Abstract
In this paper, output feedback tracking sliding mode control was considered for uncertain multivariable linear systems. The uncertainties included external disturbance, the system state, and control input. A new property of the loop transfer recovery (LTR) observer was first established: the state estimation error of the LTR observer can be made arbitrarily small with respect to state- and input-dependent system uncertainties. Observer-based output feedback tracking sliding mode control using the LTR observer is presented. The proposed sliding mode control approach can maintain the boundedness of the system state and drive the system outputs arbitrarily close to the desired reference outputs; the degree of closeness was determined by a design parameter in the LTR observer. In the proposed approach, the most general and simple observer-based output feedback control formulation was used to achieve global tracking. Simulations with a two-degree-of-freedom (DOF) robotic manipulator application illustrated the claimed properties, and a peaking and chattering reduction technique was demonstrated to protect the actuator.
Highlights
Sliding mode control is a widely recognized and robust control method
In most previous research on output feedback sliding mode control, uncertainty was assumed to be a function of disturbance and output, e0 = θy + d; by contrast, in the proposed approach, uncertainty was allowed to be a function of state, input, and external disturbance: e0 = ∆κ u + θ T x + d
This paper presented an output feedback tracking sliding mode control approach for uncertain linear multiple-input multiple-output (MIMO) systems with uncertainties such as external disturbance, the system state, and control input
Summary
Sliding mode control is a widely recognized and robust control method. For applications in robot manipulators, it has been developed over the past four decades [1,2,3,4,5,6]. A key solution to such problems is the observer-based structure In this design, the required state information of the control system is estimated by observers or differentiators. High-gain observer-based sliding mode control [21,22] can be used for multivariable nonlinear systems with stable zero dynamics, and a higher order sliding mode differentiator can be used to estimate the required output derivatives [23,24,25]. A novel design was proposed for observer-based output feedback sliding mode control. The resultant LTR observer-based output feedback sliding mode control drives the system state into a small residual set around the origin, with the size of the residual set controlled by a design parameter in the observer Riccati equation. A given vector x ∈ Rn , k x k denotes the usual Euclidean two-norm vector
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