Discrete-Time Sliding Mode Control
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In this study, two different approaches to the sliding surface design are presented. First, a discrete-time integral sliding mode (ISM) control scheme for sampled-data systems is discussed. The control scheme is characterized by a discrete-time integral switching surface which inherits the desired properties of the continuous-time integral switching surface, such as full order sliding manifold with eigenvalue assignment, and elimination of the reaching phase. In particular, comparing with existing discrete-time sliding mode control, the scheme is able to achieve more precise tracking performance. It will be shown that, the control scheme achieves \(O(T^2)\) steady-state error for state regulation and reference tracking with the widely adopted delay-based disturbance estimation. Another desirable feature is that the Discrete-time ISM control prevents the generation of overlarge control actions which are usually inevitable due to the deadbeat poles of a reduced order sliding manifold designed for sampled-data systems. Second, a terminal sliding mode control scheme is discussed. Terminal Sliding Mode (TSM) control is known for its high gain property nearby the vicinity of the equilibrium while retaining reasonably low gain elsewhere. This is desirable in digital implementation where the limited sampling frequency may incur chattering if the controller gain is overly high. The overall sliding surface integrates a linear switching surface with a terminal switching surface. The switching surface can be designed according to the precision requirement. The design is implemented on a specific SISO system example, but, the approach can be used in exactly the same way for any other system as long as it is SISO. The analysis and experimental investigation show that the TSM controller design outperforms the linear SM control.