Implementation of variable structure control for sampled-data systems

Abstract

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A control engineer's guide to sliding mode control

“…For unity feedback gain, the norm of the above feedback control is equal to unity for any thus it is also referred to as unit control. Unambiguously, is discontinuous on the manifold (41) Moreover, the condition (40) guarantees that sliding mode exists on inside a domain For sufficiently large , sliding mode exists for any Since the closed-loop system is asymptotically stable, sliding mode on is also asymptotically stable, i.e., on the manifold as Moreover, the dynamics of the system in sliding mode are invariant with respect to the unknown disturbance Since sliding mode is the principal mechanism with which uncertainties and disturbances are rejected in robust control of uncertain systems, the robustness of these feedback controllers with respect to unmodeled dynamics are identical to continuous-time SMC, and the respective engineering design issues can be addressed as outlined in this section.…”

“…[40], [41] that the behavior outside the sliding manifold is governed by the following second-order difference equation:…”

Model reference discrete-time sliding mode control of linear motor precision servo systems

“…To realize the controller, the unknown disturbance d k can be approximated by its one-step delayed value d kÀ1 as proposed in Su et al [9], and it can be calculated from (6)…”

“…The new definition of the discrete sliding mode (DSM) [11] enables the exclusion of the problematic discontinuous behaviour of continuous time sliding mode controllers, thus excluding the chattering problem that arises due to limitations of the physical system. Su et al in [9,10] have shown that if the matched disturbances are bounded and smooth, with a properly designed discrete-time sliding mode control (DSMC), the system is able to reach an OðT 2 Þ boundary layer of the sliding surface in finite time. However, the friction problem is not as simple as the problem of smooth exogenous disturbances and plant uncertainties.…”

Analysis of sliding mode proximate time-optimal disk drive servo control

“…In this regard, it is worthwhile to observe the unique invariance properties of sliding mode control (SMC). In SMC, plant motion constrained to the sliding mode becomes robust against certain model uncertainties (matched disturbance rejection characteristics) (Draženović 1969;Edwards and Spurgeon 1998;Drakunov and Utkin 1992;Utkin 1977Su et al 1996;Young et al 1999). The unique invariance properties of SMC enable a wide array of applications in dynamic system control.…”