Some Aspects of Continuous-time Sliding Mode Control S. Janardhanan

Overview Robustness Multivariable Sliding Mode ‘Almost’ Sliding Mode

Hence, sliding mode is robust. Robustness of CSMC In Lecture 2, When in sliding mode, entire system dynamics is governed by sliding surface parameters and not original system parameters. Hence, sliding mode is robust.

Disturbance Consider the system with disturbance Disturbance comes through input channel How does sliding mode behave in such a situation.

Disturbance Rejection The control law is designed so as to bring the system to the sliding surface. Let us see dynamics confined to the sliding surface Thus, Therefore, And Again, dynamics independent of disturbance. Hence disturbance rejection.

What if more than one input ? If system has more than one input, then the system can be transformed to the form With having more than one elements. Thus, will also have multiple rows. Hence, the system can have more than one sliding surface

Approach to sliding surface Sliding mode will start when all sliding functions are zero. I.e, intersection of all sliding surfaces. Approach to the intersection Direct to intersection (Eventual) Surface by surface In particular order (Fixed Order) First approach (Free order)

Eventual Sliding Mode In this type of sliding mode, the state trajectory moves to the intersection of the sliding surfaces through a connected subset in the state space. It does not necessary stay on any one of the sliding surfaces on approaching it.

Eventual Sliding Mode

Fixed order Sliding Mode In fixed order sliding mode, the state trajectory moves to one pre-specified sliding surface and staying on it moves to the intersection of the first surface with the next pre-specified sliding surface

Free order sliding mode In free order sliding mode, the state trajectory remains on a sliding surface once the state approaches it. However, there is no particular order in which the surfaces are reached

Ordered Sliding Mode

Chattering Refreshed A conventional sliding mode behaviour would have a sliding surface dynamics of the form However, due to finite bandwidth of the actuator, the input cannot switch fast enough near the sliding surface Chattering – Finite frequency, finite amplitude oscillations about the sliding surface

Almost Sliding Mode To remedy chattering, the strict requirement of “movement on sliding surface” is relaxed. We try to get ‘Almost’ – sliding mode (Quasi sliding mode)

Saturation function based Sliding Mode Control Instead of Inside the band |s|<, the reaching law is linear as This is also called ‘boundary layer technique

The motion S= S=- S=0

Disadvantage ‘Almost’ is NOT exact

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