A multi-objective design optimization procedure for a general control system

With the advancement in new materials and techniques, smooth and high performance operation of critical systems, such as flight simulators, satellite navigators and robot arms, are expected. To give examples, a long duration for space shuttle after its take off cannot be tolerated in terms of its system dynamics and stability as well as high off-the-target position errors for a pick-and-place robot. In most of these military and industrial systems, control objectives are more than one and mostly intensified at minimizing overshoot from steady state response with a minimum system settling time. Stability of the systems is also another objective. Any such system can be idealized as a combination of mass-spring-dashpot system and its stability conditions can be determined from the locations of the poles of the system characteristics equation. As it is well known, when the damping ratio is zero or negative, the poles are located at the right-hand side of the s-plane presenting instability. In this study, a general mass-spring-dashpot system is considered first. Then, its mathematical differential equation is transformed into Laplace domain to formulate undamped natural frequency and damping ratio. By choosing these two as system design variables, numerical constraints are impinged on system settling time, percent overshoot and time to reach to maximum peak. Multi-objective optimization is performed using powerful method of Global Criterion Method. The cost functions are minimization of system settling time, the percent overshoot and time to reach maximum peak. Design specifications are suggested for this particular configuration in terms of relations between mass, spring and dashpot. It is intended to lay out a design optimization procedure to system designers in choosing mass, spring and dashpot characteristics for a stable system operating optimally under prescribed constraints. It is also shown that the Global Criterion Method is a versatile optimization tool for multi-criterion problems.