Fractional order terminal sliding mode control method for flexible puncture driving platform

Abstract

The invention discloses a fractional order terminal sliding mode control method for a flexible puncture driving platform, and the method comprises the following steps: building a driving platform comprising a shape memory alloy driver and a puncture device, setting the puncture device as a sliding block which is provided with a puncture needle in the horizontal direction and can slide freely, and puncturing an artificial skin tissue, under the action of the bias spring, the horizontal reciprocating motion is realized; performing mathematical model description on the flexible puncture driving platform, describing hysteresis characteristics by using an MGPI model, and constructing a second-order kinetic equation; a fractional order terminal sliding mode control method based on a disturbance observer is provided for a mathematical model of the flexible puncture driving platform; based on a mathematical model of a flexible puncture driving platform, system uncertainty and external nonlinear interference terms are considered, a disturbance observer and a sliding mode control technology are combined, a fractional calculus operator is introduced to design a terminal sliding mode surface, a signal buffeting phenomenon is weakened, and high-precision tracking of the flexible puncture driving platform on an input signal is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of precision manufacturing and intelligent drive, and particularly relates to a fractional-order terminal sliding mode control method for a flexible puncture drive platform. Background Art

[0002] In the research field of intelligent precision drive technology, the shape memory alloy (SMA) actuator, as a new type of intelligent actuator, utilizes the phase change characteristics of SMA materials to generate deformation and displacement, realizing the conversion between thermal energy and mechanical energy. The drive components designed by SMA have obvious advantages such as simple structure, high energy density, light weight, no noise, and good bionic ability. Therefore, it has broad application prospects in many fields such as medical devices, robots, and aerospace. However, while the SMA actuator realizes the drive function, there is a significant strong saturation nonlinear hysteresis phenomenon, which means that the same input will result in different outputs, making the output of the actuator uncertain, leading to problems such as drive control delay and inaccuracy, seriously affecting the application of SMA flexible actuators in the field of high-precision drive control.

[0003] Currently, the research methods for controlling the nonlinear hysteresis characteristics mainly focus on feedforward control, feedback control, and the control method combining feedforward and feedback. The idea of feedforward control is to construct a hysteresis nonlinear mathematical model and its inverse model that can describe the inside of the SMA material, and use the inverse model as a feedforward controller to eliminate the hysteresis nonlinearity inside the SMA material. The principle is simple and effective, but the mathematical solution is difficult, and in practical applications, the drive platform is often affected by external disturbances, making it difficult to accurately describe the system with the mathematical model, and the control effect is poor. Feedback control does not require constructing an inverse model. By comparing the difference between the actual output and the desired output of the drive platform and feeding it back to the drive platform, closed-loop control is achieved, and the design parameters of the controller are less affected by the physical parameters of the drive platform. Therefore, it has strong anti-interference ability. The idea of combining feedforward and feedback is to solve the inverse model to compensate for the nonlinearity of the SMA drive platform, and then apply feedback control to achieve closed-loop control. However, the accuracy of solving the inverse model has always been a problem. In practical applications, the model of the drive platform is time-varying, and the model parameters in the control loop cannot be immediately changed accordingly. Therefore, in a complex environment, the method of inverse model feedforward is difficult to apply.

[0004] In the flexible puncture drive platform, there is no time-varying inverse model that can accurately describe its drive characteristics. Considering that the disturbance observer can well estimate the uncertainty and external disturbance terms of the drive platform, feedback control is adopted, combined with the fractional-order calculus operator, to design a terminal sliding mode control method. Summary of the Invention

[0005] The main objective of the present invention is to overcome the drawbacks and deficiencies of the prior art and provide a fractional-order terminal sliding mode control method for a flexible puncture driving platform.

[0006] To achieve the above objective, the present invention adopts the following technical solutions: The present invention discloses a fractional-order terminal sliding mode control method for a flexible puncture driving platform. The fractional-order terminal sliding mode control method includes the following steps: S1. Establish a flexible puncture driving platform, including a shape memory alloy driver and a puncture device. Among them, the shape memory alloy driver includes SMA wires, thermocouples, and bias springs. The puncture device includes a slider, a puncture needle, a slide rail, and a base. Set the driven component as a slider that can slide freely and is equipped with a puncture needle and a tensile-compressive force sensor. The bias spring and the SMA wire are respectively fixed at both ends of the base and are connected by the slider in the middle. The bias spring has a pre-tension to change the stretching length of the SMA wire, realizing a biased driving structure. Apply pressure to the SMA wire to change its temperature and generate a traction force to counteract the pulling force of the bias spring. When the force of the SMA wire exceeds the spring force, the SMA will pull the slider along the slide rail towards the direction of the SMA wire, and the puncture needle will penetrate the artificial tissue skin as the slider slides. The tensile-compressive force sensor measures the change in puncture force. When the heating stops and the SMA wire cools and elongates, the bias spring pulls the slider back to the initial position to realize reciprocating motion. The output displacement of the puncture needle is consistent with the output displacement of the slider and is measured by an external laser displacement sensor. S2. Conduct a mathematical description of the flexible puncture driving platform. The expression of the dynamic equation is as follows: (1) Among them, is the displacement of the slider, is the abbreviation of , and are respectively the first-order derivative and the second-order derivative of the displacement , is the input voltage signal of the flexible driving puncture platform, , , are respectively the first weight parameter, the second weight parameter, and the third weight parameter related to the internal electromechanical characteristics of the flexible puncture driving platform, represents the unknown hysteresis characteristic inside the SMA wire driving component, is the resistance received by the puncture needle, and the expression is as follows: (2) Among them, and are respectively the abbreviations of and , is the displacement of the slider at the moment when the puncture needle pierces the artificial tissue-like skin, , are the first and second parameters respectively describing the hardness force characteristics during the puncture process, , are the first and second parameters respectively describing the cutting force and friction force characteristics during the puncture process, Based on the above mathematical description, let , , the state space equation of Equation (1) is: (3) where, is the actual output displacement of the flexible puncture driving platform, is the actual moving speed of the flexible puncture driving platform, , represents the unmodeled error term of the uncertainty and external disturbance of the flexible puncture driving platform; S3. Design a fractional-order terminal sliding mode controller, define the tracking error as: (4) where, is the desired tracking trajectory, Define the virtual control law as: (5) where, is the first positive constant to be designed for adjusting the tracking error, is the first-order derivative of, is the sliding mode surface to be designed, Introduce the non-linear term and the fractional-order calculus term , design the fractional-order calculus terminal sliding mode surface, define the terminal sliding mode surface to be designed as: (6) where, , are the second and third positive constants to be designed for adjusting the tracking error, is the fractional-order calculus operator, is the fractional-order integration order, is the positive constant to be designed in the terminal sliding mode surface, Define the sliding mode surface control law as: (7) where, is The upper limit value, Design improvement reaching law is: (8) wherein, 、 、 、 are respectively the first, second, third, and fourth to-be-designed positive constants for adjusting the tracking error of the flexible puncture driving platform by the improved reaching law, 、 、 、 are respectively the first, second, third, and fourth to-be-designed positive constants related to the convergence speed of the flexible puncture driving platform in the improved reaching law, Define the improved sliding mode control law as: (9) Use the following disturbance observer , define the auxiliary variable to estimate in formula (7): (10) wherein, is the internal state variable for the disturbance observer to achieve the approximate estimation ability, is the first-order derivative of, is the to-be-designed positive constant for the disturbance observer to adjust the estimation error, Define the fractional-order terminal sliding mode control law as: (11) wherein, 、 are respectively the first input and the second input for the control law to adjust the tracking error; S4. According to the virtual control law of the fractional-order terminal sliding mode controller in step S3, the disturbance observer and the fractional-order terminal sliding mode control law control the flexible puncture driving platform to achieve precise tracking of the desired trajectory.

[0007] Furthermore, in the flexible puncture driving platform described in step S2, the length of the SMA wire is stretched by the pre-tension of the bias spring, and a voltage is applied to drive the SMA wire, causing the SMA wire to deform and drive the slider to reciprocate. When the puncture needle tip penetrates the artificial skin tissue, the interaction force between the puncture needle and the artificial skin tissue is divided into three parts: hardness force, friction force, and cutting force. The hardness force before piercing the artificial skin tissue is fitted with a quadratic polynomial function, and the friction force and cutting force after piercing the artificial skin tissue are fitted with a linear function, which is convenient for accurately characterizing the change of force when the puncture needle tip penetrates the artificial skin tissue.

[0008] Furthermore, the hysteresis characteristics of the SMA wire driving component described in step S2 are highly nonlinear, strongly saturated, and multi-valued mapping. Based on the generalized PI operator, a first-order linear input shape function is introduced to characterize the hysteresis characteristics of the SMA wire driving component, and the unknown hysteresis characteristics inside the SMA wire driving component are defined based on the MGPI model as: (12) where 、 、 are the first, second, and third undetermined normal constants of the MGPI model respectively, is the output signal of the MGPI model, is the generalized play operator, is the number of generalized play operators, , is the density function of the generalized play operator.

[0009] Furthermore, the fractional calculus operator described in step S3 can be used to weaken the chattering of the sliding mode control steady state based on its slow energy transfer, easy regulation, and genetic characteristics. It is calculated using the Riemann-Liouville definition formula, and the fractional calculus operator is expressed as: (13) where 、 are the upper and lower limits of the fractional calculus operator respectively, is the real part, is the abbreviated form of, The Riemann-Liouville fractional integral of order (14) The Riemann-Liouville fractional derivative of order is expressed as: (15) Among them, is an arbitrary unknown continuous function, is the Gamma function, is the independent variable of the Gamma function, is the time integration variable, is the exponential decay term, , , is greater than the smallest integer, represents an integer with a positive value.

[0010] Further, the improved reaching law described in step S3 , introducing a proportional term, a double-power term, and an improved variable-exponent term to optimize different stages of the sliding mode reaching process. The proportional term accelerates the flexible puncture driving platform to reach the sliding mode surface. The double-power term introduces an exponential function to ensure the rapid convergence of the flexible puncture driving platform when approaching and leaving the sliding mode surface. The improved variable-exponent term ensures the continuity of the driving platform to facilitate the elimination of chattering. The improved reaching law is expressed as: The proportional term is defined as: (16) Among them, is the first positive design constant related to the tracking error of the flexible puncture driving platform in the proportional term, is the positive design constant related to the convergence speed of the flexible puncture driving platform; The double-power term is defined as: (17) Among them, , are the second and third positive design constants related to the tracking error of the flexible puncture driving platform in the double-power term respectively, , are the positive design constants related to the convergence speed of the flexible puncture driving platform, , specifically accelerate the reaching rate to enable the flexible puncture driving platform to converge rapidly when approaching and leaving the sliding mode surface; The improved variable-exponent term is defined as: (18) Among them, is the fourth positive design constant related to the tracking error of the flexible puncture driving platform in the variable-exponent term, is a positive design constant related to the convergence speed of the flexible puncture driving platform. The improved variable exponent term ensures that the flexible puncture driving platform is a continuous function and eliminates the chattering of the flexible puncture driving platform.

[0011] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) For the fractional-order terminal sliding mode control method of the flexible puncture driving platform proposed by the present invention, a fractional-order calculus operator is introduced when designing the sliding mode surface. By using the slow energy transfer, easy regulation and genetic characteristics of the fractional-order calculus operator, the chattering in the steady state of the sliding mode control is weakened.

[0012] (2) In the control method proposed by the present invention, a new reaching law is designed, which combines a double power term, a proportional term and an improved variable exponent term. The double power term uses the properties of the exponential function to specifically accelerate the reaching speed at different stages of the reaching process, ensuring that the flexible puncture driving platform converges quickly when approaching and leaving the sliding mode surface. The variable exponent term ensures that the driving platform is a continuous function, avoids the discontinuous situation of the driving platform, and eliminates the chattering of the driving platform.

[0013] (3) In the control method proposed by the present invention, considering that the prior knowledge of the compound disturbance cannot be accurately obtained during the control design process, a disturbance observer is designed to estimate the modeling error, parameter variation and external disturbance term of the driving platform. While ensuring the stability of the closed-loop control, the anti-interference ability of the driving platform is improved.

[0014] (4) In the control method proposed by the present invention, an output feedback control method is used to design a fractional-order terminal sliding mode controller to perform tracking control on the SMA flexible puncture driving platform, which can achieve extremely small tracking errors and improve the robustness of the control driving platform at the same time.

[0015] (5) In the control method proposed by the present invention, the disturbance observer adopted can be used when the driving platform model is not fully known. At the same time, combined with the designed fractional-order terminal sliding mode controller, it ensures that the tracking error is globally uniformly bounded, has high control precision, and is also easy to be applied to other platforms. Description of the Drawings

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0017] Figure 1 is a schematic structural diagram of the flexible puncture driving platform in the present invention; Figure 2It is the test schematic diagram of the flexible puncture drive platform system in the present invention; Figure 3 It is the control structure block diagram of the flexible puncture drive platform in the present invention; Figure 4 It is the fractional-order terminal sliding mode control structure block diagram in the present invention; Figure 5 It is the schematic diagram of the simulated output displacement and the desired displacement of the flexible puncture drive platform under the fractional-order terminal sliding mode control and the PID control in the present invention. In the figure, the abscissa represents time and the ordinate represents displacement; Figure 6 It is the schematic diagram of the tracking error between the simulated output displacement and the desired displacement of the flexible puncture drive platform under the fractional-order terminal sliding mode control and the PID control in the present invention. In the figure, the abscissa represents time and the ordinate represents the tracking error; Figure 7 It is the schematic diagram of the actual output displacement and the desired displacement of the flexible puncture drive platform under the fractional-order terminal sliding mode control and the PID control in the present invention. In the figure, the abscissa represents time and the ordinate represents displacement; Figure 8 It is the schematic diagram of the tracking error between the actual output displacement and the desired displacement of the flexible puncture drive platform under the fractional-order terminal sliding mode control and the PID control in the present invention. In the figure, the abscissa represents time and the ordinate represents the tracking error.

[0018] Figure 9 It is the schematic diagram of the actual output displacement and the desired displacement of the flexible puncture drive platform under the fractional-order terminal sliding mode control and the terminal sliding mode control in the present invention. In the figure, the abscissa represents time and the ordinate represents displacement; Figure 10 It is the schematic diagram of the tracking error between the actual output displacement and the desired displacement of the flexible puncture drive platform under the fractional-order terminal sliding mode control and the terminal sliding mode control in the present invention. In the figure, the abscissa represents time and the ordinate represents the tracking error. Specific embodiments

[0019] In order to enable those skilled in the art of the present technology to better understand the solution of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts shall fall within the protection scope of the present application.

[0020] References to "embodiments" in this application mean that the specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of this application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0021] Embodiment 1 Figure 4 Figure 6 is a flowchart of a fractional-order terminal sliding mode control method for a flexible puncture driving platform proposed in this Embodiment 1, including the following steps: S1. Establish a flexible puncture driving platform, including a shape memory alloy actuator and a puncture device. Among them, the shape memory alloy actuator includes SMA wires, thermocouples, and bias springs, and the puncture device includes a slider, a puncture needle, a slide rail, and a base; set the driven component as a slider that can slide freely and is equipped with a puncture needle and a tensile and compressive force sensor. The bias spring and the SMA wire are respectively fixed at both ends of the base and connected by the slider in the middle. The bias spring has a pre-tension to change the stretching length of the SMA wire, realizing a biased driving structure; apply pressure to the SMA wire to change its temperature and generate a traction force to counteract the pulling force of the bias spring; when the force of the SMA wire exceeds the spring force, the SMA will pull the slider along the slide rail towards the direction of the SMA wire, and the puncture needle will penetrate the artificial tissue skin as the slider slides. The tensile and compressive force sensor measures the change in puncture force; when the heating stops and the SMA wire cools and elongates, the bias spring pulls the slider back to the initial position to realize reciprocating motion; the output displacement of the puncture needle is consistent with the output displacement of the slider and is measured by an external laser displacement sensor; For Figure 1 the structural schematic diagram of the flexible puncture driving platform shown in Figure 2 Figure 7, a control system shown in Figure 8 is designed and experimentally tested. The components of the control system are as follows:

[0022] SMA flexible actuator: Use the No. 8 nickel-titanium alloy wire developed by Fort Wayne Metals Company in the United States, which can provide a peak output displacement of 12 mm, and the input voltage range is 0 - 10V.

[0023] Laser displacement sensor: To measure the output displacement of the flexible puncture driving platform, select the HG-C1000 series laser displacement sensor of Panasonic Corporation. The repeatability accuracy of the used laser displacement sensor can reach 30μm.

[0024] Force sensor: The DYLY-108 tension and compression sensor and DY510 force transmitter of Dayang Company are selected. The power supply voltage of the DY510 force transmitter is 15~30Vdc, and the comprehensive accuracy is 0.05%.

[0025] Power amplifier: Output the amplified voltage as the driving voltage of the SMA flexible driver.

[0026] Signal acquisition and output part: The dSPACE1104 real-time simulation system is adopted. The signal acquisition and output are realized by using the A / D and D / A conversion functions of dSPACE. The connection between dSPACE1104 and MATLAB / Simulink enables online real-time monitoring and control of parameters through the ControlDesk software.

[0027] S2. Mathematically describe the flexible puncture driving platform, and the expression of the dynamic equation is as follows: (1) Among them, is the displacement of the slider, is the abbreviation of , and are the first-order derivative and second-order derivative of the displacement respectively, is the input voltage signal of the flexible driving puncture platform, , , are the first weight parameter, second weight parameter, and third weight parameter related to the internal electromechanical characteristics of the flexible puncture driving platform respectively, represents the unknown hysteresis characteristic inside the SMA wire driving component, is the resistance received by the puncture needle, and the expression is as follows: (2) Among them, and are the abbreviations of and respectively, is the displacement of the slider at the moment when the puncture needle pierces the artificial tissue-like skin, , are the first and second parameters describing the hardness force characteristics during the puncture process respectively, , are the first and second parameters describing the cutting force and friction force characteristics during the puncture process respectively, Based on the above mathematical description, let , , the state space equation of formula (1) is: (3) wherein, is the actual output displacement of the flexible puncture driving platform, is the actual moving speed of the flexible puncture driving platform, , represents the unmodeled error terms of the uncertainties and external disturbances of the flexible puncture driving platform; S3. Design a fractional-order terminal sliding mode controller, and define the tracking error as: (4) wherein, is the desired tracking trajectory, Define the virtual control law as: (5) wherein, is the first positive constant to be designed for adjusting the tracking error, is the first-order derivative of, is the sliding mode surface to be designed, Introduce the non-linear term and the fractional calculus term , design the fractional calculus terminal sliding mode surface, and define the terminal sliding mode surface to be designed as: (6) wherein, , are the second and third positive constants to be designed for adjusting the tracking error, is the fractional calculus operator, is the fractional integral order, is the positive constant to be designed in the terminal sliding mode surface, Define the sliding mode surface control law as: (7) wherein, is the upper limit value of, Design the improved reaching law as: (8) wherein, , , , are the first, second, third, and fourth positive constants to be designed for adjusting the tracking error of the flexible puncture driving platform by the improved reaching law, , , , are the first, second, third, and fourth normal constants to be designed related to the convergence speed of the flexible puncture driving platform in the improved reaching law, respectively. Define the improved sliding mode control law as: (9) Using the following disturbance observer , define the auxiliary variable to estimate in Equation (7): (10) where is the internal state variable for the disturbance observer to achieve the approximate estimation ability, is the first-order derivative of, is the normal constant to be designed for the disturbance observer to adjust the estimation error, Define the fractional-order terminal sliding mode control law as: (11) where , are the first input and the second input for the control law to adjust the tracking error, respectively; S4. According to the virtual control law of the fractional-order terminal sliding mode controller, the disturbance observer and the fractional-order terminal sliding mode control law control the flexible puncture driving platform to achieve accurate tracking of the desired trajectory.

[0028] At this time, in the flexible puncture driving platform described in step S2, the length of the SMA wire is stretched by the pre-tension of the bias spring, and a voltage is applied to drive the SMA wire, causing the SMA wire to deform and drive the slider to move reciprocally. When the puncture needle tip penetrates the artificial skin tissue, the interaction force between the puncture needle and the artificial skin tissue is divided into three parts: hardness force, friction force, and cutting force. The hardness force before piercing the artificial skin tissue is fitted with a quadratic polynomial function, and the friction force and cutting force after piercing the artificial skin tissue are fitted with a linear function to accurately characterize the change of force when the puncture needle tip penetrates the artificial skin tissue.

[0029] At this time, the hysteresis characteristics of the SMA wire driving component described in step S2 are highly nonlinear, strongly saturated, and multi-valued mapping. Based on the generalized PI operator, a first-order linear input shape function is introduced to characterize the hysteresis characteristics of the SMA wire driving component. The unknown hysteresis characteristics inside the SMA wire driving component are defined based on the MGPI model as: (12) Among them, , , are the first, second, and third positive constants to be designed in the MGPI model respectively, is the output signal of the MGPI model, is the generalized play operator, is the number of generalized play operators, , is the density function of the generalized play operator.

[0030] At this time, the fractional calculus operator described in step S3, based on its slow energy transfer, easy regulation, and genetic characteristics, can be used to weaken the chattering in the steady state of sliding mode control. It is calculated using the Riemann-Liouville definition formula, and the fractional calculus operator is expressed as: (13) Among them, , are the upper and lower limits of the fractional calculus operator respectively, is the real part, is the abbreviated form of, The Riemann-Liouville fractional integral of order (14) The Riemann-Liouville fractional derivative of order (15) Among them, is an arbitrary unknown continuous function, is the Gamma function, is the independent variable of the Gamma function, is the time integration variable, is the exponential decay term, , , is greater than the smallest integer, represents an integer with a positive value.

[0031] At this time, the improved reaching law described in step S3 , a proportional term, a double power term, and an improved variable exponent term are introduced to optimize different stages of the sliding mode approaching process. The proportional term accelerates the flexible puncture driving platform to reach the sliding mode surface. The double power term introduces an exponential function to ensure the rapid convergence of the flexible puncture driving platform when approaching and leaving the sliding mode surface. The improved variable exponent term ensures the continuity of the driving platform to facilitate the elimination of chattering. The improved reaching law is expressed as: The proportional term is defined as: (16) where is the first positive design constant related to the tracking error of the flexible puncture driving platform in the proportional term, is the positive design constant related to the convergence speed of the flexible puncture driving platform; The double power term is defined as: (17) where , are the second and third positive design constants related to the tracking error of the flexible puncture driving platform in the double power term respectively, , are the positive design constants related to the convergence speed of the flexible puncture driving platform, , specifically accelerate the approaching rate to enable the flexible puncture driving platform to converge rapidly when approaching and leaving the sliding mode surface; The improved variable exponent term is defined as: (18) where is the fourth positive design constant related to the tracking error of the flexible puncture driving platform in the variable exponent term, is the positive design constant related to the convergence speed of the flexible puncture driving platform. The improved variable exponent term ensures that the flexible puncture driving platform is a continuous function and eliminates the chattering of the flexible puncture driving platform.

[0032] In summary, Embodiment 1 proposes a fractional-order terminal sliding mode control method for a flexible puncture driving platform. Selecting appropriate control parameters and design parameters can achieve good control effects.

[0033] Embodiment 2 Based on the fractional-order terminal sliding mode control method in Embodiment 1, it is implemented according to step S3 to deduce the fractional-order terminal sliding mode controller. To verify the effectiveness of the control scheme, a Figure 3The closed-loop control block diagram shown further incorporates the controller design into the experimental environment. By comparing with the experimental results of the PID controller, the control indicators are verified using Matlab / Simulink. Therefore, based on each step of the fractional-order terminal sliding mode control method in Embodiment 1 and in combination with Parameter Tables 1 and 2, simulation and closed-loop experiments are conducted on the flexible puncture driving platform.

[0034] Simulation experiment: Tracking control is performed on the desired sine trajectory with the initial values of the system states set as: , and the controller parameters are referred to Table 1 and Table 2. The simulation step size is selected as 0.001 s, and the simulation duration is selected as 100 s. The experimental results are as shown in Figure 5 and Figure 6 . Figure 5 shows the comparison between the displacement of the SMA flexible driving component and the desired trajectory under the simulation condition, Figure 6 and shows the error curve between the actual displacement of the SMA flexible driving component and the desired trajectory under the simulation condition. Under the action of the PID controller, the maximum steady-state tracking error of the closed-loop system is 0.51%, and under the action of the fractional-order terminal sliding mode controller, the maximum steady-state tracking error of the closed-loop system is 0.03%.

[0035] Closed-loop experiment: Tracking control is performed on the desired sine trajectory with the initial values of the system states set as: , and the controller parameters are referred to Table 1 and Table 2. The sampling frequency is selected as 1 KHz, and the experimental duration is selected as 100 s. The experimental results are as shown in Figure 7 and Figure 8 . Figure 7 shows the comparison between the actual displacement of the SMA flexible driving component and the desired trajectory, Figure 8 and shows the error curve between the actual displacement of the SMA flexible driving component and the desired trajectory. Under the action of the PID controller, the maximum steady-state tracking error of the closed-loop system is 4.01%, and under the action of the fractional-order terminal sliding mode controller, the maximum steady-state tracking error of the closed-loop system is 2.36%.

[0036] Table 1. The first input parameter of the fractional-order terminal sliding mode control law

[0037] Table 2. The second input parameter of the fractional-order terminal sliding mode control law

[0038] To sum up, in this Embodiment 2, appropriate control parameters and design parameters are selected, and by comparing with the PID controller, good control effects are achieved.

[0039] Embodiment 3 Based on the fractional-order terminal sliding mode control method in Embodiment 1, it is implemented according to Step S3, and the fractional-order terminal sliding mode controller is derived. To verify the effectiveness of the control scheme, referring to the closed-loop control block diagram built in Example 2, the order of the fractional-order calculus operator and the terminal normal constant are further transformed, and Matlab / Simulink is used to verify the control indexes. Therefore, this embodiment is based on each step of the fractional-order terminal sliding mode control method in Embodiment 1, and combines Parameter Tables 3 and 4 to conduct a closed-loop experiment on the flexible puncture driving platform.

[0040] Table 3. The first input parameter of the fractional-order terminal sliding mode control law

[0041] Table 4. The second input parameter of the fractional-order terminal sliding mode control law

[0042] Closed-loop experiment: Track and control the desired sine trajectory The initial values of the system state are set as: , the controller parameters are shown in Parameter Tables 3 and 4, the sampling frequency is selected as 1KHz, and the experimental duration is selected as 120s. The experimental results are as shown in Figure 9 and Figure 10 . Figure 9 shows the comparison between the actual displacement of the SMA flexible driving component and the desired trajectory, Figure 10 shows the error curve between the actual displacement of the SMA flexible driving component and the desired trajectory. Under the action of the fractional-order terminal sliding mode controller, the maximum steady-state tracking error of the closed-loop system is 2.36%. After removing the fractional-order calculus operator and the nonlinear terminal term, the maximum steady-state tracking error of the closed-loop system is 3.94%. Therefore, introducing the fractional-order calculus operator and the nonlinear terminal term can significantly improve the tracking accuracy.

[0043] In summary, in this Embodiment 3, appropriate control parameters and design parameters are selected, and by comparing the influence of the parameters to be designed in the fractional-order calculus terminal sliding mode surface in Step S3, the effectiveness of the fractional-order terminal sliding mode control method is proved.

[0044] The good tracking performance in the figure shows that this experiment can successfully track the desired trajectory, and the maximum tracking error does not exceed 0.2mm after stabilization. A fractional-order terminal sliding mode tracking control method for a flexible puncture driving platform of the present invention can well overcome the adverse effects of the hysteresis phenomenon and external disturbances on the control system, proving the effectiveness of the proposed control strategy.

[0045] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0046] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A fractional-order terminal sliding mode control method for a flexible puncture drive platform, characterized in that: The fractional-order terminal sliding mode control method comprises the following steps: S1. Establish a flexible puncture drive platform, including a shape memory alloy driver and a puncture device, wherein the shape memory alloy driver includes an SMA wire, a thermocouple and a bias spring, and the puncture device includes a slider, a puncture needle, a slide rail and a base; set the driven component to be a slider that can slide freely and is equipped with a puncture needle and a tension pressure sensor, the bias spring and the SMA wire are respectively fixed at both ends of the base, and are connected in the middle by the slider, and the bias spring has a pre-tension to change the stretching length of the SMA wire to realize a biased drive structure; pressurize the SMA wire to change its temperature, generate traction, and counteract the tension of the bias spring; when the force of the SMA wire exceeds the spring force, the SMA will pull the slider to move along the slide rail toward the SMA wire, and the puncture needle will pierce the artificial tissue skin as the slider slides, and the tension pressure sensor will measure the change in puncture force; when the heating stops, the SMA wire cools and stretches, and the bias spring pulls the slider back to the initial position to realize reciprocating motion; the output displacement of the puncture needle is consistent with the output displacement of the slider, which is measured by an external laser displacement sensor; S2. The flexible puncture driving platform is mathematically described, and the dynamic equation is expressed as follows: （1） in, is the displacement of the slider, yes Abbreviation, and Displacement The first and second order derivatives of is the input voltage signal of the flexible drive puncture platform, , , are the first weight parameter, the second weight parameter and the third weight parameter related to the internal electromechanical characteristics of the flexible puncture drive platform, Indicates the unknown hysteresis characteristics inside the SMA wire drive component, is the resistance of the puncture needle, expressed as follows: （2） in, and They are and Abbreviation, It is the displacement of the slider at the moment when the puncture needle pierces the artificial tissue skin. , They are the first and second parameters describing the hardness characteristics during the puncture process. , They are the first and second parameters describing the cutting force and friction characteristics during the puncture process, Based on the above mathematical description, let , , the state space equation of formula (1) is: （3） in, is the actual output displacement of the flexible puncture drive platform, is the actual movement speed of the flexible puncture drive platform, , represents the uncertainty of the flexible puncture driving platform and the unmodeled error term of external disturbance; S3. Design a fractional-order terminal sliding mode controller and define the tracking error for: （4） in, To track the desired trajectory, Defining virtual control laws for: （5） in, The first constant to be designed to adjust the tracking error is, for The first-order derivative of is the sliding surface to be designed, Introducing nonlinear terms With fractional calculus terms , design the fractional calculus terminal sliding surface, define the terminal sliding surface to be designed for: （6） in, , It is the second and third constants to be designed to adjust the tracking error. is a fractional calculus operator, is the fractional integration order, is the constant to be designed in the terminal sliding surface, Define the sliding surface control law for: （7） in, for The upper limit value of Design Improvement Reaching Law for: （8） in, , , , are the first, second, third and fourth positive constants to be designed for adjusting the tracking error of the flexible puncture driving platform by improving the reaching law, , , , are the first, second, third and fourth positive constants to be designed in the improved reaching law related to the convergence speed of the flexible puncture driving platform, Define the improved sliding mode control law for: （9） Using the following disturbance observer , define auxiliary variables Estimation of formula (7) : （10） in, is the internal state variable of the disturbance observer to achieve approximate estimation capability, yes The first-order derivative of is the constant to be designed for the disturbance observer to adjust the estimated error, Define the fractional-order terminal sliding mode control law for: （11） in, , are respectively the first input and the second input of the control law used to adjust the tracking error; S4, according to the virtual control law of the fractional order terminal sliding mode controller in step S3 , disturbance observer and fractional-order terminal sliding mode control law The flexible puncture drive platform is controlled to achieve accurate tracking of the desired trajectory.

2. According to claim 1, a fractional-order terminal sliding mode control method for a flexible puncture drive platform is characterized in that: In the flexible puncture drive platform, the length of the SMA wire is stretched by the pre-tension of the bias spring, and a voltage is applied to drive the SMA wire, so that the SMA wire is deformed and the slider is pulled to move. When the puncture needle end penetrates the artificial skin tissue, the interaction force between the puncture needle and the artificial skin tissue is divided into three parts: hardness force, friction force and cutting force.

3. According to claim 1, a fractional-order terminal sliding mode control method for a flexible puncture drive platform is characterized in that: Unknown hysteresis characteristics inside the SMA wire drive component Based on the MGPI model, it is defined as: （12） in, , , are the first, second and third positive constants to be designed for the MGPI model, is the output signal of the MGPI model, is the generalized play operator, is the number of generalized play operators, , is the generalized play operator density function.

4. According to claim 1, a fractional-order terminal sliding mode control method for a flexible puncture drive platform is characterized in that: The fractional calculus operator is expressed as: （13） in, , are the upper and lower limits of the fractional calculus operator, for Real part, for The abbreviation of The Riemann-Liouville fractional integral of order is defined as: （14） The Riemann-Liouville fractional derivative is expressed as: （15） in, is any unknown continuous function, is the Gamma function, is the independent variable of the Gamma function, is the time-integrated variable, is an exponential decay term, , , is greater than The smallest integer of Indicates a positive integer value.

5. According to claim 1, a fractional-order terminal sliding mode control method for a flexible puncture drive platform is characterized in that: The improved reaching law Combining the proportional term, the double power term and the improved variable exponent term, where The proportional term is defined as: （16） in, is the first positive constant to be designed in the proportional term related to the tracking error of the flexible puncture driving platform, is a positive design constant related to the convergence speed of the flexible puncture drive platform; The double power term is defined as: （17） in, , are the second and third positive constants to be designed in the double power term related to the tracking error of the flexible puncture drive platform, , is a positive design constant related to the convergence speed of the flexible puncture drive platform, , The approach rate is accelerated in a targeted manner, so that the flexible puncture driving platform converges quickly when approaching and moving away from the sliding surface; The improved variable exponent term is defined as: （18） in, is the fourth positive design constant in the variable exponential term related to the tracking error of the flexible puncture drive platform, is a positive design constant related to the convergence speed of the flexible puncture driving platform. The improved variable exponential term ensures that the flexible puncture driving platform is a continuous function and eliminates the buffeting of the flexible puncture driving platform.

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