To begin with the controller design procedure, let us introduce the following coordinates transformation:
$$\begin{aligned} \left\{ \begin{array}{l} {e_1} = \nu ,\\ {e_i} = {x_i} – {z_i},\\ {\chi _i} = {z_i} – {\alpha _{i – 1}},\;i = 2,3, \ldots ,n, \end{array} \right. \end{aligned}$$
(3)
where \({e_i}\) is the error, \({z_i}\) is the output state that is obtained through first-order filter, \({\alpha _{i – 1}}\) is the virtual controller. The first-order filters are given as \({\varsigma _i}{\dot{z}_i} + {z_i} = {\alpha _{i – 1}},{z_i}\left( 0 \right) =…
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