Robust tracking control for a class of uncertain mechanical systems

Abstract

In this paper, it is proposed a control structure to solve the tracking problem in a class of uncertain mechanical systems. It is considered that the system is affected by unknown disturbances, discontinuous friction and uncertainties. The proposed control algorithm is based on the twisting control algorithm plus a nested signum term, moreover a disturbance estimator is used as feedback to the controller in order to compensate the non modelled parameters and uncertainties of the plant, also a velocity observer is proposed. Through the usage of Lyapunov tools, it is shown that the closed-loop nonlinear system is globally asymptotically stable and achieves zero steadystate position error, also, it is shown that while being asymptotically stable and homogeneous of degree q < 0, these systems approach the equilibrium point in finite time. Numerical simulations and real-time experiments carried out in a mass-spring-damper system show the performance and effectiveness of the control structure.

Variable-parameter double-power reaching law sliding mode control method

“…As illustrated in Figures 4 and 5, in the case of disturbance, system state s andṡ converge to the steady-state bound error limit in a finite time. The steady-state error does not exceed the result of formula formula (16), (17), (18) and (19). Moreover, system state s converges to its minimum steady-state error bounds in its entire sliding mode.…”

“…A control structure to solve the tracking problem in a class of uncertain mechanical systems is proposed in ref. [17]. The numerical simulations and real-time experiments carried out in a mass-spring-damper system show the performance and effectiveness of the control structure.…”

“…When the perturbation is d(t) = 0.3sin(3t) + 0.3cos (2t), based on the variable-parameter double-power reaching law (26), control law u is designed and simulated. The correctness of the test formula (16), (17), (18) and (19) is verified. The initial value of the system is s(0) = 5; in formula (1) and formula (2): order α 1 = 1.5, α 2 = 1.6; β 1 = 0.75, β 2 = 0.8;k 1 = 1.5, k 2 = 0.8.…”

“…The parameters were substituted into (16) and (18), and we obtained: |s| 1 ≤ 0.295, |s| 2 ≤ 0.543. A substitution of formula (17) and formula (19) can obtain |ṡ| ≤ 1.5.…”

Adaptive optimal slip ratio estimator for effective braking on a non-uniform condition road

“…The vehicle velocity cannot be measured directly due to the cost and technical issues. As a result, it may be estimated by an observer such as sliding mode [1][2][3], fusion Kalman/UFIR [4], and deadbeat dissipative FIR filtering [5].…”