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Robust passivated controller for mechanical systems

Drawbacks of system complexification are both trajectory indistinguishability and functional indeterminacy, and usual state space description adequate for single trajectory should be replaced by a more global function space approach to deal with equivalence classes of trajectories appearing from dynamical behavior. Classical tracking of single inobservable trajectory transforms into imposing the solution of system dynamics to belong to a prescribed function space, solvable by fixed point theorem giving asymptotic stability of the desired trajectory. To combine both advantages of functional and robust controls, exponentially decaying function space used for the Lyapounov theorem is enlarged without extra system information. As resulting asymptotic decay is not always exponential, improving its rate is of importance for overall system performance, mainly because of the passivation requirement for the controlled system while interacting with outer elements. So the problem is to combine exponential asymptotic stability of the adaptive approach without detailed knowledge of system dynamics, with the robust and functional method only requiring a bound on unknown parts. Analysis of the robust adaptive and intelligent controls domain from the original PID control applicable to classical systems shows that only functional control provides this possibility as it uses natural system invariants. The method combines a majorant type approach and projection onto a base set with adjustable coefficients determined by adaptive type condition, guaranteeing convergence rate. The difference to the usual adaptive method is that only representation of the global norm bounding expression is used, with corresponding simplification of controller structure here obtained in explicit form with parameter reactualization equations.