Globally optimized H∞-controllers with application to elastic robots

In H
_∞
-controller synthesis the plant model has to be extended by weighted in-/output channels. With these weights the control requirements have to be specified in the frequency domain. To fulfil time domain requirements a time consuming iterative procedure of choosing weighting filter, controller synthesis and closed loop performance analysis has to be done. In the paper this procedure is automated by global optimization. Instead of optimizing the coefficients of the weights directly, physically related parameters, for example gains and roll off frequencies, are optimized. Thus constraints in the frequency domain can easily be included in the global optimization. To improve the global optimization a new transformation is given how these physical parameters can be transformed into the weights coefficients. With the proposed setup, both time and frequency domain criteria can be used for the controller synthesis and analysis. The frequency domain critera are calculated based on a linear model, the time domain criteria are based on an arbitrary nonlinear model. The proposed procedure is applied to an elastic robot. A new in-/output channel selection is proposed, which has much benefit compared to other studied structures. Some numerical aspects of the H
_∞
-controller calculation in the context of the global optimization are given. The results have been experimentally proven on a robot testbed.