Optimal Sliding Mode Cascade Control for Stabilization of Underactuated Nonlinear Systems

Abstract

This paper presents an optimal sliding mode cascade control for stabilization of a class of underactuated nonlinear mechanical systems. A discrete-time, nonlinear model predictive control structure is used to optimally select and update the parameters of the sliding mode control surfaces at specified intervals in order to achieve a desired performance objective. The determination of these surface parameters is subject to constraints that arise from the stability conditions imposed by the sliding mode control law and the physical limits on the system such as input saturation. Nominal stability of the optimal cascade control structure is demonstrated and its robust performance is illustrated using an experimental rotary inverted pendulum system.

Output‐feedback stabilisation control for a class of under‐actuated mechanical systems

“…The stabilisation for such systems might be solved with either discontinuous or time-varying control law. Different control strategies are discussed in literature, for example, sliding-mode control [7][8][9][10], motion-planningbased control [11,12], backstepping control [13,14], fuzzy control [15,16]. However, these controllers are either too complicated to be adopted in practical applications or only applicable for specific systems considered.…”

Adaptive control of rotary inverted pendulum system with time-varying uncertainties

“…Park et al [29] presented a swing-up and stabilization control with coupled sliding mode control. Some other robust designs can be found in the recent papers by Iraj et al [21], Muske et al [24], Ashrafiuon and Whitman [4], and Uchiyama et al [33]. A common assumption to these robust designs is that the variation bounds of the uncertainties and disturbances have to be available; otherwise, the design is not feasible.…”

Adaptive fuzzy sliding mode control for uncertain nonlinear underactuated mechanical systems

“…Then (1) can be rewritten as (2) By substituting iju = -lvI,-;ul(lvluaija + hu + rlu) obtained fr om the second row of (2) into the first row, we get where qd E � n is the desired trajectory, in which ea = qa -q� E � m and eu = qu -q� E � nm . The problem is to find a suitable control strategy to drive the tracking error to zero subject to nonlinearities and uncertainties of the system.…”

“…The SMC approach consists of designing a switching function and selecting a control law which will make the system trajectories attractive to the sliding surface [1]. The dynamic performance of a sliding mode controller, however, is a complex function of the effort, surface, and system parameters [2].…”