Introduction to Robust Control Techniques

The theory of "Robust" Linear Control Systems has grown remarkably over the past ten years. Its popularity is now spreading over the industrial environment where it is an invaluable tool for analysis and design of servo systems. This rapid penetration is due to two major advantages: its applied nature and its relevance to practical problems of automation engineer. To appreciate the originality and interest of robust control tools, let us recall that a control has two essential functions: • shaping the response of the servo system to give it the desired behaviour, • maintaining this behaviour from the fluctuations that affect the system during operation (wind gusts for aircraft, wear for a mechanical system, configuration change to a robot.). This second requirement is termed "robustness to uncertainty". It is critical to the reliability of the servo system. Indeed, control is typically designed from an idealized and simplified model of the real system. To function properly, it must be robust to the imperfections of the model, i.e. the discrepancies between the model and the real system, the excesses of physical parameters and the external disturbances. The main advantage of robust control techniques is to generate control laws that satisfy the two requirements mentioned above. More specifically, given a specification of desired behaviour and frequency estimates of the magnitude of uncertainty, the theory evaluates the feasibility, produces a suitable control law, and provides a guaranty on the range of validity of this control law (strength). This combined approach is systematic and very general. In particular, it is directly applicable to Multiple-Input Multiple Output systems. To some extent, the theory of Robust Automatic Control reconciles dominant frequency (Bode, Nyquist, PID) and the Automatic Modern dominated state variables (Linear Quadratic Control, Kalman). It indeed combines the best of both. From Automatic Classic, it borrows the richness of the frequency analysis systems. This framework is particularly conducive to the specification of performance objectives (quality of monitoring or regulation), of band-width and of robustness. From Automatic Modern, it inherits the simplicity and power of synthesis