A New Concept Reaching the Best Achievable Control by Decomposing the Sensitivity Function – Part 2

Optimization of the design loss
The optimization of the design loss results in selecting the fastest reference models under the amplitude constraints of the actuators. It is possible to develop an iterative redesign technique for the selection of best reachable reference model. It is very rare then we have an analytical solution for this optimization, instead repeated simulation runs results in the best reference model. The optimization process is presented by several simulation examples.
Optimization of the realizability loss
For the optimization of the realizability loss new (energy and supremum) norms E₂ and E_͚ are applied instead of the classical norms H₂ and H_͚. Unfortunately these last norms are not applicable for such – mostly integrating – regulator classes, which are important for industrial applications. The norms E₂ and E_͚ are certain generalizations of the classical norms H₂ and H_͚^. The optimization of E₂ can be usually solved by the application of certain Diophantine equations. The optimization of E_͚ can be usually solved by the iterative solution of a nonlinear equation system. Several simple examples are shown to ease the understanding of the high level mathematical procedures.
Optimization of the modeling loss
The modeling loss considers the process identification in two parallel closed loops, where one is the original and the other is based on the available model. The optimization of the modeling loss results in a special binary form of the reference signal, where the switching condition can be computed via a specially formed filter. It is interesting that the optimal reference signal excitation concentrates the frequency weights around the cutting frequency. Simple but convincing simulation runs are presented to prove the much higher efficiency of the optimal identification comparing to other excitation signals.