The previous chapter relied heavily on analysis methods for the frequencyand s-domains. The models that were used were exclusively transfer functions. Moreover, the control systems were strictly SISO systems. SISO systems are ones in which the objective is to control the dynamic response of a single output by varying a single input. Controllers for MIMO systems are more commonly designed in the state space. The methods from Chapter 9 focus on placing the dominant closed-loop poles such that they have the desired overall overshoot and settling time. This presumes that there exists a set of poles that are sufficiently dominant to dictate the overall response. That is not always the case. A more robust method would allow one to specify placement of all closed-loop poles. As we saw in the previous chapter, PID and lead-lag compensation rely on adjustment of a gain and the placement of at most two zeros and poles to modify the closed-loop dynamic response. For higher-order systems, these are not sufficient terms to control the placement of all closed-loop poles. State-space methods overcome this shortcoming by introducing additional adjustable parameters and methods for deriving those parameter values (Nise 2011). They utilize state feedback to generate control inputs that are generally a function of all the system states. Given your knowledge of the previous chapter, ask yourself the following:
B How do you specify the placement of all closed-loop poles to meet specified design criteria?