Research

ROBUST CONTROL

At present, I am doing an MSc in the Electrical and Computer Systems Engineering Department at Monash University. My area of Research is Robust Control. 

Without control systems there could be no manufacturing, no vehicles, no computers, no regulated environment - in short, no technology. Control systems are what make machines, in the broadest sense of the term, function as intended. Control systems are most often based on the principle of feedback, whereby the signal to be controlled is compared to a desired reference signal and the discrepancy used to compute corrective control action.

Control Systems are designed so that certain designated signals, such as tracking errors and actuator inputs, do not exceed pre-specified levels. Hindering the achievement of this goal are uncertainty about the plant to be controlled (the mathematical models that we use in representing real physical systems are idealizations) and errors in measuring signals (sensors can measure signals only to a certain accuracy). Despite the seemingly obvious requirement of bringing the plant uncertainty explicitly into control problems, it was only in the 1980s that control researches re-established the link to the classical work of Bode and others by formulating a tractable mathematical notion of uncertainty in an input-output framework and developing rigorous mathematical techniques to cope with it.

Systems that can tolerate plant variability and uncertainty are called robust. Roughtly speaking, robust control is a control scheme that achieves desired performance in the presence of uncertainties such as disturbances. The basis for control design  and stability analysis is a dynamic model that captures prominent features of the system under consideration. To account for unnoticeable and unknown aspects of the real system in the mathematical model, one often uses the notion of uncertainty. Uncertainty denotes any obscure element in the dynamics of the real system. Possible uncertainties include unknown parameters, unknown functions, disturbances, and unmodeled dynamics. In general, uncertainties can be either stochastic or deterministic; control design and performance analysis must be done accordingly. Uncertainties can also be classified as either structured or unstructured. Structured uncertainties are those dynamics that have a known functional form but unknown parameters while unstructured uncertainties are simply those that are not structured. Unstructured uncertainties include friction, disturbances, and unmodeled dynamics. 

For uncertain systems, the problem is to devise a control that uses the dynamic equation to govern the trajectory of the system with acceptable performance guarantee. Depending on the nature of the uncertainties, different designs can be used to achieve effective control. In terms of mathematical tools, uncertain systems can be classified as either linear or nonlinear. Robust Control is a control of fixed structure that guarantees stability and performance for uncertain systems. Its design only requires some knowledge about bounding functions on the largest possible size of the uncertainties. Robust control of nonlinear uncertain systems has attracted much attention in the last fifteen years. Robust Control is in itself a very wide area of research. My area of research under Robust Control is centred around Gain-Scheduling and Linear Matrix Inequalities (LMI).