PI Passivity-Based Control : Application to Physical Systems

Abstract : One of the best known forms of feeding back a system is through a three-term control law called PID (Proportional-Integral-Derivative) controller. PID controllers are sufficient for many control problems, particularly when process dynamics are not highly nonlinear and the performance requirements are modest. Besides, because of its simple structure, the PID controller is the most adopted control scheme by industry and practitioners, beeing the PI the form mostly employed. Since the PI tuning methods are based on the linearization, commissioning a PI to operate around a single operating point is relatively easy, however, the performance will be below par in wide operating regimes. To overcome this drawback the current practice is to re-tune the gains of the PI controllers based on a linear model of the plant evaluated at various operating points, a procedure known as gain-scheduling. There are several disadvantages of gain-scheduling including the need to switch (or interpolate) the controller gains and the non-trivial definition of the regions in the plants state space where the switching takes place - both problems are exacerbated if the dynamics of the plant is highly nonlinear. In other common scenarios, a little information about the process dynamics or only a "good" linear approximation is taken into account when designing the control design. This impedes to analyse the global stability of the system. In this context, the current thesis work is aimed at the designing of PI controllers, based on the passivity theory, such that the stability of the closed-loop system is guarantied. One of the main advantages of passivity concepts is that they offer a physical and intuitive appeal. The primary idea in passive systems is that the power flowing into the system is not less that the increase of storage. Thus, they cannot store more energy than is supplied to it from the outside, with the difference being the dissipated energy. Thus, introducing the concept of energy, this methodology allows to recast the control problem as finding a dynamical system such that system energy function takes the desired form. Also, with this formulation, the communication between practitioners and control theorists is facilitated, incorporating prior knowledge of the system and providing physical interpretations of the control action. In this thesis, a constructive methodology for deriving PI passivity-based controllers is presented and motivated by the application to physical systems.
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Rafael Cisneros Montoya. PI Passivity-Based Control : Application to Physical Systems. Automatic. Université Paris-Saclay, 2016. English. ⟨NNT : 2016SACLS187⟩. ⟨tel-01368308⟩

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