Page - (000046) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

Chapter5 PerformanceandRobustnessMeasures A theory of design tradeoffs requires broadly applicable measures of cost, per- formance, stability, and robustness. For example, the PID controller in the pre- vious example performs reasonably well, but we ignored costs. That PID con- trollerachievedgoodtrackingperformancebyusinghighgainamplificationof low- frequency input signals. High gain in a negative feedback loop quickly drives the error tozero. Highgainhastwopotentialproblems.First,highsignalamplificationmayrequire excessiveenergyinphysicalorbiologicalsystems.Wemustconsider thosecostsfor ahighgaincontroller. Second,highgaincancause systeminstability,withpotential for systemfailure. Wemust consider the tradeoff between the benefits of high gain and the loss of robustnessagainstperturbationsoruncertainties in systemdynamics. Beyond the simplePIDexample,wemust consider avarietyof tradeoffs inper- formance and robustness (Zhou and Doyle 1998; Qiu and Zhou 2010). Earlier, I discussed tradeoffs in systemsensitivities todisturbanceandnoise. I alsopresented qualitativedescriptionsofsystemperformanceintermsofresponsetimeandtracking performance. Toadvance the theory,weneedspecificmeasuresof cost, performance, stability and robustness.Wealsoneed techniques tofindoptimaldesigns in relation to those conflictingmeasuresof systemattributes. Wewill neverfindaperfect universal approach.There are toomanydimensions of costs and benefits, and toomany alternativeways tomeasure systemattributes. Nonetheless, basic measures and simple optimization methods provide consider- able insight into the nature of design. Those insights apply both to the building of human-designed systems to achieve engineering goals and to the interpretation and understanding of naturally designed biological systems built by evolutionary processes. ©TheAuthor(s)2018 S.A.Frank,ControlTheoryTutorial, SpringerBriefs inAppliedSciences andTechnology,https://doi.org/10.1007/978-3-319-91707-8_5 37