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An iterative approach for the determination of an input-output inversion feedforward control law for residual vibration reduction is proposed in this paper. In particular, point-to- point motion planning of vibratory servosystems is considered. The method aims at estimating recursively the parameters of the system in order to determine the exact command input to be applied to the control system in order to achieve a predefined motion without oscillations. In this context, a gradient based minimisation of the integrated square error cost function is performed. Simulation results show the effectiveness of the methodology.

A new iterative approach for the determination of a noncausal feedforward control law suitable for set-point regulation is presented in this paper. The technique aims at estimating recursively the parameters of the system to be controlled in order to determine the exact noncausal command input to be applied to the closed-loop system in order to achieve a predefined output transition. In this context, a gradient based minimization of the integrated square error cost function is performed. Simulation results show the effectiveness of the methodology for different system characteristics.

A new method for PID controller tuning based on Bode's integrals is proposed. It is shown that the derivatives of amplitude and phase of a plant model with respect to frequency can be approximated by Bode's integrals without any model of the plant. This information can be used to design a PID controller for slope adjustment of the Nyquist diagram and improve the closed-loop performance. Besides, the derivatives can be also employed to estimate the gradient and the Hessian of a frequency criterion in an iterative PID controller tuning method. The frequency criterion is defined as the sum of squared errors between the desired and measured gain margin, phase margin and crossover frequency. The method benefits from specific feedback relay tests to determine the gain margin, the phase margin and the crossover frequency of the closed-loop system. Simulation examples and experimental results illustrate the effectiveness and the simplicity of the proposed method to design and tune the PID controllers.