Mechanical arm sliding mode control buffeting analysis method

Abstract

The invention discloses a buffeting analysis method for sliding mode control of a mechanical arm. The buffeting analysis method comprises the following steps that a mechanical arm input torque and angular displacement response model is constructed, and model parameters are identified; designing a sliding mode controller, converting intermittent input into a piecewise function, and obtaining a buffeting analysis model of the sliding mode controller; and according to the response characteristics of the mechanical arm, historical information of a certain length is intercepted, and optimal estimation is conducted on the buffeting analysis model. According to the method, the relationship between the sliding mode control buffeting of the mechanical arm and the system response characteristics and historical input is established, a basis is provided for buffeting analysis, and a solution is provided for buffeting optimization. According to the method, the mechanical arm response equivalent simplified model is established by utilizing the input and output response characteristics, the output memory characteristics of the mechanical arm are researched, complex modeling of factors such as a complex mechanical structure and uneven materials of the mechanical arm is avoided, model identification is simplified, and only few unknown parameters such as differential orders and constants need to be identified.

Description

Technical Field

[0001] The present application belongs to the field of robot control technology, and specifically relates to a chattering analysis method for sliding mode control of a robot arm. Background Art

[0002] Robots have broad application prospects in the fields of precision instruments, aviation, aerospace, etc. The control accuracy of the robotic arm is directly related to the control performance of the robot. Studying the dynamic model of the robotic arm and improving the control accuracy of the robotic arm are important contents of robot research.

[0003] However, the robot arm is often not in an ideal state. For example, the moment of inertia is related to the material, structure, and process of the robot arm. It is impossible to consider the above factors and establish a mathematical model based on the physical mechanism. Even if a mathematical model is established, the identification of many unknown parameters will be a prominent problem. Therefore, modeling is difficult, and it is even more difficult to study how to control it based on the mathematical model.

[0004] In engineering, sliding mode control is one of the common methods to solve the above problems. Because sliding mode control uses the difference between the target state and the current state to design a stable sliding mode surface, and designs the sliding mode arrival law so that the state error is always on the stable sliding mode surface. Once it deviates from the sliding mode surface, according to the sliding mode arrival law, the state error quickly reaches the stable sliding mode surface, thereby achieving stable control. Sliding mode control is highly favored in the field of robotics because it does not rely on mathematical models and has good robustness to noise and parameter perturbations. However, the above implementation is based on the state error, and the robot state error is obtained through computer periodic sampling. Its sampling feedback is not continuous, but periodic intermittent sampling. This determines the periodic intermittent nature of the feedback. At the same time, any robot arm is not an ideal impulse response system. When the input changes, its output response has a process, and this response cannot be completed instantly. When the input is constantly switched due to the sliding mode surface, the alternating changes in its input will inevitably lead to the jitter of the robot arm output angular displacement θ.

[0005] Chattering has become the main factor restricting the application of sliding mode control in the field of robotics, because it will reduce the control accuracy of the robot arm, generate noise due to oscillation, and reduce the service life of the equipment. Excessive chattering may even cause system crashes and equipment paralysis.

[0006] Therefore, analyzing the chattering of the robot sliding mode control and studying the factors that affect the chattering are of great significance to reducing the complexity of robot control, improving the robot control accuracy, and optimizing the robot working environment. Summary of the invention

[0007] The present application provides a chattering analysis method for sliding mode control of a robot arm to solve the above-mentioned technical problems.

[0008] In order to solve the above technical problems, a technical solution adopted in the present application is: a chattering analysis method of a sliding mode control of a robot arm, comprising the following steps:

[0009] Construct the input torque and angular displacement response model of the robot arm and identify the model parameters;

[0010] Design a sliding mode controller, transform the intermittent input into a piecewise function, and obtain the chattering analysis model of the sliding mode controller;

[0011] According to the response characteristics of the robot arm, a certain length of historical information is intercepted to make the optimal estimation of the vibration analysis model.

[0012] Furthermore, the method for constructing the input torque and angular displacement response model of the robot arm includes:

[0013] Based on formulas (1)-(2), the input torque and angular displacement response model of the robot arm is obtained; formulas (1)-(2) are:

[0014] θ(t)=h(t)*τ(t) (1);

[0015]

[0016] Where θ(t) is the angular displacement, τ(t) is the input torque, and h(t) = [h1(t), h2(t)] T , h(t) represents the system impulse response; k and α are model parameters, k i =[k i1 ,k i2 ] T is the constant coefficient to be determined, α=[α1,α2] T , M is an integer. The higher M is, the higher the modeling accuracy is, but the more difficult the parameter identification is.

[0017] Furthermore, the method for identifying model parameters includes:

[0018] Based on formula (3), the cumulative formula of the discretized model is obtained and the displacement and input torque of the robot angle are discretized and sampled; formula (3) is:

[0019]

[0020] Based on formula (4), the cost function is constructed; formula (4) is:

[0021]

[0022] Among them, C α (n) is the cost function, θ(i) is the angular displacement collected in the experiment, The angular displacement estimate obtained for the convolution;

[0023] Based on the discretization model accumulation formula and the least squares method, the model parameter k is obtained;

[0024] The model parameter α is identified based on the combination of particle swarm optimization search algorithm and least square method.

[0025] Furthermore, based on the combination of the particle swarm optimization search algorithm and the least square method, the method for identifying the model parameter α includes:

[0026] Initialize the particle swarm optimization search algorithm and define the number of particles as the initial position of the model parameter α;

[0027] Based on the particle swarm optimization search algorithm, the particle position is locally updated, and the model parameter k and the cost function are calculated;

[0028] Based on the particle swarm optimization search algorithm, the particle positions are globally updated, and the model parameters k and cost functions are calculated;

[0029] Determine whether the cost function is less than a preset threshold; if so, repeat the above steps; if not, take the last identified model parameters α and k as the optimal identification results.

[0030] Furthermore, the method for obtaining the chattering analysis model includes:

[0031] Based on formula (5), the sliding mode control equation is obtained; formula (5) is:

[0032]

[0033] Among them, θ(t) is the current position of the robot arm; is the target position; e θ (t) is the angular displacement error; l is the lth control cycle; u(e θ (t)) is a sliding mode controller designed according to the position error;

[0034] Based on formula (6), a sliding mode controller is obtained; wherein formula (6) is:

[0035]

[0036] Where, u(t) is the sliding mode controller, and p is the control parameter;

[0037] Based on the unit step function and formula (7), the controller piecewise function equation is obtained; where formula (7) is:

[0038]

[0039] Based on formula (8), the angular displacement equation of the robot arm is obtained; wherein formula (8) is:

[0040]

[0041] The steady-state output and transient output of the angular displacement of the robot arm are separated, and the vibration analysis of the sliding mode controller is performed.

[0042] The beneficial effects of the present application are as follows: the present application establishes the relationship between the chattering of the sliding mode control of the robot arm and the system response characteristics and historical inputs, provides a basis for chattering analysis, and provides a solution for optimizing chattering. The present application uses the input-output response characteristics to establish a simplified equivalent model of the robot arm response and studies the output memory characteristics of the robot arm, which not only avoids the complex modeling of factors such as the complex mechanical structure and uneven materials of the robot arm, but also simplifies the model identification: only a few unknown parameters such as differential orders and constants need to be identified. The present application analyzes chattering by intercepting a certain length of historical information based on the system attenuation characteristics, which not only takes into account the accuracy of the chattering analysis, but also avoids unnecessary computational overhead, reduces the complexity of the analysis, and improves the engineering application capabilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of the working of a traditional robotic arm;

[0044] Figure 2 It is a flow chart of an embodiment of a method for analyzing chattering of a sliding mode control of a robot arm of the present application;

[0045] Figure 3 is a schematic diagram of a mechanical arm sliding mode control according to an embodiment of a mechanical arm sliding mode control chattering analysis method of the present application;

[0046] Figure 4 is a graph showing the attenuation of the impulse response over time of an embodiment of the chattering analysis method for sliding mode control of a robot arm of the present application;

[0047] Figure 5 It is a transient analysis diagram of the angular displacement diagram of the robot arm angular displacement of α=0.5 in the first embodiment of the robot arm sliding mode control chattering analysis method of the present application;

[0048] Figure 6 It is a transient analysis diagram of the angular displacement diagram of the robot arm angular displacement of α=0.8 in the first embodiment of the robot arm sliding mode control chattering analysis method of the present application;

[0049] Figure 7 is a transient analysis diagram of the angular displacement diagram of the robot arm when α=1 in an embodiment of the robot arm sliding mode control chattering analysis method of the present application;

[0050] Figure 8 is a simulation diagram of the chattering analysis of the robot arm control when p=2 in the first embodiment of the robot arm sliding mode control chattering analysis method of the present application;

[0051] Fig. 9This is a simulation diagram of the chattering analysis of the robot arm control when p=5 in an embodiment of the robot arm sliding mode control chattering analysis method of the present application. DETAILED DESCRIPTION

[0052] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with specific embodiments.

[0053] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways than those described herein. Therefore, the present invention is not limited to the specific embodiments of the following disclosure.

[0054] See also Figure 1 , Figure 1 The following model is usually established for the robot arm to study the relationship between the robot arm torque and angle position:

[0055]

[0056] Where θ=[θ1,θ2] T ,τ=[τ1,τ2] T , J(θ) represents the moment of inertia matrix, represents the Coriolis and centripetal force matrices, represents the friction torque, G(θ) represents the gravity torque, and τ represents the external force torque.

[0057] Theoretically, the above model can be established through the mechanical structure parameters to obtain the model parameters. The kinematics of the robot arm can be studied based on the model parameters, and the position and posture control of the robot arm can be achieved by controlling the external force and torque of the robot arm.

[0058] See also Figure 2 , Figure 2 : is a flow chart of an embodiment of a method for analyzing chattering of a sliding mode control of a robot arm of the present application, the method comprising:

[0059] Step S1. Construct the input torque and angular displacement response model of the robot arm and identify the model parameters.

[0060] Specifically, step S1 includes:

[0061] Step S11. Based on formula (1), obtain the input torque and angular displacement response model of the robot arm; formula (1) is:

[0062] θ(t)=h(t)*τ(t) (1);

[0063] Any robot input torque and angular displacement is always a BIBO (bounded input bounded output) system, which can always be represented by the following model:

[0064]

[0065] Among them, k i =[k i1 ,k i2 ] T is the constant coefficient to be determined, α=[α1,α2] T , M is an integer. The higher M is, the higher the modeling accuracy is, but the more difficult the parameter identification is.

[0066] According to the "intermediate process" theory, any complex process has an intermediate equivalent simplified process, and any complex model has an equivalent simplified model. Therefore, no matter how large M is, there is always an equivalent simplified model as follows:

[0067]

[0068] Where θ(t) is the angular displacement, τ(t) is the input torque, and h(t) = [h1(t), h2(t)] T , h(t) represents the system impulse response; k and α are model parameters.

[0069] Step S12. Based on formula (3), obtain the cumulative formula of the discretized model and discretize the displacement and input torque of the robot arm angle.

[0070] Specifically, the sampling interval is T. The input torque and angular displacement are recorded as: τ(0), τ(1), τ(2), ..., τ(N) and θ(0), θ(1), θ(2), ..., θ(N) respectively represent the driving torque and angular displacement of the robot at the initial time 1T, 2T, ...NT, and N represents the total number of sampling times. The discretized model is obtained:

[0071] θ(n)=h(n)*τ(n);

[0072] Among them, θ(n)=θ(nT), h(n)=h(nT), τ(n)=τ(nT).

[0073] Convert the convolutional model into a convolutional model accumulation expression:

[0074]

[0075] The angular displacement obtained from the experiment is denoted as θ(n), and the angular displacement estimate obtained by convolution of the input moment according to formula (3) is denoted as

[0076] Step S13: Obtain model parameter k using the least squares method.

[0077] Specifically, formula (3) is expressed as a matrix:

[0078] θ=kH α ;

[0079] Where θ=[θ1,θ2,...,θ N ] T ,

[0080]

[0081] Using the least squares method we get:

[0082]

[0083] in, express The inverse matrix of .

[0084] Step S14. Based on formula (4), construct a cost function; formula (4) is:

[0085]

[0086] Among them, C α (n) is the cost function, θ(i) is the angular displacement collected in the experiment, The angular displacement estimate obtained for the convolution;

[0087] Step S15: Identify the model parameter α based on the combination of particle swarm optimization search algorithm and least square method.

[0088] Specifically, step S15 includes:

[0089] Step S151. Initialize the particle swarm optimization search algorithm and define the number of particles as the initialization position of the model parameter α;

[0090] Step S152. Based on the particle swarm optimization search algorithm, locally update the particle position, turn to step S13, calculate the model parameter k and the cost function;

[0091] Step S153. Based on the particle swarm optimization search algorithm, globally update the particle position, turn to step S13, calculate the model parameter k and the cost function;

[0092] Step S154: Determine whether the cost function is less than a preset threshold; if not, repeat the above steps; if so, take the last identified model parameters α and k as the optimal identification result.

[0093] Step S2: Design a sliding mode controller, convert the intermittent input into a piecewise function, and obtain a chattering analysis model of the sliding mode controller.

[0094] For details, see Figure 3 , construct a sliding mode controller, step S2 includes:

[0095] Set the current position θ(t) and target position of the robot Define angular displacement error:

[0096]

[0097] Step S21. Based on formula (5), obtain the sliding mode control equation; formula (5) is:

[0098]

[0099] Among them, θ(t) is the current position of the robot arm; is the target position; e θ (t) is the angular displacement error; l is the lth control cycle; u(e θ (t)) is a sliding mode controller designed based on the position error.

[0100] Step S22. Establish the sliding mode control torque equation, as shown in the following formula:

[0101]

[0102] Among them, u(t) is the sliding mode controller, p is the control parameter, e lθ (t) The error obtained by the lth sampling. θ l (t) The angular displacement obtained by the lth sampling. Then the controller is obtained:

[0103]

[0104] Step S23. Based on the unit step function and formula (7), obtain the controller piecewise function equation; wherein formula (7) is:

[0105]

[0106] Step S24. Based on formula (8), obtain the robot arm angular displacement equation; wherein formula (8) is:

[0107]

[0108] Step S25: Separate the steady-state output and transient output of the angular displacement of the robot arm, and perform a chattering analysis on the sliding mode controller.

[0109] Specifically, according to the system response characteristics, the input before the current moment not only affects the current output, but also affects the future output. The output sampled at time lT is recorded as θ st (lT) steady-state output, the output at the future moment is transient outputθ tr (lT).

[0110] θ(t)=θ st(lT)+θ tr (lT);

[0111]

[0112]

[0113] Among them, θ tr (lT) represents the transient output formed by the input torque before time lT after time lT. It can be proved that this output is not 0 and is related to all historical input processes.

[0114] In formula (10), if the historical input changes alternately, it will inevitably cause the robot arm to vibrate. The vibration decays over time and tends to 0 when the time is long enough. The vibration frequency is related to the switching amplitude.

[0115] The above process shows that the jitter is related to all historical inputs. However, it is impossible to study the jitter characteristics of the robot arm based on all historical inputs in engineering. Instead, a certain length of historical information is intercepted to estimate the jitter.

[0116] Step S3: According to the response characteristics of the robot arm, a certain length of historical information is intercepted to perform optimal estimation on the vibration analysis model.

[0117] For details, see Figure 4 According to the research results of step S1, the model h(t)=kt in formula (2) can be obtained α Parameter analysis system impulse response attenuation characteristics such as Figure 3 According to the attenuation characteristics, the appropriate L can be selected. When the historical information exceeds L, the impact on the transient state is small and can be ignored.

[0118] A certain length of historical information is intercepted for chattering analysis, as shown in the following formula:

[0119]

[0120] According to [L / T], appropriate historical information is selected for chattering analysis, where [L / T] represents the rounding of L / T. The chattering estimation of the manipulator sliding mode control is obtained.

[0121] See also Figure 5-7 , let h(t)=t α , control torque τ(t)=aa coa(2.5t)[ω(t)-ω(t-0.6)], simulation diagram when aa=1 and aa=-1.

[0122] Figure 5 Angular displacement diagram of the robot arm when α = 0.5; Figure 6 Angular displacement diagram of the robot arm when α = 0.8; Figure 7 Angular displacement diagram of the robot arm when α=1.

[0123] The above simulation shows that except for the integer order system α=1 (ideal impulse response system), all systems have transient characteristics. Transient response is related to the system response characteristics and input.

[0124] See also Figure 8-9 , h(t)=[t 0.5 ,t 0.7 ] T , simulate the sliding mode control chattering process. Figure 8 The chattering diagram of sliding mode control when p = 2; Fig. 9 This is the chattering diagram of sliding mode control when p=5.

[0125] Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0126] 1. This application proposes a method for analyzing the chattering of a robot arm sliding mode control. This method establishes the relationship between the chattering of the robot arm sliding mode control and the system response characteristics and historical inputs, provides a basis for chattering analysis, and provides solutions for optimizing chattering.

[0127] 2. This application uses the input-output response characteristics to establish an equivalent simplified model of the robot arm response and studies the output memory characteristics of the robot arm. It avoids the complex modeling of factors such as the complex mechanical structure and uneven materials of the robot arm, and simplifies the model identification: only a few unknown parameters such as differential orders and constants need to be identified.

[0128] 3. This application intercepts a certain length of historical information to analyze jitter according to the system attenuation characteristics, which not only takes into account the accuracy of jitter analysis, but also avoids unnecessary computing overhead, reduces analysis complexity, and improves engineering application capabilities.

[0129] The above descriptions are merely embodiments of the present application and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A chattering analysis method for sliding mode control of a robot arm, characterized in that: The following steps are involved: Construct the input torque and angular displacement response model of the robot arm and identify the model parameters; Design a sliding mode controller, convert the intermittent input into a piecewise function, and obtain a chattering analysis model of the sliding mode controller; According to the response characteristics of the robot arm, a certain length of historical information is intercepted to perform an optimal estimation on the chattering analysis model.

2. The chattering analysis method of a robot arm sliding mode control according to claim 1, characterized in that: The method of constructing a robot arm input torque and angular displacement response model includes: Based on formulas (1)-(2), the input torque and angular displacement response model of the robot arm is obtained; the formulas (1)-(2) are: θ(t)=h(t)*τ(t) (1); Where θ(t) is the angular displacement, τ(t) is the input torque, and h(t) = [h1(t), h2(t)] T , h(t) represents the system impulse response; k and α are model parameters, k i =[k i1 ,k i2 ] T is the constant coefficient to be determined, α=[α1,α2] T , M is an integer. The higher M is, the higher the modeling accuracy is, but the more difficult the parameter identification is.

3. The chattering analysis method of a robot arm sliding mode control according to claim 1, characterized in that: Methods for identifying model parameters include: Based on formula (3), the cumulative formula of the discretized model is obtained and the displacement and input torque of the pair of robot angles are discretized and sampled; the formula (3) is: Based on the discretization model accumulation formula and the least squares method, a model parameter k is obtained; Based on formula (4), a cost function is constructed; the formula (4) is: Among them, C α (n) is the cost function, θ(i) is the angular displacement collected in the experiment, The angular displacement estimate obtained for the convolution; The model parameter α is identified based on the combination of particle swarm optimization search algorithm and least square method.

4. The chattering analysis method of a robot arm sliding mode control according to claim 3, characterized in that: The method for identifying the model parameter α based on the combination of particle swarm optimization search algorithm and least square method includes: Initializing the particle swarm optimization search algorithm, defining the number of particles as the initialization position of the model parameter α; Based on the particle swarm optimization search algorithm, locally update the particle position, calculate the model parameter k and the cost function; Based on the particle swarm optimization search algorithm, globally update the particle position, calculate the model parameter k and the cost function; Determine whether the cost function is less than a preset threshold; if so, repeat the above steps; if not, take the last identified model parameters α and k as the optimal identification result.

5. The chattering analysis method of a robot arm sliding mode control according to claim 3, characterized in that: Methods for obtaining a chattering analysis model include: Based on formula (5), the sliding mode control equation is obtained; the formula (5) is: Among them, θ(t) is the current position of the robot arm; is the target position; eθ(t) is the angular displacement error; l is the lth control cycle; u(e θ (t)) is a sliding mode controller designed according to the position error; Based on formula (6), the sliding mode controller is obtained; wherein the formula (6) is: Where, u(t) is the sliding mode controller, and p is the control parameter; Based on the unit step function and formula (7), the controller piecewise function equation is obtained; wherein the formula (7) is: Based on formula (8), the angular displacement equation of the robot arm is obtained; wherein, the formula (8) is: The steady-state output and transient output of the angular displacement of the robot arm are separated, and a chattering analysis is performed on the sliding mode controller.

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