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Controller Design
Consider a nonlinear system presented by a n-th order scalar differential equation with uncertainty:
We define the trajectory tracking error as:
where our goal is to drive .
We "Replace" the n-th order problem with an equivalent 1st order problem. Create an intermediate variable s, such that:
In finite time, if s remains bounded close to zero, the trajectory error is bounded as follows:
The Sliding Condition is defined as:
and outside the bounds of s, it may be defined as:
We determine the control law as follows:
which suffers from control chattering due to the switching function. Example implementation shown in SlidingMode_sign.mdl.
The chattering may be eliminated by using a saturation function instead as follows:
Example implementation shown in SlidingMode_sat.mdl.
Note: For previous versions of MATLAB (tested MATLAB 2018 and older), please use the .mdl files with 'prev' extension.