Novel quasi-continuous super-twisting high-order sliding mode controllers for output feedback tracking control of robot manipulators

Abstract

In this paper, a robust output feedback tracking control scheme for uncertain robot manipulators with only position measurements is investigated. First, a quasi-continuous second-order sliding mode (QC2S)-based exact differentiator and super-twisting second-order sliding mode (STW2S) controllers are designed to guarantee finite time convergence. Although the QC2S produces continuous control and less chattering than that of a conventional sliding mode controller and other high-order sliding mode controllers, a large amount of chattering exists when the sliding manifold is defined by the equation [Formula: see text]. To decrease the chattering, an uncertainty observer is used to compensate for the uncertainty effects, and this controller may possess a smaller switching gain. Compared to the QC2S controller, the STW2S has less chattering and tracking error when the system remains on the sliding manifold [Formula: see text]. Therefore, to further eliminate the chattering and obtain a faster transient response and higher tracking precision, we develop a quasi-continuous super-twisting second-order sliding mode controller, which integrates both the merits of QC2S and STW2S controllers. The stability and convergence of the proposed scheme are theoretically demonstrated. Finally, computer simulation results for a PUMA560 robot comparing with conventional QC2S and STW2S controllers are shown to verify the effectiveness of the proposed algorithm.

Output‐feedback finite‐time and exponential tracking continuous control for mechanical systems with constrained inputs

“…Through such a tuning, overshoot was observed at every link position error response in Experiment 1. On the contrary, the results from Experiment 2 show that the relaxed criterion from (18) made it possible to eliminate the overshoot in links 1 and 2 and lower it down in link 3. This advantage was made possible thanks to the flexibility given by ( 18) with respect to the above mentioned fixed relation stated for a j , j = 2, 3, (in terms of a 1 ∈ (0, 1)) from the homogeneity-based output-feedback regulation results from the works by Zamora-Gómez et al 12,15 Figure 5…”

“…One notes from the graphs that, while the proposed scheme achieved the tracking control objective in finite time and avoiding input saturation, this could not be avoided by the (infinite-time) controller L16, which generated control signals that did reach and actually stayed at the actuator saturation levels during several time intervals along the transient. Actuator saturation is generally undesirable in practice, as pointed out for instance in the work by Aguiñaga-Ruiz et al 39 4) was run applying the fixed relation from the homogeneity-based output-feedback regulation approaches by Zamora-Gómez et al, 12,15 giving a 2 = a 1 = 0.6 and a 3 = (1 + a 1 )∕2 = 0.8, while in Experiment 2 (solid line on Figure 4) we took a 2 = 0.7 > 0.6 = a 1 and a 3 = 0.83 < 0.9 = 1 + a 1 − a 2 , in accordance to the criterion stated in this work through (18). For both implementations, we took control gains K 1 = diag[80, 60, 5], K 2 = diag[200, 60, 12], K 3 = diag [4,2,11] and K 4 = diag[54, 30,21], which were chosen so as to generate closed-loop responses that may be considered acceptably fast.…”

“…The remaining tests were added as a suggestion from an anonymous reviewer. In particular, Test 3 aims to show a profit over counting on the finite-time convergence criterion stated through (18) with respect to that obtained through homogeneity in the regulation cases from the works by Zamora-Gómez et al 12,15 -namely a 1 ∈ (0, 1), a 2 = a 1 and a 3 = (1 + a 1 )∕2-which happens to be a very particular case included in (18). Finally, Test 4 shows the closed-loop system performance when a 1 and a 2 take a common low value.…”

“…Moreover, the corresponding search for a suitable control scheme becomes particularly defying if the referred problem is aimed to be solved through dynamic dissipation, instead of involving an observer. The latter would involve further reproduction of the system dynamics entailing further dependence of the overall control scheme on the system model, as can be corroborated from observer-based previous works related to the topic; 17,18 these have actually drawn on sliding-mode related techniques, involving discontinuities in the considered auxiliary dynamics, to deal with perturbation terms. The former could simply involve a suitable nonlinear version of the dirty derivative, characterized by its very simple model-free dynamics.…”

Implementation of an Adaptive Neural Terminal Sliding Mode for Tracking Control of Magnetic Levitation Systems

“…Therefore, the chattering attenuation issue has become a popular topic. Some methods have been proposed for resolving this issue, such as the use of quasi-sliding mode [32], [33], low pass filters [34], [35], fuzzy-SMC [36], [37], neural networks-SMC (NN-SMC) [38]- [42], or suppertwisting SMC methods [47], [48]. The method of using NN to reduce the chattering in the control input is to use a NN to approximate the unknown components that affect the system.…”