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Abstract
In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.
Highlights
Sliding Mode Control of SampledSliding mode control is a well-known variable structure method
This paper focuses on the reaching law, and its tuning will be demonstrated
In order to determine the properties of the closed loop system in which the sliding variable evolves according to the above equation, one needs first to calculate the maximum possible value of the expression cT {d(kT ) − d[(k − 1) T ]}
Summary
Sliding mode control is a well-known variable structure method. Its foundations were laid out in the previous century, both for continuous [1], and for discrete time systems [2]. The reaching law approach was applied in numerous practical control systems, such as PMSM speed control [19] as it has some important advantages over the previously mentioned method It allows to limit [20]. This allows to have more control over the system dynamics prior to the start of the sliding mode It is demonstrated, that the presented disturbance compensation scheme improves the robustness, and that tuning the reaching law allows to obtain a satisfactory compromise between fast convergence and minimization of the control signal and state variables. We present the switching reaching law approach, modify it to a non-switching one, to minimize the energy expenditure of the control signal For both methods, we calculate the width of the quasi-sliding mode band, as well as the bounds of the state errors, both of which are measures of the robustness. We consider the state values at the sampling instants, but we find the greatest possible deviation between the sampling instants
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