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1. Anti-windup Compensation for Stable and Unstable Systems with Quantized and Saturated Inputs

   https://doi.org/10.23919/ACC55779.2023.10156408  

   Richards, Christopher M.; Turner, Matthew C. (May 2023, Proceedings of the American Control Conference)

   It is well known that actuator saturation can cause destabilization and degradation in performance; similar problems are faced when actuation is quantized. This paper proposes the design of an anti-windup compensator for systems with actuators that are limited to a finite number of quantization levels. This combination of discrete level actuation and saturation poses a unique anti-windup problem that has not yet been solved. To surmount this combined issue, an anti-windup compensator is proposed which provides ultimateboundedness of the system state within a prescribed region, and also guarantees that the state does not stray outside a larger compact set. A numerical simulation example illustrates the effectiveness on a rigid-body system which inspired this work. 

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2. Anti-Windup Compensator Design for Guidance and Control of Quadrotors

   https://doi.org/10.23919/ACC60939.2024.10644412  

   Shahbazzadeh, Majid; Richards, Christopher (July 2024, IEEE)

   In this paper, the problem of anti-windup compensator (AWC) design for guidance and control of quadrotors in an unknown environment is addressed. Quadrotors can be affected by disturbances (such as wind), which potentially result in saturation of the propellers. When saturation occurs, the flight can become unstable, leading to a crash. On the other hand, designing an AWC to mitigate the saturation effects in the control system of a quadrotor can be a challenging task due to the heavy couplings and complex nonlinear dynamics. For this reason, we propose a new structure to design an AWC-based control system to solve this problem. Simulation results are presented in three cases: 1-without saturation, 2-with saturation - without AWC, 3-with saturation - with AWC. The effectiveness of the proposed theoretical results are verified by comparisons. 

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3. Two-stage anti-windup compensation for systems subject to actuator quantization and saturation

   https://doi.org/10.1080/00207179.2024.2337228  

   Turner, M C; Richards, C M (May 2024, International Journal of Control)

   This paper proposes a two stage anti-windup compensation scheme for systems subject to both input saturation and input quantization. The paper makes two main contributions: (i) it proposes a new partitioning of the saturation/quantization nonlinearity; and (ii) it formulates and solves a two-stage anti-windup problem on the basis of this partitioned nonlinearity. The anti-windup compensator contains two distinct elements: one to assuage the effects of quantization, the other to do the same when saturation occurs. Theoretical results provide conditions which must be satisfied in order for the two-stage anti-windup compensator to bestow stability on the resulting closed-loop system. These results are expressed as linear matrix inequalities and naturally lead to algorithms for anti-windup design. Simulation examples illustrate the effectiveness of the techniques. 

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4. Model reference adaptive anti-windup compensation

   https://doi.org/10.1109/CDC51059.2022.9992768  

   Sofrony, Jorge; Turner, Matthew; Richards, Christopher (December 2022, IEEE)

   This paper proposes an anti-windup mechanism for a model reference adaptive control scheme subject to actuator saturation constraints. The proposed compensator has the same architecture as well known non-adaptive schemes, which rely on the assumption that the system model is known fairly accurately. This is in contrast to the adaptive nature of the controller, which assumes that the system (or parts of it) is unknown. The approach proposed here uses of an “estimate” of the system matrices for the anti-windup compensator formulation and modifies the adaptation laws that update the controller gains. It will be observed that if the (unknown) ideal control gain is reached, a type of “model recovery anti-windup” formulation is obtained. In addition, it is shown that if the ideal control signal eventually lies within the control constraints, then, under certain conditions, the system states will converge to those of the reference model as desired. The paper highlights the main challenges involved in the design of anti-windup compensators for model-reference adaptive control systems and demonstrates its success via a flight control simulation. 

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5. Dynamic Gain Adaptation in Linear Quadratic Regulators

   https://doi.org/10.1109/TAC.2023.3344551  

   Komaee, Arash (August 2024, IEEE Transactions on Automatic Control)

   In feedback control of dynamical systems, the choice of a higher loop gain is typically desirable to achieve a faster closed-loop dynamics, smaller tracking error, and more effective disturbance suppression. Yet, an increased loop gain requires a higher control effort, which can extend beyond the actuation capacity of the feedback system and intermittently cause actuator saturation. To benefit from the advantages of a high feedback gain and simultaneously avoid actuator saturation, this paper advocates a dynamic gain adaptation technique in which the loop gain is lowered whenever necessary to prevent actuator saturation, and is raised again whenever possible. This concept is optimized for linear systems based on an optimal control formulation inspired by the notion of linear quadratic regulator (LQR). The quadratic cost functional adopted in LQR is modified into a certain quasi-quadratic form in which the control cost is dynamically emphasized or deemphasized as a function of the system state. The optimal control law resulted from this quasi-quadratic cost functional is essentially nonlinear, but its structure resembles an LQR with an adaptable gain adjusted by the state of system, aimed to prevent actuator saturation. Moreover, under mild assumptions analogous to those of LQR, this optimal control law is stabilizing. As an illustrative example, application of this optimal control law in feedback design for dc servomotors is examined, and its performance is verified by numerical simulations. 

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