Nonlinear model matching: a local solution and two worked examples

The model matching problem consists of designing a compensator for a given system, called the plant, in such a way that the resulting input-output behavior matches that of a prespecified model. In a recent paper it was shown that in case the model is decouplable by static state feedback and generic conditions on the plant are satisfied, the model matching problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model around the equilibrium point. In this paper this local solution will be presented and we will investigate the question to what extent we can use the feedback that solves the corresponding linear model matching problem in order to approximately solve the original nonlinear problem. This will be done by means of two examples: the double pendulum and a two-link robot arm with a flexible joint

Input-output decoupling with stability for Hamiltonian systems

The input-output decoupling problem with stability for Hamiltonian systems is treated using decoupling feedbacks, all of which make the system maximally unobservable. Using the fact that the dynamics of the maximal unobservable subsystem are again Hamiltonian, an easily checked condition for input-output decoupling with (critical) stability is deduced

Local nonlinear model matching: from linearity to nonlinearity

The model matching problem consists of designing a compensator for a given system, called the plant, in such a way that the resulting input-output behaviour matches that of a prespecified model. In this paper a local solution of the nonlinear model matching problem is given for the case that the model is decouplable by static state feedback. The main theorem states that under generic conditions on the plant the problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model. The generic conditions are identified. They naturally appear in the solution of the dynamic input-output decoupling problem for the plant. The theory is illustrated by means of two examples

Dynamic disturbance decoupling of nonlinear systems and linearization

In this paper we investigate the connections between the solvability of the dynamic disturbance decoupling problem with exponential stability (DDDPes) for a nonlinear system and the solvability of the same problem for its linearization around an equilibrium point. It is shown that under generic conditions the nonlinear DDDPes is solvable for a nonlinear system if and only if the static disturbance decoupling problem with stability (DDPs) is solvable for its linearization around an equilibrium point

Minimality of dynamic input-output decoupling for nonlinear systems

In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem

Nonlinear disturbance decoupling and linearization: a partial interpretation of integral feedback

The relation between the solvability of the disturbance decoupling problem for a nonlinear system and its linearization around a working point is investigated. It turns out that generically the solvability of the disturbance decoupling via regular dynamic state feedback is preserved under linearization. This result gives a partial interpretation of introducing integral action in classical PID-control applied to nonlinear systems. The theory is illustrated by means of a worked example

Generalized controlled invariance for nonlinear systems

A general setting is developed which describes controlled invariance for nonlinear control systems and which incorporates the previous approaches dealing with controlled invariant (co-)distributions. A special class of controlled invariant subspaces, called controllability cospaces, is introduced. These geometric notions are shown to be useful for deriving a (geometric) solution to the dynamic disturbance decoupling problem and for characterizing the so-called fixed dynamics for the general input-output noninteracting cont.rol problem via dynamic compensation. These fixed dynamics are a major issue for studying noninteracting control with stability. The class of quasi-static state feedbacks is used