Optimal Sensor and Actuator Location for Unstable Systems

Accurate and reliable process measurements play a key role in the success of process control. In addition to selecting the instrumentation hardware, it is important to determine which variables should be measured in a process. Therefore it is important to study techniques for placing sensors on the processes. Dually the problem of placing actuators on the processes is equally important. In this paper, the problem of determining optimal sensor and actuator locations for the linear systems is addressed. The problem of the sensor locations is viewed as the problem of maximizing the output energy generated by a given state and for the actuator locations is viewed as the problem of minimizing the input energy required to reach a given state. Such design problems occur in many applications, and therefore have been studied extensively. Unfortunately, the results in this context, which have been proposed so far, only support stable systems. However, in industrial practices it is often the case that the system, which is needed to be controlled, is not stable. The method which is proposed in this paper is a general method in the sense that it supports both stable and unstable systems. The technique is successfully used for determining the optimal sensor locations of the linearized Continuous Stirred-Tank Reactor unstable model.