero load and θf load. Figure 8 In (a), it can be seen that the ESO in ADRSMC is affected by the angular velocity observation, regardless of whether there is no load or a load. The angular velocity θr2 output through the TD process can always be tracked. Figure 8 (b) shows the nonlinear uncertainty terms when there is no load and when there is a load force. The results show that the observed disturbance value It changes with the load, which is consistent with the actual situation.

[0191] During the initial tracking phase, the ADRSMC tracking error was maximum (1.69°) without load and 1.03° with load. The corresponding errors for the PID control were 7.29° and 2.51°, respectively. The maximum error for the ADRSMC control was smaller than that for the PID control in both test scenarios. This is because the ADRSMC control introduces a tracking differentiator (TD) that outputs a transient signal, θr1, which better matches the system's initial capabilities.

[0192] Figure 7 (a) Figure 7 (d) and Figure 7 (c) Figure 7 By comparing (f) in the figure, it can be seen that when there is no load and with load force, the response time of ADRSMC to reach a stable state is shorter than that of PID controller. After ADRSMC reaches a stable state, the root mean square error (RSME) and mean absolute error (MAE) are smaller than those of PID, as shown in Table 3.

[0193] Table 3 Sine wave trajectory tracking control performance

[0194]

[0195] When PID is used as a controller, under no-load conditions, the output curve will experience high-frequency vibration when tracking the sine wave instruction (see Figure 7In (c), when there is load force, PID is used as the controller and the high frequency vibration is weakened (see Figure 7 (f)); When ADRSMC is used as a controller, no high-frequency vibration occurs when there is no load or a load force; at the peak of the sine wave curve, the output signal can quickly track the given signal and can adapt well to changes in control conditions (see Figure 7 (a) and Figure 7 (d)). However, when there is no load or a load force, the output signal of PID has a certain delay compared with the given signal, and the controller parameters cannot adapt to the change of the target value (see Figure 7 (c) and Figure 7 Sine command tracking experiments show that ADRSMC has better control effects than PID in terms of response time, stability, and accuracy.

[0196] Example 2

[0197] The second group of experiments is the trajectory tracking control experiment of the optimal wrist motion curve. The experimental results are as follows: Figure 9 As shown, Figure 9 (a) is the experimental curve of the optimal trajectory tracking control of the ADRSMC wrist when there is no load. Figure 9 (b) is the error between ADRSMC and PID control when there is no load. Figure 9 (c) is the experimental curve of the optimal trajectory tracking control of the PID wrist when there is no load. Figure 9 (d) is the experimental curve of the optimal trajectory tracking control of the ADRSMC wrist when there is load force. Figure 9 (e) is the experimental curve ADRSMC of wrist optimal trajectory tracking control and PID control error, Figure 9 (f) is the experimental curve of the optimal trajectory tracking control of the PID wrist when there is a load force. The results of the ESO estimation of angular velocity and disturbance in the experiment are as follows: Figure 10 As shown, Figure 10 (a) in the equation is the angular velocity estimation. Figure 10 (b) in the figure is the perturbation estimate.

[0198] The root mean square error (RSME) and mean absolute error (MAE) of the ADRSMC and PID controllers under given signals are shown in Table 4.

[0199] Table 4 Wrist optimal curve trajectory tracking control performance

[0200]

[0201]

[0202] from Figure 9 、 Figure 10As can be seen from Table 4, the results of Example 2 are similar to those of Example 1. ADRSMC is superior to PID in terms of tracking time to reach a stable state, stability, and accuracy.

[0203] In summary, the present invention provides a wrist rehabilitation robot using a foldable airbag as its driving element. Due to its use of flexible materials as a driver, the overall device is lightweight and compact. When the wrist becomes uncomfortable with its current bending angle, the airbag easily compresses, allowing the wrist to maintain a certain positional deviation from the commanded value, thus enhancing the comfort of the subject during rehabilitation training. The manufacturing cost of the foldable airbag is lower than that of pneumatic muscles and motors, resulting in a lower overall device price.

[0204] Because the flexible material of the folded airbag is used as the actuator, its compressibility and the nonlinear effects of the control elements make control difficult. The examples provided by this invention demonstrate that the ADRSMC can overcome the effects of nonlinearity, achieving overall control accuracy within ±1° and achieving good control results. At the peak of the sine wave, when the subject participates in rehabilitation training, the ADRSMC tracking trajectory exhibits some fluctuation. This is because when the human wrist joint moves to its extreme angle, a nonlinear resistance interference is generated, affecting the tracking accuracy of the rehabilitation device. The ADRSMC estimates the magnitude of this interference force in real time through the ESO and compensates for it in the SMC controller, thereby improving control accuracy at the peak position. During the wrist optimal curve trajectory tracking process, when the ADRSMC controller was used for no-load testing, when the command angle was less than 10°, the tracking accuracy under load was significantly improved compared to the no-load state. This is mainly due to the low internal pressure of the airbag under no-load conditions, resulting in a deflation rate lower than the command speed. However, when the subject participates in rehabilitation training, the airbag compresses, generating pressure, accelerating the deflation rate, thereby improving control accuracy during this process. In future work, the deflation valve can be replaced with a negative pressure pump to increase the deflation rate and achieve even better angle control accuracy.

[0205] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An active disturbance rejection sliding mode composite control system for a wrist rehabilitation robot, characterized in that: The wrist rehabilitation robot uses a folding airbag as a driving element. The control system includes: Tracking differentiator, used to track and differentiate the input target angle signal; Extended State Observer for real-time estimation of system state and total disturbance; Sliding mode controller for designing nonlinear control rates; Dead zone nonlinear inverse function control module, used to compensate for the nonlinear control rate of the sliding mode controller and eliminate the dead zone nonlinearity of the high-speed switching valve; Adaptive combination valve, including two high-speed switching valves, a control unit and a pressure sensor, used to execute control instructions and monitor the pressure inside the folding airbag; The energy conservation equation of the folded airbag is: Where, P q is the internal pressure of the folded airbag, q m1 is the net mass flow rate in the airbag cavity, q m1 =q m2 -q m3 , where q m2 is the mass flow rate of inflating the folded airbag, q m3 is the mass flow rate of the folded airbag deflation, K is the air specific heat ratio, R is the ideal gas constant, V q is the volume of the folded airbag, T u For temperature.

2. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 1, characterized in that: The mathematical model of the high-speed switching valve is: Among them, f(u) is the effective opening area coefficient of the valve, u is the input duty cycle, and u s is the dead-band duty cycle.

3. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 1, characterized in that: The dynamic model of the folding airbag-driven wrist rehabilitation robot is: Where θ f is the rotation angle of the wrist rehabilitation robot, r is the distance from the center of the folded airbag to the wrist joint rotation axis, S is the contact area between the folded airbag and the base plate, K is the air specific heat ratio, R is the ideal gas constant, T is the temperature, q m is the mass flow rate of the gas in the folding airbag, J is the moment of inertia of the joint rotor, f(u) is the effective opening area coefficient of the valve, b v is the joint damping coefficient, m is the mass of the hand support plate, g is the acceleration of gravity, F h is the force exerted on the wrist rehabilitation robot when the wrist interacts with it, b0 is a constant term, a1, a2, and a3 are fitting coefficients used to fit the volume V of the folded airbag q The rotation angle θ of the wrist rehabilitation robot f Functional relationship: make and: Then the state space equation of the control system is: Among them, is regarded as an unknown nonlinear term of the control system.

4. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 3, characterized in that: The tracking differentiator is designed as follows: fhan(θ r1 -θ d ,θ r2 ,r0,h0)The specific expression is as follows: in: Where: r0 is the speed factor of the tracking differentiator. The larger r0 is, the faster the tracking speed is. h0 is the filter factor of the differential tracker. θ d is the input target angle signal of the tracking differentiator; θ r1 is the input tracking signal of the tracking differentiator; θ r2 is θ r1 The differential signal.

5. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 4, characterized in that: The unknown nonlinear terms of the control system As the state variable of the extended state observer, let The derivative of Right now The third-order extended state observer is designed as follows: Where ε1 is the angle observation value and output angle The error, and They are and The estimated value of β 01 , β 02 and β 03 are the gain coefficients of the extended state observer; fal(ε i ,a i ,δ) function is defined as follows: in, i=1,2,3.

6. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 5, characterized in that: The nonlinear control rate of the sliding mode controller is as follows: where, f u is the sliding mode control rate; s is the sliding mode surface; e1 and e2 are the errors between the θ r1 , θ r2 signals generated by the tracking differentiator and the estimated values generated by the extended state observer; η > 0, and 0 < q / p < 1, where p and q are both positive numbers; λ1 and λ2 are the coefficients of the reaching law, and the reaching law is as follows: Where x represents the system state, which is used to represent the distance from the system state point to the sliding surface, and α is a variable coefficient. is the variable gain term of the convergence rate, and c is the control parameter used to control the smooth continuity of sigmoid(s).

7. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 1, characterized in that: The dead zone nonlinear inverse function control module takes the effective opening area coefficient f(u) of the inflation and deflation valve output by the sliding mode controller as input, and uses f -1 (f(u)) is used as the input duty cycle command u for the high-speed on-off valve for charging and discharging to eliminate the dead zone nonlinearity of the high-speed on-off valve. The expression of the control rate u is: When f(u)>0, the control rate u1=u is obtained, which serves as the input duty cycle of the high-speed switching valve to control the inflation flow of the folding airbag; when f(u)<0, the control rate u2=-u is obtained, which serves as the input duty cycle of the high-speed switching valve to control the deflation flow of the folding airbag.

8. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 1, characterized in that: The control system further comprises: Sine wave function generation module, used to generate target angle signal: i d =Asin(πft-0.5π)+B Among them, θ d is the target angle signal, A=25 is the amplitude of the sine wave, f=0.025Hz is the frequency of the sine wave, and B=35 is the offset of the sine wave angle; Minimum acceleration model generation module, used to generate the optimal wrist motion curve: θ0=10,θ1=10when t∈[nT,1 / 4T+nT) θ0=10,θ1=50when t∈[1 / 4T+T,1 / 2T+nT) θ0=50,θ1=50when t∈[1 / 2T+nT,3 / 4T+nT) θ0=50,θ1=10when t∈[3 / 4T+nT,T+nT) Among them, θ0 is the initial position of the joint movement, θ1 is the stop position of the joint movement, T is the period of the optimal control curve of the wrist movement, n is the number of times the wrist movement control curve is repeated, t is the time value, d is the interval time, t1 is the moment when the joint movement stops, and t0 is the moment when the joint movement starts.

9. The active disturbance rejection sliding mode composite control system of a wrist rehabilitation robot according to claim 1, characterized in that: The operation process of the control system is as follows: The S1 tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal; The S2 extended state observer estimates the system state and total disturbance based on the system input and output; The S3 sliding mode controller designs nonlinear control rates based on state estimation and disturbance estimation; The S4 dead zone nonlinear inverse function control module compensates for the nonlinear control rate and eliminates the dead zone nonlinearity of the high-speed switching valve; The S5 adaptive combination valve executes the compensated control instructions to adjust the gas flow in the folding airbag; The S6 encoder records the wrist joint rotation angle in real time and feeds it back to the control system to form a closed-loop control.

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