Abstract
Most mechanical systems are described by Lagrangian equation of motion and their controllers consist of the conventional PID one. In the previous chapter and [10, 14], the inverse Open image in new window optimality of PID control was proved for mechanical control systems, inspired by the extended disturbance input-to-state stability(ISS) of PID control under some conditions for gains. Also, it was proved that an inverse optimal PID controller exists if and only if the mechanical control system is extended disturbance input-to-state stable(ISS). However, an inverse optimal PID controller brings the performance limitation for trajectory tracking mechanical systems. In this chapter, we derive several performance tuning methods of an inverse optimal PID control from its performance limitation.
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