State estimation of a robot joint by a novel nonlinear tracking differentiator

Abstract

Purpose This paper aims to present a method for improving the state estimation of a robot in the presence of noise measurement, which can improve the performance of the robot controller. Design/methodology/approach In this work, a novel nonlinear tracking differentiator (NTD) was formulated to solve the problems of phase lag, low stability and amplitude attenuation faced by traditional tracking differentiators, which can be used for the state estimation of a robot. Based on the user-defined function stu() with linear and nonlinear characteristics, the authors establish a new acceleration function of NTD and confirm its global asymptotic stability by using the Lyapunov method and the system equivalence method. Phase plane analysis shows that the origin is its stable nodal point or focus point and uncovers the basic constraint conditions for parameter regulation. In addition, the convergence property and robustness performance against noises are studied by describing function method. Findings Comparative simulations, robot state estimation experiments and joint trajectory tracking experiments have indicated that NTD proposed integrates tracking rapidness, accuracy and transitional stability and has high approximation and filtering effects on generalized derivatives of the signal, which contribute to an excellent performance of robot controller in stability and response speed in practice. Originality/value The main contribution of this paper lies in the design of a novel NTD, which successfully improves the state estimation of a robot joint in noisy surroundings, the tracking performance of robot controller and the stability of the system.

Active Disturbance Rejection Control of Multi-Joint Industrial Robots Based on Dynamic Feedforward

“…Based on the semi-closed-loop control structure, we regulate the parameters of the two controllers to optimize the following performance. The parameters of the two controllers in Equations (15)(16)(17)(18)(19)(20) and (36-38) are listed in Table 2. The servo periods of the position loop and the velocity loop were 2 ms and 200 µs, respectively, and the sampling period was 200 µs.…”

“…Many simulation studies show during ADRC control, the estimation demand of 0 B is not high, and the relative error is within 30%, and when it is higher, it does not affect the closed-loop control quality. Thus, ζ is usually considered as constant in practical applications [19].…”

“…The first part is about arranging the transition process, which is implemented in tracking differentiator, as in Equations (17) and (18), used to produce smooth instruction curves and differential curves. The second part is the design of ESO, as the first three equations in Equations (19) and (20), which are used to observe the disturbance in the corresponding loop.…”

“…The third part of ADRC is the feedback controller. The control laws u v in Equation (19) and u i in Equation (20) adopt the simple P control laws combing basic function fal(). When the controller structure has been determined, appropriate ESO and PID control laws could be designed/selected according to real situations, so as to improve the system robustness.…”

“…When the controller structure has been determined, appropriate ESO and PID control laws could be designed/selected according to real situations, so as to improve the system robustness. More details can be found in [11,12,15,19].…”