Robust pole location for an interacting tank system with uncertain parameters

This paper addresses the problem of robust control design for an interacting tank system (ITS) model by means of state feedback gains. Specifically, the design of controllers that assure a robust pole location of the closed-loop system inside a circular region on the left-hand side of complex plane is investigated. The ITS modeled is a pilot plant with industrial sensors and actuators. The parameters of the ITS model are supposed to vary as a function of the operating points, being thus, uncertain parameters that can be described by convex polytopes. Three sufficient conditions for the existence of a robust stabilizing state feedback gain are addressed: the quadratic stability based gain, a published condition that uses an augmented space and a condition that uses an extended number of equations. The last condition provides a parameter dependent state feedback gain which assures to the uncertain closed-loop system a prespecified pole location inside a circle on the left-hand half of the complex plane. The robust stabilizability conditions are formulated in terms of a set of linear matrix inequalities involving only the vertices of the uncertainty polytope. The parameter dependent gain proposed allows to impose to the closed-loop system pole locations that in some situations cannot be obtained with constant feedback gains.