Abstract
This paper investigates the problem of nonsmooth feedback stabilization for the higher order uncertain chain of integrators. For achieving the specified goal, the integral term of classical Proportional-Integral (PI) controller is replaced by an integral of the discontinuous function. Replacing this integrator, the overall control becomes absolutely continuous rather than discontinuous as in the first order sliding mode control. With this proposed scheme, the property of invariance concerning the matched Lipschitz uncertainty is still preserved. The main technical contribution of the paper is a sound and non-trivial Lyapunov analysis of the closed loop system controlled by nonsmooth PI controller. The effectiveness of the proposed controller is illustrated with the help of numerical simulation on the magnetic suspension system.
Highlights
Stability, of a perturbed system, is one of the classical problems in the control literature [1]
Consider the system χ = F(χ, ρ(t)) + G(χ, ρ(t))u; σ = h(χ) where u is the control signal, χ is the states of the system, σ is the output, and ρ(t) represents unknown external perturbations or model uncertainties
SIMULATION We demonstrate the robustness of nonsmooth PI control for the third order uncertain chain of integrators containing constant or time-varying matched disturbances
Summary
Of a perturbed system, is one of the classical problems in the control literature [1]. Consider the system χ = F(χ , ρ(t)) + G(χ , ρ(t))u; σ = h(χ) where u is the control signal, χ is the states of the system, σ is the output, and ρ(t) represents unknown external perturbations or model uncertainties. One of the main objectives is to construct a feedback control law u such that the output σ robustly tracks a reference signal σ0, despite unknown external perturbations or model uncertainties. There are several different methodologies already reported in the literature to simplify the above-mentioned problem for the design of a feedback control u. One such strategy is known as a normal form [7], [8].
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