Discrete-Time ℋ_∞ Integral Control Via LMIs Applied to a Furuta Pendulum

The Furuta pendulum represents a challenging problem in the control area due to its nonlinear dynamics and unstable equilibrium point. Besides those issues, the implementation of control techniques in Furuta pendulum prototypes also needs to deal with possible uncertainties in parameter values, noises, and non-modeled dynamics, which can lead the controlled system to instability. The ℋ_∞ control tends to be an interesting approach for this type of application since this technique is able to mitigate the effect of the disturbances that can act on the controlled system and has been successfully applied in systems with uncertainties. In this paper, we present an ℋ_∞ control strategy applied to a Furuta pendulum system that uses, in addition to the state feedback, an integrator in the feedback loop. The controller was designed, simulated, and put into practice in a real prototype. The controller was implemented via a digital computer; then analog/digital and digital/analog converters were presented in the control loop to interface the continuous signal of the plant with the discrete nature of the controller. This fact was considered in the control design by representing the system dynamics in discrete time. Since not all variables required for state feedback are physically measured in the prototype used, a state observer was employed in the control loop in order to estimate the state variables. In addition, the adopted design procedure that used LMIs established a maximum value for the ℋ_∞ norm of the closed-loop system, as well as limited the norm of the state feedback gain and ensured an adequate decay rate. Thus, it was possible to guarantee the suitable performance of the controlled system. The same integral control structure was also used with a feedback gain designed through the pole placement technique, and its results were used for performance comparison. The outcomes, both from simulations and from the real equipment, show the efficiency of the applied control regarding disturbance rejection and that the adopted design procedure is adequate for controlling physical systems.