LMI-based control of linear systems with actuator amplitude and rate nonlinearities

Dynamic Output Feedback for Discrete-Time Systems Under Amplitude and Rate Actuator Constraints

“…This result will follow the ideas discussed in Section III. Since the equivalent representation of the closed-loop system (14) presents two deadzone nonlinearities, two generalized sector conditions (12) and respective set inclusion conditions are considered in order to take into account the nonlinear behavior of the system. In order to compute the matrices of the dynamic compensator, the ideas proposed in [22], where appropriated change of variables allows the formulation of synthesis conditions in LMI form, are here adapted to also include the anti-windup gains (E c and F c ) and the variables associated to the sector conditions.…”

“…In this case, when the time constant of the actuator dynamics tends to zero, the behavior of the position-feedback-type model tends to the "ideal" rate limiter, or, equivalently to the notion of a rate saturation operator as introduced in [5]. However, as pointed out in [12] and [13], if, in fact, the actuator dynamics is not represented by a first order model, the closed-loop stability cannot be ensured by the proposed methods. Furthermore, the position-feedback-type model seems to be unsuitable or imprecise for dealing with the rate saturation phenomenon in a discrete-time framework, representing a digital control system.…”

“…An alternative approach for dealing with the rate saturation problem without resorting to the position-feedback-type model, has been proposed in [12], [13] (considering continuous-time systems) and in [14] (considering discrete-time systems). The basic idea consists of introducing a rate limiter inside the controller in order to prevent the control signal (to be sent to the actuator) violating the rate bounds.…”

“…This is accomplished by introducing a nonlinear integrator in the controller structure. In particular, in [12] and [14], stabilizing synthesis conditions for this kind of controller structure have been proposed in the form of nonlinear matrix inequalities, both for state and dynamic output feedback cases. The saturation nonlinear effects are taken into account by the application of classical sector bound conditions.…”

“…The multipliers associated to the sector conditions are seen as tuning parameters and are supposed to be a priori fixed. As in [10], in [12] and [14] the size and the shape of the domain of ensured stability is not taken directly into account in the design procedure. This domain is computed a posteriori, which can lead to small regions of stability for the closed-loop system.…”