Using the transfer function based technique, compensators are designed to predominantly control the response of second-order systems in frequency domain. By adjusting, the control gain, the adverse effect of vibration on the system is compensated. The effect of higher-order poles are either neglected or compensated separately using notch filters. In case of full-state feed-back control, on the other hand, controllers could be designed to regulate the behaviour of second and even higher order systems. Although, such design is based on idealistic assumption of sensing all the states of the system, in reality, only some of the states are measured while the rest are estimated using numerical simulation.

Figure 25.1: Open and closed loop control system

Figure 25.1 shows the open-loop and closed-loop (full state-feedback) representation of a state space system. Before designing any such closed-loop configuration, one has to make sure that the system is controllable for a given pair of A (plant) and B (actuator-influence) matrix.