Design of adaptive PID controller based on maximum modulus theorem for inverted pendulum on a cart

Stabilization of a pendulum in inverted position when the base is moving is one of the challenging tasks in aircraft, automobile and ship industries. So in this paper the system under consideration is inverted pendulum on a cart which has single degree of freedom (angular rotation of pendulum). In industries depending upon the variation in operating conditions controller have to be tuned accordingly. That is depending upon the desired conditions, controller parameters should have flexibility i.e. the principle of adaptive control. This paper in brief discuss about design of a tuning parameter based on Maximum Modulus Theorem so that the required time domain specifications can be achieved.