A Padé approximation based technique for designing a suboptimal controller is presented. The technique uses matching of both time moments and Markov parameters for model order reduction. In this method, the suboptimal controller is first derived for reduced order model and then implemented for higher order plant by partial feedback of measurable states.

The design of an optimal control law for large scale systems is inconvenient due to one of the main drawbacks of optimal control theory that requires feedback from all state variables that are defined to describe the dynamics of the plant. It is rare that all the states are available for measurement [

The plant (higher order system) can be reduced by Padé approximation technique (matching of both time moments and Markov parameters) into reduced order model, and then, with the help of reduced order controller, one can design the suboptimal controller for plant (higher order systems). The usefulness of techniques for deriving reduced order approximations of high order system has been already accepted due to the advantages of reduced computational effort and increased understanding of original system [

Consider a single-input single-output linear (

Block diagram of controlled system.

The control action of the plant is given as

Consider a

Using (

The suboptimal controller [

See Figure

Flow diagram of suboptimal control design.

Using (

The step-by-step procedure to obtain reduced the order model is explained with the help of the example presented below and procedure is derived for suboptimal controller.

Consider the following 4th order system [

By solving (

Step response of higher order system and reduced order model.

Model (

The optimal controller and suboptimal controller can be designed for a particular performance index by solving Riccati equation (

The optimal controller for actual higher order system (

Step response of higher order and reduced order model with optimal controller.

It is found that (

The suboptimal controller (

Thus

The step response of higher order system with optimal and with suboptimal controller.

The step responses of higher order system with optimal controller (

Consider the higher order system [

It is clear that the step response of higher order system with optimal controller (

The suboptimal gain matrix is obtained for the system (

The closed loop transfer function of higher order system (

Step response of higher order system and reduced order model with optimal controller.

The step response of higher order system with optimal and suboptimal controller.

The results of the two examples signify that the suboptimal control provides a good platform for controlling the higher order system and reduces the complexity and cost of control action.

For purpose of comparison, the suboptimal controller is also derived using the technique in [

A design technique of suboptimal controller using partial feedback is proposed. The method is based on the Padé approximation technique (matching of both time moments and Markov parameters) for model order reduction which results in better overall time response approximation. In this method, the suboptimal controller is first derived for reduced order model and then implemented for higher order plant. This reduces the design complexity and cost of control action. The method also avoids use of observer or Kalman filter for reconstruction of missing states.

In this paper equal emphasis is given for matching of time moments and Markov parameters; however, the optimal choice of Markov parameters and time moments to be matched remains unresolved and it is open to further investigation.

The authors declare that there is no conflict of interests regarding the publication of the paper.