Linear active disturbance rejection controller and method for force feedback manipulator

Abstract

The application discloses a linear active disturbance rejection controller and method of a force feedback manipulator, comprising the following steps: step one, establishing a kinematic model and a dynamic model; step two, determining a state space expression; step three, a linear active disturbance rejection controller processing a displacement signal; and step four, the linear active disturbance rejection controller outputting a control quantity; the active disturbance rejection controller adopts linear active disturbance rejection control design, reduces the parameters to be adjusted to three, and greatly improves the design efficiency of the control method and the applicability of the control algorithm; the active disturbance rejection controller can estimate and compensate the total disturbance of the force feedback system in real time through an extended state observer, and thus has strong adaptability and robustness; compared with the existing linear active disturbance rejection control technology, the application prevents oscillation and disturbance caused by the input control signal in the force feedback system under the condition of discontinuity or with random disturbance through a tracking differentiator, so that the quality of the active disturbance rejection controller is improved.

Description

Technical Field

[0001] This invention relates to a linear active disturbance rejection controller and method for force feedback manipulators. Background Technology

[0002] With the increasing prevalence of population aging, chronic diseases, disabilities, and movement disorders are on the rise, leading to a growing demand for self-rehabilitation. Many patients with neurological disorders such as stroke, spinal cord injury, and myasthenia gravis, or those with arm injuries, require long-term self-rehabilitation, but traditional rehabilitation methods often have limitations. For example, traditional physical therapy and drug treatment may not be able to achieve precise and personalized rehabilitation. Rehabilitation robotic gloves are rehabilitation devices that utilize robotic technology to provide patients with assisted training. By accurately sensing, mimicking, and controlling hand movements, they provide personalized rehabilitation plans, thereby improving rehabilitation outcomes. Using rehabilitation robotic gloves allows patients to rehabilitate more conveniently, enhancing their confidence and self-assurance. Furthermore, rehabilitation robotic gloves can promote the development of robotics technology, enabling the creation of intelligent and personalized rehabilitation plans. Rehabilitation robotic gloves are a branch of force feedback robotic hands, which have a broader range of applications.

[0003] The existing force feedback systems in force feedback manipulators have the following drawbacks in terms of controllers and control methods: First, disturbance factors significantly interfere with the dynamic model, resulting in poor controller adaptability and robustness; second, the parameters of nonlinear active disturbance rejection control are too numerous and the parameter tuning is too complex, leading to low design efficiency of the control method. Summary of the Invention

[0004] The purpose of this invention is to provide a linear active disturbance rejection controller and method for a force feedback manipulator to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a linear active disturbance rejection controller for a force feedback manipulator, comprising a tracking differentiator, a PD control combination, and a linear extended state observer, wherein the output terminal of the tracking differentiator is connected to the PD control combination, the output terminal of the PD control combination is connected to the linear extended state observer, and the output terminal of the linear extended state observer is connected to the input terminal of the PD control combination.

[0006] Preferably, the input terminal of the tracking differentiator is connected to a signal input module, and the output terminal of the PD control combination is connected to a force feedback system.

[0007] The linear active disturbance rejection control method for a force feedback manipulator includes the following steps: Step 1, establishing a kinematic model and a dynamic model; Step 2, determining the state-space expression; Step 3, the linear active disturbance rejection controller processes the displacement signal; and Step 4, the linear active disturbance rejection controller outputs the control quantity.

[0008] In step one above, the kinematic and dynamic models of the force feedback manipulator are built.

[0009] In step two above, the state-space expression of the force feedback system is determined.

[0010] In step three above, the linear active disturbance rejection controller processes the displacement signal specifically through the following steps:

[0011] 1) The signal input module obtains the displacement signal v and inputs it into the tracking differentiator. The tracking differentiator outputs signals v1 and v2.

[0012] 2) The inputs e1 and e2 of the PD control combination are obtained by subtracting the outputs z1 and z2 of the linear extended state observer from the v1 and v2 signals, respectively. The PD control combination uses the PD control law to linearly combine the discrete error signal e1 and the discrete error differential signal e2, and the output obtained after calculation is u0.

[0013] 3) In the linear extended state observer, the original state variable is extended, and the total disturbance of the sum of external disturbance and internal disturbance is transformed into a new state variable. The input signals of the linear extended state observer are b0u and y, and the outputs are z1, z2 and z3.

[0014] In step four above, the linear active disturbance rejection controller outputs a compensated control quantity u, which acts on the force feedback system to achieve precise control.

[0015] Preferably, in step one, the kinematic model includes a theoretical model of the spring tension and a displacement model of the motor driven by the track, with the following formulas:

[0016] f(t) = kx

[0017]

[0018] By combining the two equations and differentiating them separately, we can obtain the speed control quantity for the DC motor:

[0019]

[0020] The controlled object based on the second-order force feedback system is:

[0021]

[0022] The above equation can be transformed to obtain:

[0023]

[0024] Preferably, in step two, the state variable x1 = x, If x³ = f, then let x³ = f, and denote... For the expanded state variables including displacement, velocity, and disturbance, the state-space expression of the force feedback system is:

[0025]

[0026] in,

[0027] Preferably, in step three, the output v1 of the tracking differentiator is the transitioned signal of the input displacement signal v, and the output v2 signal is the differential signal of the displacement signal v1; the discrete formulas for v1 and v2 are as follows:

[0028]

[0029] The formula for the tracking differentiator includes a core algorithm: the steepest control function fhan(v1,v2,r,h0), which allows the entire tracking differentiator to quickly and smoothly track changes in the input signal. Its tracking formula is as follows:

[0030]

[0031] The tracking differentiator includes the tracking speed factor r and the filter factor h0, both of which are preset parameters.

[0032] Preferably, in step three, the expression for the PD control combination is as follows:

[0033]

[0034] After parameterization, you can select...

[0035]

[0036] The parameters included in the PD control combination are w c .

[0037] Preferably, in step three, the expression for the linear extended state observer assisted by the second-order force feedback system model, based on the state-space expression, is as follows:

[0038]

[0039] Among them, u c =[uy] T It is a combination of control variables and state output variables, y c It is the output of the linearly extended state observer. C = [1 0 0], where L is the gain matrix of the linear extended state observer to be designed;

[0040] To design a linearly extended state observer, the poles of its characteristic equation can be placed at the same location -w0, which yields:

[0041] λ(s)=|sI-(A-LC)|=(s+w0) 3

[0042] The gain matrix of the linearly extended state observer can be obtained as follows:

[0043] L = [l1 l2 l3] T

[0044] Expanding the above equation and comparing the coefficients, we obtain the following parameters:

[0045]

[0046] Substituting into the above equation, we obtain the following form of the linear extended state observer assisted by the second-order force feedback system model:

[0047]

[0048] y c =z

[0049] As t→∞, the observed state variable z1→x in the linearly extended state observer, z3→f;

[0050] The discrete linear extended state observer form corresponding to the continuous linear extended state observer form is:

[0051]

[0052] Among them, u d (k)=[u(k)y(k)] T For a force feedback system, y is a combination of discrete control variables and state variables. d (k) represents the output of the discrete linear extended state observer. The discretized system matrices of the force feedback system are φ, Γ, and H, respectively, while L c This refers to the state feedback gain matrix of the discrete linear extended state observer that we need to design separately; similarly, we can choose the bandwidth β of the discrete linear extended state observer such that the discrete characteristic equation satisfies:

[0053] λ(z)=|zI-(φ-φL c H)|=(z-β) 3

[0054] The linearly extended state observer includes parameters w0 and β.

[0055] Preferably, in step four, the formula for the compensated control quantity is as follows:

[0056]

[0057] The linear active disturbance rejection controller of the aforementioned force feedback manipulator contains a total of ω c The three parameters are ω0 and β.

[0058] Compared with the prior art, the beneficial effects of the present invention are as follows: The active disturbance rejection controller of the present invention adopts a linear active disturbance rejection control design, reducing the parameters that need to be tuned to three, which greatly improves the design efficiency of the control method and the applicability of the control algorithm; The active disturbance rejection controller of the present invention can estimate and compensate for the total disturbance received by the force feedback system in real time by extending the state observer, thus having strong adaptability and robustness. Compared with the existing linear active disturbance rejection control technology, the present invention prevents oscillations and disturbances caused by discontinuous or random disturbances in the input control signal in the force feedback system by using a tracking differentiator, thereby improving the quality of the active disturbance rejection controller. Attached Figure Description

[0059] Figure 1 This is a block diagram of the linear active disturbance rejection controller of the present invention;

[0060] Figure 2 This is a flowchart of the method of the present invention;

[0061] Figure 3 This is a simulation connection diagram of the linear active disturbance rejection controller of the present invention;

[0062] Figure 4 This is the dynamic model of the force feedback system of the present invention;

[0063] In the diagram: 1. Tracking differentiator; 2. PD control combination; 3. Linear extended state observer. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] Please see Figure 1An embodiment of the present invention provides a linear active disturbance rejection controller for a force feedback manipulator, comprising a tracking differentiator 1, a PD control assembly 2, and a linear extended state observer 3. The output of the tracking differentiator 1 is connected to the PD control assembly 2, the output of the PD control assembly 2 is connected to the linear extended state observer 3, and the output of the linear extended state observer 3 is connected to the input of the PD control assembly 2. The input of the tracking differentiator 1 is connected to a signal input module, and the output of the PD control assembly 2 is connected to a force feedback system.

[0066] Please see Figure 2-4 The present invention provides an embodiment of a linear active disturbance rejection control method for a force feedback manipulator, comprising: step one, establishing a kinematic model and a dynamic model; step two, determining a state-space expression; step three, the linear active disturbance rejection controller processing the displacement signal; and step four, the linear active disturbance rejection controller outputting a control quantity.

[0067] In step one above, the kinematic and dynamic models of the force feedback manipulator are constructed; specifically, a theoretical model of the spring tension is established.

[0068] f(t) = kx

[0069] In the formula, k is the spring constant (N / mm), and x is the slider displacement (mm);

[0070] Establish a displacement model of the motor driven by the track, for

[0071]

[0072] In the formula, v is the spring constant (mm / s);

[0073] Differentiating both sides after combining the equations, we obtain the speed regulation value of the DC motor:

[0074]

[0075] The controlled object based on the second-order force feedback system is:

[0076]

[0077] In the formula, x is the state variable, u is the control quantity, i.e., the motor output torque, and w is the disturbance of the force feedback system. Since the parameters c, m, k, n, and R can all be measured practically, the parameters of the state variable and control quantity of the second-order force feedback system are known, while the disturbance w is unknown. Therefore, the formula can be transformed to obtain:

[0078]

[0079] in, The total disturbance is actually unknown, and It includes the total disturbance of both unknown total disturbance and total disturbance of known model information;

[0080] In step two above, the state-space expression of the force feedback system is determined, and the state variable x1 = x is taken. If x³ = f, then let x³ = f, and denote... For the expanded state variables including displacement, velocity, and disturbance, the state-space expression of the force feedback system is:

[0081]

[0082] in, C = [1 0 0];

[0083] In step three above, the linear active disturbance rejection controller processes the displacement signal specifically through the following steps:

[0084] 1) Set the parameters r and h0 in the tracking differentiator 1, and the adjustable parameter ω of the model. c ω0 and β are used to obtain the displacement signal v from the signal input module, which is then input into the tracking differentiator 1. The tracking differentiator 1 outputs signals v1 and v2. The output v1 of the tracking differentiator 1 is the transitioned signal of the input displacement signal v, and the output v2 is the differential signal of the displacement signal v1. The discrete formulas for v1 and v2 are as follows:

[0085]

[0086] The formula for tracking differentiator 1 includes a core algorithm component, namely the steepest control function fhan(v1,v2,r,h0), which enables the entire tracking differentiator 1 to quickly and smoothly track changes in the input signal; its tracking formula is as follows:

[0087]

[0088] The tracking differentiator 1 includes the tracking speed factor r and the filter factor h0, both of which are preset parameters;

[0089] 2) Subtracting the outputs z1 and z2 of the linear extended state observer 3 from the v1 and v2 signals respectively yields the inputs e1 and e2 of the PD control combination 2. The PD control combination 2 uses the PD control law to linearly combine the discrete error signal e1 and the discrete error differential signal e2, and the calculated output is u0. The expression for the PD control combination 2 is shown below:

[0090]

[0091] After parameterization, you can select...

[0092]

[0093] The parameters included in PD control combination 2 are w c ;

[0094] 3) In the linear extended state observer 3, the original state variables are expanded, transforming the total disturbance of the sum of external and internal disturbances into a new state variable. The input signals of the linear extended state observer 3 are b0u and y, and the outputs are z1, z2, and z3. According to the state-space expression, the expression of the linear extended state observer 3 assisted by the second-order force feedback system model is:

[0095]

[0096] Among them, u c =[uy] T It is a combination of control variables and state output variables, y c It is the output of the linearly extended state observer 3. C = [1 0 0], where L is the gain matrix of the linear extended state observer 3 to be designed;

[0097] For the design of the linearly extended state observer 3, the poles of the characteristic equation of the linearly extended state observer 3 can be placed at the same location -w0, that is:

[0098] λ(s)=|sI-(A-LC)|=(s+w0) 3

[0099] The gain matrix of the linearly extended state observer 3 can be obtained as follows:

[0100] L = [l1 l2 l3] T

[0101] Expanding the above equation and comparing the coefficients, we obtain the following parameters:

[0102]

[0103] Substituting into the above equation, we obtain the following form of the linear extended state observer 3 assisted by the second-order force feedback system model:

[0104]

[0105] y c =z

[0106] As t→∞, the observed state variable z1→x in the linearly extended state observer 3, z3→f;

[0107] The discrete linear extended state observer form 3 corresponding to the continuous linear extended state observer form 3 is as follows:

[0108]

[0109] Among them, u d (k)=[u(k) y(k)] T For a force feedback system, y is a combination of discrete control variables and state variables. d (k) represents the output of the discrete linear extended state observer 3. The discretized system matrices of the force feedback system are φ, Γ, and H, respectively, while L c This refers to the state feedback gain matrix of the discrete linear extended state observer 3 that we need to design separately; similarly, we can choose the bandwidth β of the discrete linear extended state observer 3 such that the discrete characteristic equation satisfies:

[0110] λ(z)=|zI-(φ-φL c H)|=(z-β) 3

[0111] The linearly extended state observer 3 contains parameters w0 and β;

[0112] In step four above, the compensated control quantity u output by the linear active disturbance rejection controller acts on the force feedback system to achieve precise control; the formula for the compensated control quantity is as follows:

[0113]

[0114] The linear active disturbance rejection controller of the aforementioned force feedback manipulator contains a total of ω c The three parameters are ω0 and β.

[0115] Based on the above, the advantages of this invention are as follows: When used, the controller of this invention adopts a linear active disturbance rejection control design, reducing the number of parameters that need to be tuned from eleven to three, which greatly improves the design efficiency of the controller and the applicability of the control algorithm; the controller can estimate and compensate for the total disturbances experienced by the force feedback system in real time by extending the state observer, and has strong adaptability and robustness, and can perform force feedback control without depending on the specific system model; and compared with the existing linear active disturbance rejection control technology, this invention optimizes the second-order force feedback control system by adding a tracking differentiator 1 to prevent oscillations and disturbances caused by discontinuous or random disturbances in the input control signal of the force feedback system, and extracting a continuous differentiable displacement signal from it can prevent overshoot caused by a large initial control output of the system, thereby improving the quality of the force feedback active disturbance rejection controller.

[0116] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A linear active disturbance rejection control method for a force feedback manipulator, comprising: Step 1, establishing a kinematic model and a dynamic model; Step 2, determining a state-space expression; Step 3, a linear active disturbance rejection controller processing displacement signals; Step 4, a linear active disturbance rejection controller outputting a control quantity; characterized in that: In step one above, the kinematic and dynamic models of the force feedback manipulator are built. In step two above, the state-space expression of the force feedback system is determined. In step three above, the linear active disturbance rejection controller processes the displacement signal specifically through the following steps: 1) The signal input module obtains the displacement signal. The input is fed into the tracking differentiator (1), and the tracking differentiator (1) outputs... Signals and Signal; 2) Signals and The signals are compared with the output of the linear extended state observer (3). and Subtraction yields the input of the PD control combination (2). and ;PD control combination (2) uses PD control law to control discrete error signals and discrete error differential signal After performing a linear combination, the output obtained is: ; 3) In the linear extended state observer (3), the original state variable is extended, and the total disturbance of the sum of external disturbances and internal disturbances is transformed into a new state variable. The input signal of the linear extended state observer (3) is: and The output is , and ; In step four above, the linear active disturbance rejection controller outputs the compensated control quantity. Acting on a force feedback system; In step one, the kinematic model includes a theoretical model of the spring tension and a displacement model of the motor driven by the track, with the following formulas: ， ， In the formula The spring constant is... This represents the slider displacement; By combining the two equations and differentiating them separately, we can obtain the speed control quantity for the DC motor: ， The controlled object based on the second-order force feedback system is: ， In the formula, For state variables, The control quantity is the motor output torque. To represent the disturbance in the force feedback system, the above equation is transformed to obtain: ； in, The total disturbance is actually unknown; and It includes the total disturbance of both unknown total disturbance and total disturbance of known model information; In step two, the state variable is taken. , then remember For the expanded state variables including displacement, velocity, and disturbance, the state-space expression of the force feedback system is: ， in, , , , .

2. The linear active disturbance rejection control method for a force feedback manipulator according to claim 1, characterized in that: In step three, the output of the tracking differentiator (1) is... It is the input displacement signal The signal after transition is output. The signal is a displacement signal. The differential signal; and The discrete formula is as follows: ， The formula for the tracking differentiator (1) contains a core algorithmic component, namely the steepest control function. This allows the entire tracking differentiator (1) to quickly and smoothly track changes in the input signal; Its tracking formula is as follows: ， The tracking differentiator (1) includes the tracking velocity factor as a parameter. and filter factor All of these are preset parameters.

3. The linear active disturbance rejection control method for a force feedback manipulator according to claim 1, characterized in that: In step three, the expression for the PD control combination (2) is as follows: ， After parameterization, selection ， The parameters included in the PD control combination (2) are: .

4. The linear active disturbance rejection control method for a force feedback manipulator according to claim 3, characterized in that: In step three, according to the state-space expression, the expression for the linear extended state observer (3) assisted by the second-order force feedback system model is: ， in, It is a combination of control variables and state output variables as input. It is the output of the linearly extended state observer (3). , , , The gain matrix of the linear extended state observer (3) to be designed; For the design of the linearly extended state observer (3), the poles of the characteristic equation of the linearly extended state observer (3) are placed in the same position. Up, that is: ， The gain matrix of the linear extended state observer (3) is obtained as follows: ， Expanding the above equation and comparing the coefficients, we obtain the following parameters: ， Substituting into the above equation, we obtain the following form for the linear extended state observer (3) assisted by the second-order force feedback system model: ， ， when At that time, the observed state variables in the linearly extended state observer (3) , , ; The discrete linear extended state observer (3) corresponding to the continuous linear extended state observer (3) is: ， in, For a force feedback system, it is a combination of discrete control variables and state output variables. For the output of the discrete linear extended state observer (3), the discretized system matrices of the force feedback system are as follows: , , ,and It is the state feedback gain matrix of the separately designed discrete linear extended state observer (3); similarly, the bandwidth of the discrete linear extended state observer (3) is taken. Make the discrete characteristic equation satisfy: ， The parameters included in the linearly extended state observer (3) are: and .

5. The linear active disturbance rejection control method for a force feedback manipulator according to claim 4, characterized in that: In step four, the formula for the compensated control quantity is as follows: ， The linear active disturbance rejection controller of the aforementioned force feedback manipulator includes a total of , and These three parameters.

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