Flexible actuator, design and control method based on time-varying disturbance and continuous sliding mode

Abstract

The present invention relates to the field of robot control driven by a flexible actuator, and discloses a flexible actuator based on time-varying disturbance and continuous sliding film, including a first observer, a second observer, a first continuous sliding film controller, and a second continuous sliding film controller. The present invention also discloses a design method and a control method of a flexible actuator based on time-varying disturbance and continuous sliding film. The present invention uses a sliding mode controller, which can improve the anti-interference performance of the system from the feedback channel, and the observer uses a reduced-order observer, which can not only complete the function of disturbance estimation, but also reduce the calculation burden when the algorithm is implemented.

Description

Technical Field

[0001] The present invention relates to the field of robot control driven by a flexible actuator, and in particular to a flexible actuator based on time-varying disturbance and continuous sliding mode, and a design and control method thereof. Background Art

[0002] With the rapid development of robotics technology, robots driven by flexible actuators have received much attention in the industrial and aerospace fields. Flexible actuator-driven robots have the characteristics of high load, light weight, and low power consumption. However, due to the particularity of its structure, the robot arm will deform and vibrate during movement, which brings many problems to the positioning and tracking control of the flexible actuator-driven robots. From the perspective of the application field and scope of flexible actuator-driven robots, their work tasks are diverse and the working environment changes with the work tasks. Therefore, flexible actuator-driven robots not only require high-precision position control, but also need to have the ability to resist various disturbances in the unknown working environment.

[0003] Traditional flexible actuator-driven robots use the PD control method, which is relatively common and easy to implement. However, the actual flexible actuator-driven robot system is a nonlinear system. Since the dynamic model of the entire system is difficult to include all dynamic factors, there are a large number of unmodeled dynamic factors in the control system of the flexible actuator-driven robot. To solve this problem, a large number of researchers have proposed different control strategies. However, these control methods do not reasonably eliminate the uncertainty of the system and the influence of external disturbances.

[0004] Therefore, there is an urgent need to design a control system for a robot driven by a flexible actuator based on matching / non-matching time-varying disturbance compensation and continuous sliding mode control, which can enable the system to have good position tracking performance and a certain degree of anti-interference ability. Summary of the invention

[0005] The present invention provides a flexible actuator based on time-varying disturbance and continuous sliding mode, a design and control method, based on the mathematical model of a robot driven by a flexible actuator, the expression form is changed and simplified to facilitate control, and a continuous sliding mode controller is designed without disturbance; secondly, two reduced-order generalized proportional integral observers are designed using the measurable information of the system, which are respectively used to observe the matching / non-matching time-varying disturbances existing in the robot system driven by the flexible actuator; finally, the disturbance estimation values ​​of the two reduced-order generalized proportional integral observers are fed forward to the continuous sliding mode controller to form a composite controller. Compared with the traditional cascade linear control strategy, this method is easy to implement and has good anti-interference performance and convergence speed. At the same time, the control method of the present invention can be applied to many different types of interference suppression situations.

[0006] The present invention is achieved through the following technical solutions:

[0007] A flexible actuator based on time-varying disturbance and continuous sliding mode, comprising:

[0008] The first observer receives the actual position signal q on the arm side and the actual position signal θ on the motor side transmitted by the generalized object module, and obtains the arm side disturbance estimation signal according to the actual position signal q on the arm side, the actual position signal θ on the motor side and the arm side time-varying disturbance signal ρ1

[0009] The second observer receives the actual position signal θ of the motor side and the output torque τ of the composite anti-interference motor side position controller transmitted by the generalized object module, and obtains the motor side disturbance estimation signal according to the actual position signal θ of the motor side, the output torque τ of the composite anti-interference motor side position controller and the motor side time-varying disturbance signal ζ1

[0010] The first continuous sliding mode controller: According to the input arm side reference position signal q r , arm side actual position signal q and arm side disturbance estimation signal Get the motor side reference position signal θ r ;

[0011] The second continuous sliding mode controller: According to the motor side reference position signal θ r , the actual position signal θ on the motor side and the disturbance estimation signal on the motor side Get the input torque that drives the generalized object module

[0012] As an optimization, the first observer and the second observer are both reduced-order generalized proportional-integral observers, namely, ROGPIO observers, and the reduced-order generalized proportional-integral observers are:

[0013]

[0014] Among them, z2, z3, …, z p+2 is the state variable of the ROGPIO observer, u is the control input, They are They are The estimated value of β i >0, (i=0, 2, ..., p+1) are the coefficients of the reduced-order generalized proportional-integral observer, which are parameters that need to be adjusted through the simulation output results and are undetermined parameters; p represents the order of the system, and the state equation of the system where the reduced-order generalized proportional-integral observer is located is:

[0015]

[0016] where x1, x2, …, x n is the system state, u is the control input, b is the system parameter, ξ is the total time-varying disturbance,

[0017] As an optimization, the expression of the first continuous sliding mode controller in the absence of disturbance is:

[0018] θ r1 =(u eq1 +u v1 );

[0019]

[0020] Among them, θ r1 is the motor side reference position signal output by the first continuous sliding mode controller under the condition of no disturbance; 1，1 =q r -q, c 1,1 >0,c 1,2 >0; k>0, sgn(·) is the standard sign function, q is the actual position signal of the arm side; is the first-order differential of the arm-side reference position signal; is the first-order differential of the actual arm side position signal; is the second-order differential of the actual position signal q on the arm side, for u v1 The first-order differential of , σ1 is the continuous sliding mode surface of the first continuous sliding mode controller, where c 1，1 , c 1，2 , k are the corresponding first continuous sliding mode controller coefficients respectively;

[0021] The state equation of the system of the first continuous sliding mode controller in the absence of disturbance is:

[0022]

[0023] Where x1 = q, θ is the actual position signal on the motor side, ρ1 is the time-varying disturbance signal on the arm side, is the first-order differential of x2.

[0024] As an optimization, the first observer and the first continuous sliding mode controller constitute a composite anti-interference arm side position controller, and the expression of the composite anti-interference arm side position controller is:

[0025]

[0026] in, is the disturbance estimation signal of the first reduced-order generalized proportional-integral observer, that is, is the estimated signal of the arm side time-varying disturbance signal ρ1, θ r It is the motor side reference position signal output by the composite anti-interference arm side position controller.

[0027] As an optimization, the expression of the second continuous sliding mode controller in the absence of disturbance is:

[0028] τ1=J(u eq2 +u v2 );

[0029]

[0030] Where τ1 is the output torque of the second continuous sliding mode controller in the absence of disturbance; e 2,1 =θ r -θ c 2，1 >0,c c2,2 >0; v>0, v is an adjustable parameter of the second continuous sliding mode controller, that is, v is an undetermined parameter of the second continuous sliding mode controller, and its specific value needs to be adjusted through simulation, and its size affects the anti-disturbance performance. sgn(·) is a standard sign function, which is the actual position signal on the motor side; is the first-order differential of the actual position signal θ on the motor side; θ r It is the reference position signal of the input motor side; The reference position signal θ is input to the motor side r is the first-order differential of ; σ2 is the continuous sliding mode surface of the second continuous sliding mode controller, The reference position signal θ is input to the motor side r The second-order differential of for u v2 The first-order differential of , where c 2,1 ,c 2,2 , v are the corresponding second continuous sliding mode controller coefficients, J is the motor inertia coefficient; J is the motor inertia coefficient;

[0031] The state equation of the system of the second continuous sliding mode controller in the absence of disturbance is:

[0032]

[0033] Where x1 = θ, is the actual position signal on the motor side, τ1 is the output torque of the second continuous sliding mode controller without disturbance, ζ1 is the time-varying disturbance signal on the motor side.

[0034] As an optimization, the second observer and the second continuous sliding mode controller constitute a composite anti-interference motor side position controller, and the expression of the composite anti-interference motor side position controller is:

[0035]

[0036] in, is the output torque of the motor side position controller output by the composite anti-interference motor side position controller, is the disturbance estimation signal of the second reduced-order generalized proportional-integral observer, that is, is the estimated signal of the time-varying disturbance signal ζ1 on the motor side.

[0037] The present invention also discloses a design method of a flexible actuator based on time-varying disturbance and continuous sliding mode, comprising:

[0038] S1. Based on the mathematical model of the robot driven by the flexible actuator, a first continuous sliding mode controller and a second continuous sliding mode controller are designed without disturbance;

[0039] S2. Designing a first reduced-order generalized proportional integral observer and a second reduced-order generalized proportional integral observer using measurable information of the system, wherein the first reduced-order generalized proportional integral observer and the second reduced-order generalized proportional integral observer are used to observe matching / non-matching time-varying disturbances existing in the system where the robot driven by the flexible actuator is located and obtain corresponding disturbance estimates;

[0040] S3, the actual arm position signal q in the system where the flexible actuator drives the robot is fed back to the first continuous sliding mode controller, the first reduced-order generalized proportional integral observer feeds forward the obtained arm disturbance estimation signal to the first continuous sliding mode controller, and the first continuous sliding mode controller combines the arm reference signal q r Get the motor side reference position signal θ r ;

[0041] S4, feeding back the actual position signal θ of the motor side in the system where the flexible actuator-driven robot is located to the second continuous sliding mode controller, and at the same time, the second reduced-order generalized proportional integral observer feeds forward the disturbance estimation signal of the motor side to the second continuous sliding mode controller, and the second continuous sliding mode controller combines the reference position signal θ of the motor side r Get the output torque of the robot The robot operates by driving flexible actuators.

[0042] As an optimization, the first reduced-order generalized proportional-integral observer is:

[0043]

[0044] Among them, z1，2 , z 1，3 , z 1，4 is the observer state variable, They are The estimated value of β 1，1 >0,β 1，2 >0,β 1，3 >0;β 1，1 , β 1，2 , β 1，3 are the parameters of the first reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, and θ is the actual position signal on the motor side.

[0045] As an optimization, the second reduced-order generalized proportional integral observer is:

[0046]

[0047] Among them, z 2，2 , z 2，3 , z 2，4 is the state variable of the second reduced-order generalized proportional-integral observer, They are The estimated value of β 2，1 >0,β 2，2 >0,β 2，3 >0;β 2，1 , β 2，2 , β 2，3 β 1，3 are the parameters of the second reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, θ is the actual position signal on the motor side, is the input torque.

[0048] The present invention also discloses a control method of a flexible actuator based on time-varying disturbance and continuous sliding mode, and uses the flexible actuator based on time-varying disturbance and continuous sliding mode to control a robot, comprising:

[0049] The first observer obtains the actual position signal q of the robot's arm side and the actual position signal θ of the motor side, and obtains the arm side disturbance estimation signal according to the actual position signal q of the arm side, the actual position signal θ of the motor side and the arm side time-varying disturbance signal ρ1.

[0050] The second observer obtains the actual position signal θ of the robot's motor side and the output torque τ of the composite anti-interference motor side position controller, and obtains the motor side disturbance estimation signal according to the actual position signal θ of the motor side, the output torque τ of the composite anti-interference motor side position controller and the motor side time-varying disturbance signal ζ1.

[0051] The first continuous sliding mode controller inputs the arm side reference position signal q r , the actual position signal q of the arm side and the disturbance estimation signal of the arm side to obtain the reference position signal θ of the motor side r ;

[0052] The second continuous sliding mode controller is based on the motor side reference position signal θ r , the actual position signal θ on the motor side and the disturbance estimation signal on the motor side to obtain the input torque on the input arm side of the driving robot

[0053] According to the input torque The present invention has the following advantages and beneficial effects compared with the prior art:

[0054] 1. Compared with the traditional cascade linear control strategy, the present invention is easy to implement and has good anti-interference performance and convergence speed. At the same time, the control method of the present invention can be applied to various types of interference suppression situations.

[0055] 2. The present invention uses a sliding mode controller, which can improve the anti-interference performance of the system from the feedback channel. The observer uses a reduced-order observer, which can not only complete the function of disturbance estimation, but also reduce the computational burden when implementing the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0057] Figure 1 This is a schematic diagram of the traditional PD control system principle;

[0058] Figure 2 It is a schematic diagram of the principle of a robot driven by a flexible actuator;

[0059] Figure 3 It is the overall principle block diagram of the flexible actuator of the present invention;

[0060] Figure 4 It is a comparison diagram of the simulation results of the arm side position output of the robot under the traditional control method and the control method of the present invention;

[0061] Figure 5 It is a comparison diagram of the simulation results of the position output of the robot motor side under the traditional control method and the control method of the present invention;

[0062] Figure 6 It is a comparison diagram of the simulation results of the arm side position error output under the traditional control method and the control method of the present invention;

[0063] Figure 7 and Figure 8 is a graph of the output result of the first observer under the control mode of the present invention;

[0064] Fig. 9 and Fig.10 It is a diagram of the output result of the second observer under the control mode of the present invention. DETAILED DESCRIPTION

[0065] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0066] First, the mathematical model of the robot driven by the flexible actuator of the present invention is introduced as follows:

[0067]

[0068] Among them, q is the actual position signal of the arm side, is the first-order differential of the actual position signal q on the arm side, is the second-order differential of the actual position signal q on the arm side, θ is the actual position signal on the motor side, is the first-order differential of the actual position signal θ on the motor side, The second-order differential of the actual position signal θ on the motor side, is the input torque on the arm side; M(q) is the generalized moment of inertia, are the Coriolis force and centripetal force, G(q) is the gravitational torque; K is the joint stiffness coefficient, J is the motor inertia coefficient, B is the damping coefficient; D1 is the external disturbance on the arm side, and D2 is the external disturbance on the motor side.

[0069] In order to facilitate the control of the robot driven by the flexible actuator, it is expressed as follows:

[0070]

[0071] Finally, it can be simplified into the following model:

[0072]

[0073] Among them, M -1 (q) K = 1, ρ1=-M -1 (q)Kq-M -1 (q)G(q)+M-1 (q)D1, ρ1 is the time-varying disturbance signal on the arm side; ζ1 is the time-varying disturbance signal on the motor side.

[0074] Next, a design method of a flexible actuator based on time-varying disturbance and continuous sliding mode of the present invention is introduced.

[0075] Example 1

[0076] The present invention also provides a design method for a flexible actuator based on time-varying disturbance and continuous sliding mode, comprising:

[0077] S1. Based on the mathematical model of the robot driven by the flexible actuator, a first continuous sliding mode controller and a second continuous sliding mode controller are designed without disturbance;

[0078] S2. Designing a first reduced-order generalized proportional integral observer and a second reduced-order generalized proportional integral observer using measurable information of the system, wherein the first reduced-order generalized proportional integral observer and the second reduced-order generalized proportional integral observer are used to observe matching / non-matching time-varying disturbances existing in the system where the robot driven by the flexible actuator is located and obtain corresponding disturbance estimates;

[0079] S3, the actual arm position signal q in the system where the flexible actuator drives the robot is fed back to the first continuous sliding mode controller, the first reduced-order generalized proportional integral observer feeds forward the obtained arm disturbance estimation signal to the first continuous sliding mode controller, and the first continuous sliding mode controller combines the arm reference signal q r Get the motor side reference position signal θ r ;

[0080] S4, feeding back the actual position signal θ of the motor side in the system where the flexible actuator-driven robot is located to the second continuous sliding mode controller, and at the same time, the second reduced-order generalized proportional integral observer feeds forward the disturbance estimation signal of the motor side to the second continuous sliding mode controller, and the second continuous sliding mode controller combines the reference position signal θ of the motor side r Get the output torque of the robot The robot operates by driving flexible actuators.

[0081] According to the general system composed of flexible actuators and robots:

[0082]

[0083] where x1, x2, …, x n is the system state, u is the control input, y is the control output, b is the system parameter, ξ=f(x1,x2,…x n, w(t), t) is an uncertain parameter, which is the total time-varying disturbance of the system, including unknown parameters, environmental variables, chattering, unmodeled dynamics, etc., and w(t) is the external disturbance of the system;

[0084] The continuous sliding surface can be designed as The continuous sliding mode controller is designed as u = b -1 (u eq +u v ),u eq =c n x n +…+c2x2+c1x1, where sgn(·) is the standard sign function, k>0, c i >0, i=1, 2, …n, where k is the same as v, in other words, and is related to the anti-disturbance performance of the continuous sliding mode controller, c is related to the convergence speed, n is the system order, and for this model p=n=2.

[0085] The design process of the first continuous sliding mode controller without disturbance is as follows:

[0086] For the above simplified model, the following system state equation can be obtained:

[0087]

[0088] Where x1 = q, θ is the actual position signal on the motor side, ρ1 is the time-varying disturbance signal on the arm side, is the first-order differential of x2, θ is in the second-order system model, and it is written as a state equation in this form. ρ1 is the actual time-varying disturbance, is an estimate of it.

[0089] The continuous sliding surface of the first continuous sliding mode controller is The first continuous sliding mode control law is designed as θ r1 =(u eq1 +u v1 ), Among them, θ r1 is the motor side reference position signal output by the first continuous sliding mode controller under the condition of no disturbance; 1，1 =q r -q, c 1，1 >0,c 1，2 >0; k>0, k is an adjustable parameter that affects the anti-disturbance performance of the first continuous sliding mode controller, sgn(·) is a standard sign function, and q is the actual position signal of the arm side; is the first-order differential of the arm-side reference position signal; is the first-order differential of the actual arm side position signal; is the second-order differential of the actual position signal q on the arm side, for u v1 The first-order differential of , σ1 is the continuous sliding mode surface of the first continuous sliding mode controller, where c 1，1 , c 1，2 , k are the coefficients of the corresponding first continuous sliding mode controller (k is the anti-disturbance performance parameter of the first continuous sliding mode controller). The controller coefficient is a parameter that needs to be set, and its size needs to be adjusted according to the simulation results, analogous to the kp and kd items of pd control. This is a routine operation of those skilled in the art and will not be repeated here.

[0090] The design process of the second continuous sliding mode controller without disturbance is as follows:

[0091] For the simplified model above, the following system state equation can be obtained:

[0092]

[0093] where x1 = θ, is the actual position signal on the motor side, τ1 is the output torque of the second continuous sliding mode controller without disturbance,

[0094] The continuous sliding mode surface of the second continuous sliding mode controller is designed as: The second continuous sliding mode control law is designed as: τ1 = J(u eq2 +u v2 ), where e 2，1 =θ r -θ, c 2，1 >0,c 2，2 >0;v>0,c 2,1 ,c 2,2 ,v are the corresponding coefficients of the second continuous sliding mode controller respectively. v is an adjustable parameter of the second continuous sliding mode controller, that is, v is an undetermined parameter of the second continuous sliding mode controller. Its specific value needs to be adjusted through simulation, and its size affects the anti-disturbance performance. sgn(·) is a standard sign function.

[0095] Next, the reduced-order generalized proportional-integral observer is designed:

[0096] Considering the time-varying disturbance of the system, the system state equation is rewritten as:

[0097]

[0098] where x1, x2, …, x nis the system state, u is the control input, where u is a generic input. For this application, the control input u specifically refers to the actual position θ and input torque τ of the motor side, and b is the system parameter. The determination of the system parameter b depends on the definition of the system model. For this system, b is 1 and j respectively. -1 (see the corresponding state equation), is a known physical parameter, ξ is the total time-varying disturbance of the system, including unknown parameters, environmental variables, chattering, unmodeled dynamics, etc.,

[0099] According to the above state equation, the reduced-order generalized proportional integral observer is designed as:

[0100]

[0101] Among them, z2, z3, …, z p+2 is the observer state variable, u is the control input, They are They are The estimated value of β i >0, (i=0, 2, ..., p+1) are the coefficients of the reduced-order generalized proportional-integral observer, and p represents the order of the system. For example, for a second-order system, p is 2.

[0102] The input of the reduced-order generalized proportional-integral observer is v0, which is the actual position signal q on the arm side or the actual position signal θ on the motor side. The output is the left side of all equations. From the system state equation, it can be seen that z1 is actually an estimate of the input v0. Because of the use of reduced-order gpio, the design of the reduced-order generalized proportional-integral observer does not need to include the z1 term, which simplifies the observer design. The z terms in the formula all include estimates of the next term. The last term z p+2 In fact, it is an estimate of the p-th derivative of the total time-varying disturbance (including external disturbance). Therefore, the reduced-order generalized proportional integral observer can estimate the disturbance value of the system, and the external disturbance is only a part of it.

[0103] According to the above system, taking p = 2, the first reduced-order generalized proportional integral observer can be designed ( Figure 3 The ROGPIO observer in I) is:

[0104]

[0105] Among them, z 1，2 , z 1，3 , z 1，4 is the state variable of the first reduced-order generalized proportional-integral observer, They are The estimated value of β 1，1 >0,β1，2 >0,β 1，3 >0;β 1，1 , β 1，2 , β 1，3 are the parameters of the reduced-order generalized proportional-integral observer respectively. Here, θ is the u in the system state equation when considering the time-varying disturbance of the system.

[0106] According to the above system, the second reduced-order generalized proportional integral observer can be designed ( Figure 3 ROGPIO Observer II) in is:

[0107]

[0108] Among them, z 2，2 , z 2，3 , z 2，4 is the state variable of the second reduced-order generalized proportional-integral observer, They are The estimate of β 2，1 >0,β 2，2 >0,β 2，3 >0;β 2，1 , β 2，2 , β 2，3 They are the parameters of the reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, and J -1 τ is the u in the system state equation when considering time-varying disturbances of the system.

[0109] According to the attached Figure 3 It can be seen that the block diagram of the composite control system of the present invention is as follows: The disturbance values ​​estimated by two reduced-order generalized proportional-integral observers are fed forward to the continuous sliding mode controller, and the final composite controller is designed.

[0110] The continuous sliding surface can be designed as The continuous sliding mode control law is designed as u eq =c n x n +…+c2x2+c1x1, where sgn(·) is the standard sign function, k>0, c i >0, i=1, 2, ... n, is the estimate of the variable disturbance by the reduced-order generalized proportional-integral observer.

[0111] The first composite controller (composite anti-interference arm side position controller) based on the first reduced-order generalized proportional-integral observer and the first continuous sliding mode control is designed:

[0112] Design the first continuous sliding surface as The first continuous sliding mode control law is designed as where e 1，1 =q r -q, c 1，1 >0,c 1，2 >0; k>0, c 1，1 , c 1，2 , k are the corresponding first continuous sliding mode controller coefficients, k is an adjustable parameter that affects the anti-disturbance performance of the first continuous sliding mode controller, sgn(·) is a standard sign function, is the disturbance estimation signal of the first reduced-order generalized proportional-integral observer, that is, the disturbance estimation signal on the arm side, that is, is the estimated signal of the arm side time-varying disturbance signal ρ1.

[0113] Design of the second composite controller (composite anti-interference motor side position controller) based on the second reduced-order generalized proportional-integral observer and continuous sliding mode control:

[0114] Design the second continuous sliding surface as The second continuous sliding mode control law is designed as where e 2，1 =θ r -θ, c 2，1 >0,c 2，2 >0; v>0, sgn(·) is the standard sign function, is the disturbance estimation signal of the second reduced-order generalized proportional-integral observer, that is, the disturbance estimation signal on the motor side, namely is the estimated signal of the time-varying disturbance signal ζ1 on the motor side.

[0115] Therefore, the flexible actuator based on time-varying disturbance and continuous sliding mode of the present invention is designed through the above-mentioned design method, such as Example 2.

[0116] Example 2

[0117] The first observer receives the actual position signal q on the arm side and the actual position signal θ on the motor side transmitted by the generalized object module, and obtains the arm side disturbance estimation signal according to the actual position signal q on the arm side, the actual position signal θ on the motor side and the arm side time-varying disturbance signal ρ1

[0118] The second observer receives the actual position signal θ of the motor side and the output torque τ of the composite anti-interference motor side position controller transmitted by the generalized object module, and obtains the motor side disturbance estimation signal according to the actual position signal θ of the motor side, the output torque τ of the composite anti-interference motor side position controller and the motor side time-varying disturbance signal ζ1.

[0119] The first continuous sliding mode controller ( Figure 3CSMC controller I): According to the input arm side reference position signal q r , arm side actual position signal q and arm side disturbance estimation signal Get the motor side reference position signal θ r ;

[0120] The second continuous sliding mode controller ( Figure 3 CSMC controller II): According to the motor side reference position signal θ r , the actual position signal θ on the motor side and the disturbance estimation signal on the motor side Get the input torque driving the robot's arm side

[0121] The generalized object module can be understood as a robot controlled by flexible actuators.

[0122] Next, the control method of the flexible actuator controlling the robot of the present invention is introduced.

[0123] Example 3

[0124] Attached Figure 1 This is a schematic diagram of the control system principle of the present invention, Figure 2 It is a detailed block diagram of the generalized object controlled by the present invention. According to these two figures, it is easy to know that

[0125] The implementation process of the present invention comprises the following steps:

[0126] The first observer obtains the actual position signal q of the robot's arm side and the actual position signal θ of the motor side, and obtains the arm side disturbance estimation signal according to the actual position signal q of the arm side, the actual position signal θ of the motor side and the arm side time-varying disturbance signal ρ1.

[0127] The second observer obtains the actual position signal θ of the robot's motor side and the output torque τ of the composite anti-interference motor side position controller, and obtains the motor side disturbance estimation signal according to the actual position signal θ of the motor side, the output torque τ of the composite anti-interference motor side position controller and the motor side time-varying disturbance signal ζ1.

[0128] The first continuous sliding mode controller inputs the arm side reference position signal q r , arm side actual position signal q and arm side disturbance estimation signal Get the motor side reference position signal θ r ;

[0129] The second continuous sliding mode controller is based on the motor side reference position signal θ r , the actual position signal θ on the motor side and the disturbance estimation signal on the motor side Get the input torque on the input arm side of the driving robot

[0130] According to the input torque The robot is driven.

[0131] As attached Figure 4 As shown, by comparing the control method of the present invention with the traditional control method (PD control), it can be seen that the control method of the present invention enables the robot system driven by the flexible actuator to quickly reach a stable value in the arm side position after startup, with a small system overshoot and a short adjustment time; and after interference is applied (t=5s), the system can recover quickly compared to PD control, with an extremely short adjustment time and almost no impact from external interference.

[0132] As attached Figure 5 As shown ( Figure 5 PD Control in the figure has both dotted lines and points, and the representative points are on the dotted lines). By comparing the control method of the present invention with the traditional control method (PD control), it can be seen that the control method of the present invention enables the robot system driven by the flexible actuator to effectively track the input motor side position after startup, and the overshoot is slightly smaller than the traditional control method; and after the interference is applied (t=5s), the system can respond more quickly and adjust in time. Compared with the traditional control, its anti-interference ability is stronger.

[0133] As attached Figure 6 As shown in the figure, the arm position reference value q of the three methods: the traditional control method (PD control), the continuous sliding mode controller, and the continuous sliding mode controller with reduced-order generalized proportional integral observer r The difference between the actual arm side position q and the continuous sliding mode controller can be seen from the figure that compared with the traditional PD control, the difference of the robot system driven by the flexible actuator decreases rapidly after startup; and after the interference is applied at (t=5s), the difference of the PD control becomes significantly larger, while the continuous sliding mode controller has a smaller fluctuation, and the difference of the continuous sliding mode controller with a reduced-order generalized proportional-integral observer has no obvious fluctuation, which shows that the control method of the present invention has good anti-disturbance performance and is not easily affected by interference.

[0134] As attached Figure 7 and attached Figure 8 As shown, it is the disturbance estimation of the output of the first reduced-order generalized proportional integral observer under the control mode of the present invention. And the estimated result diagram of the actual position signal q on the arm side. Figure 7 The perturbation estimate shown in The curve shows that the system disturbance of the robot system driven by the flexible actuator is quickly suppressed to a stable value after startup. After the disturbance (30-valued sine wave) is applied at (t=5s), the observed disturbance The trend of the graph over time is consistent with the applied disturbance. Figure 8 The estimated curve of the actual position signal q of the middle arm side shows that the observer can accurately observe the dynamics of the arm side position change of the flexible actuator-driven robot system in real time, including the situation where the system is disturbed by external load at (t = 5s). Figure 4 It is easy to see that the changing trend of the estimated value over time is consistent with the actual position signal q of the arm side.

[0135] As attached Fig. 9 and attached Fig.10 As shown, it is the disturbance estimation signal output by the second reduced-order generalized proportional integral observer under the control mode of the present invention. And the estimated result diagram of the actual position signal θ on the motor side. Fig. 9 The disturbance estimation signal shown in The curve shows that the system disturbance of the robot system driven by the flexible actuator is quickly suppressed to a stable value after startup. After the disturbance (30-valued sine wave) is applied at (t=5s), the observed disturbance The trend of the graph over time is consistent with the applied disturbance. Fig.10 The estimated curve of the motor side position θ in shows that the observer can accurately observe the dynamics of the motor side position change of the flexible actuator driven robot system in real time, including the situation that the system is disturbed by external load at (t = 5s). Figure 5 It is easy to see that the changing trend of the estimated value over time is consistent with the actual position signal θ on the motor side.

[0136] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of 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. A flexible actuator based on time-varying disturbance and continuous sliding mode, characterized in that: include: The first observer receives the actual position signal q on the arm side and the actual position signal θ on the motor side transmitted by the generalized object module, and obtains the arm side disturbance estimation signal according to the actual position signal q on the arm side, the actual position signal θ on the motor side and the arm side time-varying disturbance signal ρ1 The first observer is a first reduced-order generalized proportional-integral observer, specifically: where z 1，2 , z 1，3 , z 1，4 is the state variable of the first reduced-order generalized proportional-integral observer, They are ρ1, The estimated value of β 1，1 >0,β 1，2 >0,β 1，3 >0;β 1，1 , β 1，2 , β 1，3 are the parameters of the first reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, and θ is the actual position signal on the motor side; The second observer receives the actual position signal θ of the motor side and the output torque τ of the composite anti-interference motor side position controller transmitted by the generalized object module, and obtains the motor side disturbance estimation signal according to the actual position signal θ of the motor side, the output torque τ of the composite anti-interference motor side position controller and the time-varying disturbance signal ζ1 of the motor side. The second observer is a second reduced-order generalized proportional-integral observer, specifically: Among them, z 2，2 , z 2，3 , z 2，4 is the state variable of the second reduced-order generalized proportional-integral observer, They are ζ1, The estimated value of β 2，1 >0,β 2，2 >0,β 2，3 >0;β 2，1 , β 2，2 , β 2，3 are the parameters of the second reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, θ is the actual position signal on the motor side, and τ is the input torque; The first continuous sliding mode controller: According to the input arm side reference position signal q r , arm side actual position signal q and arm side disturbance estimation signal Get the motor side reference position signal θ r ; The expression of the first continuous sliding mode controller in the absence of disturbance is: θ r1 =(in eq1 +in v1 ); Among them, θ r1 is the motor side reference position signal output by the first continuous sliding mode controller under the condition of no disturbance; 1，1 =q r -q, c 1，1 >0,c 1，2 >0; k>0, sgn(·) is the standard sign function, q is the actual position signal of the arm side; is the first-order differential of the arm-side reference position signal; is the first-order differential of the actual arm side position signal; is the second-order differential of the actual position signal q on the arm side, for u v1 The first-order differential of , σ1 is the continuous sliding mode surface of the first continuous sliding mode controller, where c 1，1 , c 1，2 , k are the corresponding first continuous sliding mode controller coefficients respectively; The state equation of the system of the first continuous sliding mode controller in the absence of disturbance is: Where x1 = q, θ is the actual position signal on the motor side, ρ1 is the time-varying disturbance signal on the arm side, is the first-order differential of x2; The second continuous sliding mode controller: According to the motor side reference position signal θ r , the actual position signal θ on the motor side and the disturbance estimation signal on the motor side The input torque τ of the driving generalized object module is obtained; The expression of the second continuous sliding mode controller in the absence of disturbance is: τ1=J(u eq2 +in v2 ); Where τ1 is the output torque of the second continuous sliding mode controller in the absence of disturbance; e 2，1 =θ r -θ, c 2,1 >0,c 2,2 >0; v>0, sgn(·) is the standard sign function, θ is the actual position signal on the motor side; is the first-order differential of the actual position signal θ on the motor side; θ r It is the reference position signal of the input motor side; The reference position signal θ is input to the motor side r is the first-order differential of ; σ2 is the continuous sliding mode surface of the second continuous sliding mode controller, The reference position signal θ is input to the motor side r The second-order differential of for u v2 The first-order differential of , where c 2,1 ,c 2,2 , v are the corresponding second continuous sliding mode controller coefficients, J is the motor inertia coefficient; The state equation of the system of the second continuous sliding mode controller in the absence of disturbance is: Where x1 = θ, is the actual position signal on the motor side, τ1 is the output torque of the second continuous sliding mode controller without disturbance, ζ1 is the time-varying disturbance signal on the motor side, K represents the joint stiffness coefficient, B is the damping coefficient, and D2 is the external disturbance on the motor side.

2. A flexible actuator based on time-varying disturbance and continuous sliding mode according to claim 1, characterized in that: The first observer and the second observer are both reduced-order generalized proportional-integral observers, i.e., ROGPIO observers, and the reduced-order generalized proportional-integral observers are: Among them, z2, z3, …, z p+2 is the state variable of the ROGPIO observer, u is the control input, u0, They are x1, The estimated value of are ψ0, ψ1, The estimated value of β i >0, (i=0, 2, ..., p+1) is the coefficient of the reduced-order generalized proportional-integral observer; p represents the order of the system, and the state equation of the system where the reduced-order generalized proportional-integral observer is located is: Among them, x1, x2, …, x n is the system state, u is the control input, b is the system parameter, ξ is the total time-varying disturbance, ψ0=ξ, ψ p-1 =ξ (p-1) .

3. The flexible actuator based on time-varying disturbance and continuous sliding mode according to claim 1, characterized in that: The first observer and the first continuous sliding mode controller constitute a composite anti-interference arm side position controller, and the expression of the composite anti-interference arm side position controller is: in, is the disturbance estimation signal of the first reduced-order generalized proportional-integral observer, that is, is the estimated signal of the arm side time-varying disturbance signal ρ1, θ r is the motor side reference position signal output by the composite anti-interference arm side position controller, and k is the first continuous sliding mode controller coefficient.

4. The flexible actuator based on time-varying disturbance and continuous sliding mode according to claim 1, characterized in that: The second observer and the second continuous sliding mode controller constitute a composite anti-interference motor side position controller, and the expression of the composite anti-interference motor side position controller is: Wherein, τ is the output torque of the motor side position controller output by the composite anti-interference motor side position controller, is the disturbance estimation signal of the second reduced-order generalized proportional-integral observer, that is, is the estimated signal of the time-varying disturbance signal ζ1 on the motor side.

5. A design method for a flexible actuator based on time-varying disturbance and continuous sliding mode, characterized in that: include: S1. Based on the mathematical model of the robot driven by the flexible actuator, a first continuous sliding mode controller and a second continuous sliding mode controller are designed without disturbance; S2. Designing a first reduced-order generalized proportional integral observer and a second reduced-order generalized proportional integral observer using measurable information of the system, wherein the first reduced-order generalized proportional integral observer and the second reduced-order generalized proportional integral observer are used to observe matching / non-matching time-varying disturbances existing in the system where the robot driven by the flexible actuator is located and obtain corresponding disturbance estimates; S3, the actual arm position signal q in the system where the flexible actuator drives the robot is fed back to the first continuous sliding mode controller, the first reduced-order generalized proportional integral observer feeds forward the obtained arm disturbance estimation signal to the first continuous sliding mode controller, and the first continuous sliding mode controller combines the arm reference signal q r Get the motor side reference position signal θ r ; S4, feeding back the actual position signal θ of the motor side in the system where the flexible actuator-driven robot is located to the second continuous sliding mode controller, and at the same time, the second reduced-order generalized proportional integral observer feeds forward the disturbance estimation signal of the motor side to the second continuous sliding mode controller, and the second continuous sliding mode controller combines the reference position signal θ of the motor side r The output torque τ of the robot is obtained to drive the robot driven by the flexible actuator to operate; The first reduced-order generalized proportional-integral observer is: where z 1，2 , z 1，3 , z 1，4 is the state variable of the first reduced-order generalized proportional-integral observer, They are ρ1, The estimated value of β 1，1 >0,β 1，2 >0,β 1，3 >0;β 1，1 , β 1，2 , β 1，3 are the parameters of the first reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, and θ is the actual position signal on the motor side; The second reduced-order generalized proportional-integral observer is: Among them, z 2，2 , z 2，3 , z 2，4 is the state variable of the second reduced-order generalized proportional-integral observer, They are ζ1, The estimated value of β 2，1 >0,β 2，2 >0,β 2，3 >0;β 2，1 , β 2，2 , β 2，3 are the parameters of the second reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, θ is the actual position signal on the motor side, and τ is the input torque; The expression of the first continuous sliding mode controller in the absence of disturbance is: θ r1 =(in eq1 +in v1 ); Among them, θ r1 is the motor side reference position signal output by the first continuous sliding mode controller under the condition of no disturbance; 1，1 =q r -q, c 1，1 >0,c 1，2 >0; k>0, sgn(·) is the standard sign function, q is the actual position signal of the arm side; is the first-order differential of the arm-side reference position signal; is the first-order differential of the actual arm side position signal; is the second-order differential of the actual position signal q on the arm side, for u v1 The first-order differential of , σ1 is the continuous sliding mode surface of the first continuous sliding mode controller, where c 1，1 , c 1，2 , k are the corresponding first continuous sliding mode controller coefficients respectively; The state equation of the system of the first continuous sliding mode controller in the absence of disturbance is: Where x1 = q, θ is the actual position signal on the motor side, ρ1 is the time-varying disturbance signal on the arm side, is the first-order differential of x2; The expression of the second continuous sliding mode controller in the absence of disturbance is: τ1=J(u eq2 +in v2 ); Where τ1 is the output torque of the second continuous sliding mode controller in the absence of disturbance; e 2，1 =θ r -θ, c 2，1 >0,c 2，2 >0; v>0, sgn(·) is the standard sign function, θ is the actual position signal on the motor side; is the first-order differential of the actual position signal θ on the motor side; θ r It is the reference position signal of the input motor side; The reference position signal θ is input to the motor side r is the first-order differential of ; σ2 is the continuous sliding mode surface of the second continuous sliding mode controller, The reference position signal θ is input to the motor side r The second-order differential of for u v2 The first-order differential of , where c 2,1 ,c 2,2 , v are the corresponding second continuous sliding mode controller coefficients, J is the motor inertia coefficient; The state equation of the system of the second continuous sliding mode controller in the absence of disturbance is: Where x1 = θ, is the actual position signal on the motor side, τ1 is the output torque of the second continuous sliding mode controller without disturbance, ζ1 is the time-varying disturbance signal on the motor side, K represents the joint stiffness coefficient, B is the damping coefficient, and D2 is the external disturbance on the motor side.

6. A control method of a flexible actuator based on time-varying disturbance and continuous sliding mode, using a flexible actuator based on time-varying disturbance and continuous sliding mode as claimed in any one of claims 1 to 4 to control a robot, characterized in that: include: The first observer obtains the actual position signal q of the robot's arm side and the actual position signal θ of the motor side, and obtains the arm side disturbance estimation signal according to the actual position signal q of the arm side, the actual position signal θ of the motor side and the arm side time-varying disturbance signal ρ1. The second observer obtains the actual position signal θ of the robot's motor side and the output torque τ of the composite anti-interference motor side position controller, and obtains the motor side disturbance estimation signal according to the actual position signal θ of the motor side, the output torque τ of the composite anti-interference motor side position controller and the motor side time-varying disturbance signal ζ1. The first continuous sliding mode controller inputs the arm side reference position signal q r , arm side actual position signal q and arm side disturbance estimation signal Get the motor side reference position signal θ r ; The second continuous sliding mode controller is based on the motor side reference position signal θ r , the actual position signal θ on the motor side and the disturbance estimation signal on the motor side The input torque τ on the input arm side of the driving robot is obtained; driving the robot according to the input torque τ; The first reduced-order generalized proportional-integral observer is: where z 1，2 , z 1，3 , z 1，4 is the state variable of the first reduced-order generalized proportional-integral observer, They are ρ1, The estimated value of β 1,1 >0,β 1,2 >0,β 1，3 >0;β 1，1 , β 1,2 , β 1,3 are the parameters of the first reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, and θ is the actual position signal on the motor side; The second reduced-order generalized proportional-integral observer is: Among them, z 2，2 , z 2，3 , z 2,4 is the state variable of the second reduced-order generalized proportional-integral observer, They are ζ1, The estimated value of β 2，1 >0,β 2,2 >0,β 2,3 >0; β 2,1 , β 2，2 , β 2，3 are the parameters of the second reduced-order generalized proportional-integral observer, J is the motor inertia coefficient, θ is the actual position signal on the motor side, and τ is the input torque; The expression of the first continuous sliding mode controller in the absence of disturbance is: θ r1 =(in eq1 +in v1 ); Among them, θ r1 is the motor side reference position signal output by the first continuous sliding mode controller under the condition of no disturbance; 1，1 =q r -q, c 1，1 >0,c 1，2 >0; k>0, sgn(·) is the standard sign function, q is the actual position signal of the arm side; is the first-order differential of the arm-side reference position signal; is the first-order differential of the actual arm side position signal; is the second-order differential of the actual position signal q on the arm side, for u v1 The first-order differential of , σ1 is the continuous sliding mode surface of the first continuous sliding mode controller, where c 1，1 , c 1，2 , k are the corresponding first continuous sliding mode controller coefficients respectively; The state equation of the system of the first continuous sliding mode controller in the absence of disturbance is: Where x1 = q, θ is the actual position signal on the motor side, ρ1 is the time-varying disturbance signal on the arm side, is the first-order differential of x2; The expression of the second continuous sliding mode controller in the absence of disturbance is: τ1=J(u eq2 +in v2 ); Where τ1 is the output torque of the second continuous sliding mode controller in the absence of disturbance; e 2，1 =θ r -θ, c 2，1 >0,c 2，2 >0; v>0, sgn(·) is the standard sign function, θ is the actual position signal on the motor side; is the first-order differential of the actual position signal θ on the motor side; θ r It is the reference position signal of the input motor side; The reference position signal θ is input to the motor side r is the first-order differential of ; σ2 is the continuous sliding mode surface of the second continuous sliding mode controller, The reference position signal θ is input to the motor side r The second-order differential of for u v2 The first-order differential of , where c 2,1 ,c 2,2 , v are the corresponding second continuous sliding mode controller coefficients, J is the motor inertia coefficient; The state equation of the system of the second continuous sliding mode controller in the absence of disturbance is: Where x1 = θ, is the actual position signal on the motor side, τ1 is the output torque of the second continuous sliding mode controller without disturbance, ζ1 is the time-varying disturbance signal on the motor side, K represents the joint stiffness coefficient, B is the damping coefficient, and D2 is the external disturbance on the motor side.

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