Showing papers by "Hassan K. Khalil published in 2015"

Design and Analysis of Sliding Mode Controller Under Approximate Hysteresis Compensation

Abstract: A sliding mode controller (SMC) is proposed for a class of systems comprising a hysteresis operator preceding a linear system with an all-pole transfer function. The hysteresis operator is modeled with uncertain piecewise linear characteristics, and a nominal inverse operator is included to mitigate the hysteresis effect. A classical SMC design typically uses a constant coefficient in the switching component, which is tuned via trial-and-error. In this paper, a state- and time-dependent coefficient is proposed based on the derived inversion error, which eliminates the need for parameter tuning and ensures the convergence of the sliding surface to the boundary layer without compactness assumptions. In addition, singular perturbation is used to analyze the system behavior within the sliding-surface boundary layer for the case of a constant coefficient in the classical SMC design. In particular, analytical insight is gained on the frequency-scaling behavior of the tracking error under a periodic reference. Simulation and experimental results based on a piezoelectric actuator-based nanopositioner are presented to illustrate the design and analysis, where the hysteresis nonlinearity is represented by a Prandtal-Ishlinskii operator.

High-gain-predictor-based output feedback control for time-delay nonlinear systems

Abstract: This paper designs a high-gain predictor (HGP) for the output feedback control of nonlinear systems in the presence of control, output, and state delays. The high-gain predictor realizes the states appearing in the output feedback control in terms of predictive state, delayed state, and current state. The system is combined by internal and external dynamics, and the closed-loop system with time-delays is supposed globally asymptotically stable and locally exponentially stable. Positively invariant sets are found to verify boundedness, ultimate boundedness, and exponential stability of the closed-loop system. In the simulation, a bounded sliding mode control is applied to demonstrate the performance recovery of the closed-loop system, and the fact that the high-gain-predictor parameter has a lower bound related to the time-delays.

Lyapunov's Stability Theory.

Abstract: Lyapunov’s theory for characterizing and studying the stability of equilibrium points is presented for time-invariant and time-varying systems modeled by ordinary differential equations.