Design of non-interacting multivariable discrete time systems

The theory of decoupling a multivariable system with the help of state variable feedback is applied to discrete time systems. The system differential equations in the continuous time domain are converted to a discrete time representation. A discrete time controller is designed to control the overall input to the system such that a specified desired decoupled output response is obtained. The decoupled system behaves as a set of single-input, single-output systems and state variable techniques can be easily applied to control each output individually. Control is achieved by periodically sampling the inputs and all the states and feeding them back through a controller. For linear time invariant systems the control is time invariant. The basic theory of decoupling involves feeding back all the states twice, first to decouple the system and then to achieve a desired response. The states of the system are computed with the help of a state estimator which calculates all the present states of the system so that on-line control can be applied to real time systems. The theory is applied to a model of a nuclear rocket engine.