Signal filtering and differential acquisition are classic yet challenging issues in control engineering.The discrete-time optimal control(DTOC)based on classic tracking differentiator(TD)can effectively extract differ...Signal filtering and differential acquisition are classic yet challenging issues in control engineering.The discrete-time optimal control(DTOC)based on classic tracking differentiator(TD)can effectively extract differentiation signals and filter signals,while eliminating the chattering problem that arises during the discretization of the continuous solution.However,under external disturbance,the convergence mode may change,leading to overshoot and noise amplification.In this paper,a dual-switching strategy is proposed,which can alternate between the base double-integral system and its dual system according to the quadrant of the system’s state.And a novel linearized control law is also introduced,deriving a novel dual-switch tracking differentiator.Further analysis of system convergence and time optimality is provided.Simulation results show that the application of this dual-switching strategy notably reduces overshoot in both tracking and differential signals while enhancing noise filtering performance.Moreover,experiments conducted on a permanent magnet synchronous motor(PMSM)platform,where the proposed TD acts as a filter in the speed feedback loop,demonstrate that the standard deviation between the reference speed and the target speed(at a constant speed of 378 r/min)decreased from 5.63 r/min to 4.93 r/min,compared to the moving average algorithm.展开更多
In this paper,some kinds of linear and nonlinear tracking-differentiators are designed by using suitable exponent functions instead of switch functions,and the stability of these tracking-differentiators is proved.Fro...In this paper,some kinds of linear and nonlinear tracking-differentiators are designed by using suitable exponent functions instead of switch functions,and the stability of these tracking-differentiators is proved.From the result of simulations,it is manifest that the tracking speeds of these kinds of linear and nonlinear tracking-differentiators are very high,and their design procedures are simple.展开更多
Since the quadruped robot possesses predominant environmental adaptability,it is expected to be employed in nature environments. In some situations,such as ice surface and tight space,the quadruped robot is required t...Since the quadruped robot possesses predominant environmental adaptability,it is expected to be employed in nature environments. In some situations,such as ice surface and tight space,the quadruped robot is required to lower the height of center of gravity( COG) to enhance the stability and maneuverability. To properly handle these situations,a quadruped controller based on the central pattern generator( CPG) model,the discrete tracking differentiator( TD) and proportional-derivative( PD) sub-controllers is presented. The CPG is used to generate basic rhythmic motion for the quadruped robot. The discrete TD is not only creatively employed to implement the transition between two different rhythmic medium values of the CPG which results in the adjustment of the height of COG of the quadruped robot,but also modified to control the transition duration which enables the quadruped robot to achieve the stable transition. Additionally,two specific PD sub-controllers are constructed to adjust the oscillation amplitude of the CPG,so as to avoid the severe deviation in the transverse direction during transition locomotion. Finally,the controller is validated on a quadruped model. A tunnel with variable height is built for the quadruped model to travel through. The simulation demonstrates the severe deviation without the PD sub-controllers,and the reduced deviation with the PD sub-controllers.展开更多
Differential signals are key in control engineering as they anticipate future behavior of process variables and therefore are critical in formulating control laws such as proportional-integral-derivative(PID).The prac...Differential signals are key in control engineering as they anticipate future behavior of process variables and therefore are critical in formulating control laws such as proportional-integral-derivative(PID).The practical challenge,however,is to extract such signals from noisy measurements and this difficulty is addressed first by J.Han in the form of linear and nonlinear tracking differentiator(TD).While improvements were made,TD did not completely resolve the conflict between the noise sensitivity and the accuracy and timeliness of the differentiation.The two approaches proposed in this paper start with the basic linear TD,but apply iterative learning mechanism to the historical data in a moving window(MW),to form two new iterative learning tracking differentiators(IL-TD):one is a parallel IL-TD using an iterative ladder network structure which is implementable in analog circuits;the other a serial IL-TD which is implementable digitally on any computer platform.Both algorithms are validated in simulations which show that the proposed two IL-TDs have better tracking differentiation and de-noise performance compared to the existing linear TD.展开更多
A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified...A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified tracking differentiator by select a Lyapunov function. Through combining of the nonlinear and linear function properly, it can be sure that the state converges to the equilibrium point with high speed automatically no matter that the state was far away from the equilibrium point or near to it, and it can prevent the chattering.?Simulation results show that the modified tracking differentiator tracking results?are?superior to the classical nonlinear tracking differentiator, and the response?of state variables tracking differentiator estimated?is?almost coincide with the real state of the variables of the given system.展开更多
基金Project(QZKFKT2023-012)supported by the State Key Laboratory of Heavy-duty and Express High-power Electric Locomotive,China。
文摘Signal filtering and differential acquisition are classic yet challenging issues in control engineering.The discrete-time optimal control(DTOC)based on classic tracking differentiator(TD)can effectively extract differentiation signals and filter signals,while eliminating the chattering problem that arises during the discretization of the continuous solution.However,under external disturbance,the convergence mode may change,leading to overshoot and noise amplification.In this paper,a dual-switching strategy is proposed,which can alternate between the base double-integral system and its dual system according to the quadrant of the system’s state.And a novel linearized control law is also introduced,deriving a novel dual-switch tracking differentiator.Further analysis of system convergence and time optimality is provided.Simulation results show that the application of this dual-switching strategy notably reduces overshoot in both tracking and differential signals while enhancing noise filtering performance.Moreover,experiments conducted on a permanent magnet synchronous motor(PMSM)platform,where the proposed TD acts as a filter in the speed feedback loop,demonstrate that the standard deviation between the reference speed and the target speed(at a constant speed of 378 r/min)decreased from 5.63 r/min to 4.93 r/min,compared to the moving average algorithm.
基金Supported by the National Natural Science Foundation of China (6 0 1 740 2 1 ) and Tianjin Key NaturalScience Foundation(0 1 3 80 0 71 1 )
文摘In this paper,some kinds of linear and nonlinear tracking-differentiators are designed by using suitable exponent functions instead of switch functions,and the stability of these tracking-differentiators is proved.From the result of simulations,it is manifest that the tracking speeds of these kinds of linear and nonlinear tracking-differentiators are very high,and their design procedures are simple.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61375101)
文摘Since the quadruped robot possesses predominant environmental adaptability,it is expected to be employed in nature environments. In some situations,such as ice surface and tight space,the quadruped robot is required to lower the height of center of gravity( COG) to enhance the stability and maneuverability. To properly handle these situations,a quadruped controller based on the central pattern generator( CPG) model,the discrete tracking differentiator( TD) and proportional-derivative( PD) sub-controllers is presented. The CPG is used to generate basic rhythmic motion for the quadruped robot. The discrete TD is not only creatively employed to implement the transition between two different rhythmic medium values of the CPG which results in the adjustment of the height of COG of the quadruped robot,but also modified to control the transition duration which enables the quadruped robot to achieve the stable transition. Additionally,two specific PD sub-controllers are constructed to adjust the oscillation amplitude of the CPG,so as to avoid the severe deviation in the transverse direction during transition locomotion. Finally,the controller is validated on a quadruped model. A tunnel with variable height is built for the quadruped model to travel through. The simulation demonstrates the severe deviation without the PD sub-controllers,and the reduced deviation with the PD sub-controllers.
基金supported by National Natural Science Foundation of China(61773170,62173151)the Natural Science Foundation of Guangdong Province(2023A1515010949,2021A1515011850).
文摘Differential signals are key in control engineering as they anticipate future behavior of process variables and therefore are critical in formulating control laws such as proportional-integral-derivative(PID).The practical challenge,however,is to extract such signals from noisy measurements and this difficulty is addressed first by J.Han in the form of linear and nonlinear tracking differentiator(TD).While improvements were made,TD did not completely resolve the conflict between the noise sensitivity and the accuracy and timeliness of the differentiation.The two approaches proposed in this paper start with the basic linear TD,but apply iterative learning mechanism to the historical data in a moving window(MW),to form two new iterative learning tracking differentiators(IL-TD):one is a parallel IL-TD using an iterative ladder network structure which is implementable in analog circuits;the other a serial IL-TD which is implementable digitally on any computer platform.Both algorithms are validated in simulations which show that the proposed two IL-TDs have better tracking differentiation and de-noise performance compared to the existing linear TD.
文摘A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified tracking differentiator by select a Lyapunov function. Through combining of the nonlinear and linear function properly, it can be sure that the state converges to the equilibrium point with high speed automatically no matter that the state was far away from the equilibrium point or near to it, and it can prevent the chattering.?Simulation results show that the modified tracking differentiator tracking results?are?superior to the classical nonlinear tracking differentiator, and the response?of state variables tracking differentiator estimated?is?almost coincide with the real state of the variables of the given system.
