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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. Finite Dimensional Functional Observer Design for Parabolic Systems

   https://doi.org/10.1109/CDC45484.2021.9682848  

   Demetriou, Michael A.; Hu, Weiwei (December 2021, 2021 60th IEEE Conference on Decision and Control)

   This paper combines two control design aspects for a class of infinite dimensional systems, and each of the designs aims at significantly reducing the implementation complexity and computational load. A functional observer, and its extension of an unknown input functional observer, aims to reconstruct a functional of the infinite dimensional state. The resulting compensator only requires the solution to an operator Sylvester equation plus one differential equation for each dimension of the control signal, as opposed to an infinite dimensional filter evolution equation and an associated operator Riccati equation for the filter operator covariance. When the functional to be estimated coincides with the expression of a full state feedback control signal, then the functional observer becomes the minimum order compensator. When the parabolic system admits a decomposition whereby the system is decomposed into a lower finite dimensional subspace comprising the unstable eigenspectrum and an infinite stable subspace, then the functional observer-based compensator design becomes the minimum order compensator for the finite dimensional subsystem. This approach dramatically reduces the computation for solving the ARE needed for the full state controller and the associated Sylvester equation needed for the functional observer. Numerical results for a parabolic PDE in one and two spatial dimensions are included. 

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