The exponentially stabilizing state feedback control algorithm is developed by Lyapunov�s second method leading to the variable\nstructure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the\ncontrol law is obtained by using a simple fuzzy controller.The analytical structure of the proposed controller is derived and used\nto prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state\nto a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the\nsystem is switched to the sliding mode regime and stays in it forever.The proposed algorithm is tested on the real system in practice,\nDC servo motor, and simulation and experimental results are given.
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