What is Optimal Control

Backlash is one of several discontinuities found in different kinds of systems; it can be found in actuators of different types, such as mechanical and hydraulic, giving way to unwanted effects in the system behavior. In this chapter, three different control approaches are derived to stabilize mechanical systems in which this phenomenon is present in the actuators of the system. First, an independent joint control approach when backlash is found in the actuators is derived; then a PI loop shaping control design implementing a describing function to find the limit cycle oscillations and the appropriate control gain is developed. Finally, an optimal controller for mechanical systems with backlash is derived, obtaining the optimal control law and oscillations frequency when this nonlinearity is found implementing a describing function to model the backlash effects.