An optimal pid tuning method for a single-link manipulator based on the control parametrization technique

A control parametrization based optimal PID tuning scheme for a single-link manipulator is developed in this paper. The performance specifications of the control system are formulated as continuous state inequality constraints. Then, the PID optimal tuning problem of the single-link manipulator can be formulated as an optimal parameter selection problem subject to continuous inequality constraints. These continuous inequality constraints are handled by the constraint transcription method together with a local smoothing technique. In such a way, the transformed problem becomes an optimal parameter selection problem in a canonical form, which can be solved efficiently by control parametrization method. Since approach is using the gradient-based method, the corresponding gradient formulas for the cost function and the constraints are derived, respectively. The effectiveness of the proposed method is demonstrated by numerical simulations.