Robust control of discretized continuous systems using the theory of sliding modes. (English) Zbl 0827.93014

Tesfaye, Addisu; Tomizuka, Masayoshi

Int. J. Control 62, No. 1, 209-226 (1995).

Summary: The idea of sliding mode control (SMC) as a robust control technique is utilized to control systems where the dynamics can be described by \(\dot x(t)= (A+ \Delta A) x(t)+ (B+ \Delta B) u(t)+ d(t)\) where \(\Delta A\), \(\Delta B\) and \(d(t)\) characterize unknown plant parameters and unexpected disturbances, respectively. The analysis is described in the discrete form using the Euler operator. The proposed controller regards the influence of unknown disturbances and parameter uncertainties as an equivalent disturbance and generates a control function (estimate) to cancel their influence by the mechanism of time delay. The states of the uncertain plant are steered from an arbitrary initial state to a stable surface, \(s= 0\), and the plant output is subsequently regulated. One feature of the control is that the sliding conditions are satisfied without the discontinuous control action used in classical SMC. It therefore retains the positive features of SMC without the disadvantage of control chattering. The controller has been studied through simulations and experiment on an NSK direct drive robot arm driven by a DC motor. The results confirm that the control is robust to disturbances and parameter variations.

MSC:

93B12	Variable structure systems
93C57	Sampled-data control/observation systems
34K35	Control problems for functional-differential equations
93B35	Sensitivity (robustness)
93C73	Perturbations in control/observation systems

Keywords:

sliding mode control; robust; discrete; unknown disturbances; parameter uncertainties; time delay; chattering

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