Towards a theoretical foundation of PID control for uncertain nonlinear systems

As is well-known, the classical PID control plays a dominating role in various loops of industrial processes. However, theory that can explain rationale why linear successfully deal with ubiquitous uncertain nonlinear dynamical systems and method provide explicit design formulae for parameters are still lacking. This paper continuation authors recent endeavor towards establishing theoretical foundation systems. In contrary to most existing literature on or affine systems, we will consider class non-affine show three dimensional parameter set be constructed explicitly, such whenever chosen from this set, closed-loop globally stable regulation error converge zero exponentially fast, under some suitable conditions system uncertainties. Moreover, also simpler PI PD control, necessary sufficient condition choice one by applying Markus–Yamabe theorem differential equations. These results explicitly does indeed have strong robustness respect both uncertainties selection controller parameters.