Solmaz Sajjadi-Kia

Modified Anti-Windup Compensators for Stable Plants

We investigate the effects of deferring the activation of anti-windup by allowing actuators to remain in the saturated regime longer, without any assistance. The basic idea is to apply anti-windup when the performance of the saturated system faces substantial degradation. For this, we present a modified anti-windup scheme along with the appropriate LMIs to obtain the gains. For two examples, we show that the modified anti-windup scheme renders better performance than the immediate application of anti-windup.

Multi-stage Anti-Windup Compensation for Open-loop Stable Plants

We discuss adding a measure of scheduling to the popular Anti-Windup design. The main idea is to develop a scheme in which the Anti-Windup gains depend on how much the actuator command exceeds the saturation bound. The aim is to design and implement more aggressive Anti-windup gains in lower levels of saturation. Global stability and performance are addressed by adding an outer-loop Anti-windup compensation which become active when the system is in higher levels of saturation. We present results for both static and dynamic Anti-Windup gains, along with the convex synthesis LMIs. Benefits of the proposed design method are shown using well-known examples.

Modified Anti-windup compensators for stable plants: Dynamic Anti-windup case

This note considers the popular Anti-windup design problem for linear systems with saturating actuators. The main contribution of this paper is providing the synthesis LMIs to obtain the gains of the dynamic Anti-Windup compensator in a structure that delays the activation of the Anti-Windup. The basic idea is to apply Anti-Windup when the performance of saturated system faces substantial degradation. Benefits of the proposed design method over the immediate activation of the Anti-Windup are demonstrated using a well-known example.

Use of scheduling for anti-windup controller design

Preliminary results are presented for developing a scheduling approach for anti-windup control design. The results include state feedback controllers, though generalization to many important classes of dynamic output feedback appears reasonably straight forward. The main idea is to devise a family of controllers that can be used to override the nominal controller, depending on the response of the system. The emphasis is on providing performance guarantees, even for open loop unstable plants. The main idea is demonstrated through a third order unstable model.

Modified anti-windup compensators for stable linear systems

In this paper, we use the Small Gain Theorem to study the stability, and develop appropriate convex L2 gain LMIs for synthesis, of static anti-windup gains. The main contribution of this paper is investigating the effects of delaying the activation of anti-windup by allowing actuators to remain in the saturated regime longer, on their own. The basic idea is to apply anti-windup when the performance of saturated system faces substantial degradation. For this, we present a modified anti-windup scheme along with the appropriate convex LMIs to obtain the gains. For two well-known examples, we show that the modified anti-windup scheme renders better performance than the case of immediate application of anti-windup.

Scheduled static Anti-windup augmentation synthesis for open-loop stable plants

This note considers adding a measure of scheduling to the popular Anti-windup design for linear systems with saturating actuators. The main idea is to develop a scheduling scheme in which the anti-windup gains used depend on how much the actuator command exceeds the saturation bound. We present preliminary results for static Anti-windup gains, along with the convex synthesis LMIs, for the case of having two levels of saturation: moderate and severe. Benefits of the proposed design method over the traditional single gain Anti-Windup compensation are demonstrated using a well-known example.

Scheduling in anti-windup controllers: Output feedback case

We present results for incorporating a measure of scheduling in a form of anti-windup augmentation scheme. This is achieved by keeping a nominal linear controller as long as possible and relying on a family of controllers with decreasing authority, once the system leaves the small signal regime. The scheduling is to override the nominal controller. The emphasis is on providing performance guarantees, even for open loop unstable plants, though design of invariant sets and similar stability concepts are also possible. The guaranteed performance measures are local, in the sense that they depend on peak bounds on the disturbance, which are assumed to be known. The main idea is demonstrated through an example with an unstable plant.

Multiple stage anti-windup augmentation synthesis for open-loop stable plants

In this note we enhance the concept of scheduled anti-windup gains by developing an approach that uses a combination of dynamic and static augmentation loops, to exploit the simple structure of the static Anti-Windup techniques with the strong feasibility that is associated with dynamic Anti-Windup loops. We present preliminary results for the combination of a single static and a single dynamic Anti-Windup gains. We develop the synthesis LMIs, for two levels of saturation: moderate (static loop active) and severe (both loops active). Benefits of the proposed design method over the traditional single gain Anti-Windup compensation are demonstrated using a well-known example.

On bounded real matrix inequality dilation

We discuss a variation of dilated matrix inequalities for the conventional Bounded Real matrix inequality and other similarly structured inequalities. Here, system matrices are separated from Lyapunov matrix to allow the use of different Lyapunov matrices in multi-objective and robust problems. The search involves a bounded scalar parameter that enters the problem nonlinearly and is dealt with a line search. To demonstrate the benefits of the new dilated matrix inequalities over the conventional ones, an example of controller synthesis with ℒ2-gain performance measure (ℋ∞ control) for a system with polytopic uncertainty (robust problem) has been studied. It is shown that for the resulting robust problem the performance obtained via the dilated form is at least equal to that of the conventional one. Also, the connection between the proposed dilated form and the Full Block S-procedure is discussed.

Scheduled controllers for linear systems with bounded actuators: Slab condition

For linear systems under bounded actuators, a new scheduling scheme is used to improve the performance of the closed-loop system, in disturbance attenuation problems. The approach selects the controller, among a continuous family of controllers, that provides the best performance while avoiding saturation, based on the closed-loop behavior (i.e., the closed-loop state vector). As a result, the controller has a quasi linear parameter varying structure. Graphically, the resulting scheduling scheme relies on slab regions of the phase plain. Numerically, the family of the controllers are based on linear splines, and can be obtained by standard LMI software. Benefits of the proposed scheduling scheme is demonstrated through a numerical example.