Abstract
Variable Structure Control Systems (VSCS) are a class of systems where the control law, as a function of the system state, is deliberately changed (from one structure to another) according to some predefined rules: for example a relay system . During a sliding mode the closed-loop system response is constrained to evolve along a sliding surface in the state-space to an equilibrium point. In sliding mode schemes, a switching function typically dictates which structure of control law is to be used at a particular time instant, depending on the position of the state from the sliding surface .
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Notes
- 1.
An alternative approach to smoothing the discontinuity which leads to chattering is to use a higher order sliding mode control approach [2]. Now the sliding motion takes place on the constraint set \(\sigma =\dot{\sigma }=\cdots =\sigma ^{r-1}=0\) and is called an rth order sliding mode. Furthermore if it is possible to steer \(\sigma \) to zero using the discontinuous control based on \(\dot{u}(t)\), then the actual control signal u(t) will be continuous and the unwanted chattering effects can be alleviated [3].
- 2.
This is a well-known ‘classical’ state-space technique: for details see for example [4].
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Hamayun, M.T., Edwards, C., Alwi, H. (2016). Integral Sliding Mode Control. In: Fault Tolerant Control Schemes Using Integral Sliding Modes. Studies in Systems, Decision and Control, vol 61. Springer, Cham. https://doi.org/10.1007/978-3-319-32238-4_2
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