A Study On Energy Decoupling Control Theory

Decoupling control is an effective method in multivariable system control. In the past decades, there are two primary decoupling approaches. One is a series of state-space methods which are a kind of complete decoupling methods. These methods, based on the accurate elimination, will induce the damage of the decouple performance with little perturbation. It is the primary drawback of these methods. The other is the modern frequency domain method performed by Rosenbrock. The design objective is the diagonal dominance, not the diagonalization, so it may avoid the limitation of the complete decoupling. It is an approximate decoupling method. Considering the existence of uncertainties in the practical industrial processes, some scholars have considered the affect of the uncertainties, but it is difficult to extend the complete decoupling method to uncertain systems. However, the Rosenbrock'method is easily extended to the decoupling of uncertain systems with its approximate characteristic.This paper tries to seek an approximate decoupling method in the time-domain framework. It is called as an energy decoupling method. The object of this method is the reduction of energetic relation between inputs and outputs, i.e., the energy of every input controls mainly the energy of a corresponding output and influences the energy of the other outputs as weakly as possible. Based on the Lyapunov approach, my main results are obtained as follows:1. The decoupling of the linear time-invariant system and linear time-delay system are discussed. For linear systems with norm-bounded uncertainties, conditions for energy decoupling with input transformation or both state feedback and input transformation are given in terms of linear matrix inequalities.2. The input-output energy decoupling of linear discrete systems and uncertain linear discrete systems is considered. Conditions for energy decoupling with input transformation or both state feedback and input transformation are given in terms of linear matrix inequalities.3. Delta operator is a unified description method for linear continuous systems and linear discrete systems. Unified conditions for energy decoupling of discrete systems and continuous systems with input transformation or bothstate feedback and input transformation are given in terms of linear matrixinequalities.The conclusion and perspective are given in the end of the paper.