Anti-windup Compensator Research Articles

Static anti-windup design for nonlinear Markovian jump systems with multiple disturbances

A static anti-windup compensation problem for Markovian jump systems with nonlinearity and multiple disturbances (one disturbance being an energy bounded signal, the other generated from a system expressed in a state-space expression) is studied in this paper. Our first objective is to design stabilizing composite hierarchical anti-disturbance controllers based on output-based disturbance observers, in the absence of actuator saturation, attenuating and rejecting the above two disturbances respectively. The aim is then to design anti-windup compensation gains for the aforementioned controllers such that the system can still be stabilized and the above mentioned two disturbances can continually be attenuated and rejected, respectively, regardless of whether control saturation exists. Sufficient conditions are derived for the existence of the desired disturbance observer gains, controller matrices, and anti-windup compensation gains, guaranteeing prescribed performances.

Dynamic anti-windup compensation of nonlinear time-delay systems using LPV approach

In this paper, a novel decoupled architecture-based anti-windup compensator (AWC) synthesis technique is presented for the constrained nonlinear time-delay systems. The proposed decoupling AWC architecture is applicable to both stable and unstable nonlinear time-delay systems and it simultaneously fulfills the requirements of attainment of stability and reasonable closed-loop performance. The proposed AWC architecture is modified with the aim to characterize the synthesis goals of the delayed nonlinear AWC by using the linear parameter varying model-based reformulation property of the Lipschitz nonlinearities. To compute the gain matrices for global or local stability through the proposed AWC, several sufficient conditions have been formulated using a Lyapunov–Krasovskii functional, the $$L_2 $$ gain minimization, the generalized sector condition and the information of bounds of delay. The proposed approach is less conservative than the existing methods due to useful terms in handling the range of time-delay. Further, the resultant method is better than the conventional methods owing to the incorporation of reformulation property for efficient handling of the Lipchitz nonlinearities. The effectiveness of the proposed AWC schemes is demonstrated via simulation results.

Delay-range-dependent static anti-windup compensator design for nonlinear systems subjected to input-delay and saturation

This paper presents the novel delay-range-dependent schemes for computing the static anti-windup compensator (AWC) gain for nonlinear systems with input time-delay and saturation constraints. By utilizing the Lyapunov–Krasovskii functional, sector conditions, Lipschitz inequality, and Wirtinger-based inequality and by employing the range of input lags, time-derivative bound of delay, and L2 gain reduction for exogenous input, sufficient conditions are derived in order to ensure global and local stability of the overall closed-loop system. In contrast to the conventional approaches, the resulting AWC design methodology can be applied to nonlinear systems with input delays (due to distant placement of a system from the controller), supports static AWC design (computationally straightforward for implementation), and employs range of the input delay (rather than trivial selection of the lower delay bound as zero). Simulations are carried out for two electro-mechanical systems, namely, a nonlinear DC motor and a nonlinear flexible-link robot under input time-delay and input saturation constraints.

Robust tracking controller design for active dolly steering

In this paper, different actuation level steering control methods for an A-double vehicle combination (tractor–semitrailer–dolly–semitrailer) are proposed. The aim of the paper is to show the viability of advanced actuation control strategies for a practical vehicular application. Three different types of robust controller are proposed: a robust proportional–integral–derivative controller, an output feedback linear ℋ∞ controller and an induced ℒ2-norm minimizing linear parameter-varying controller. All controllers are augmented with anti-windup compensators to respect the steering-angle limit and the steering-rate limit. Each model-based controller robustly rejects external disturbances and tracks a reference steering angle generated by the motion control system. Frequency-domain analysis and time-domain analysis prove that the ℋ∞ controller and the linear parameter-varying controller outperform the proportional–integral–derivative controller in terms of reference tracking and disturbance rejection. Comparative simulation scenarios are provided on the basis of the high-fidelity vehicle simulator developed by Volvo Group Trucks Technology.

Anti-windup design for stochastic Markovian switching systems with mode-dependent time-varying delays and saturation nonlinearity

This paper treats the problem of anti-windup design for stochastic Markovian switching systems with mode-dependent time-varying delays and saturation nonlinearity. The anti-windup compensator is designed such that the resulting system with mode-dependent time-varying delays and saturating actuator is stochastically stable and the domain of attraction is maximized. Sufficient conditions for the corresponding problem are proposed in terms of linear matrix inequalities. Finally, an example about RLC serial circuit demonstrates the validity of the proposed results.

Finite-Time Control of Teleoperation Systems With Input Saturation and Varying Time Delays

This paper develops a finite-time control approach for nonlinear teleoperation systems, which is capable of unifying the study of model uncertainties, actuator saturation, and asymmetric time-varying delays in the same framework. First, a novel anti-windup compensator is designed to analyze the effect of actuator saturation. To achieve the finite-time tracking, a nonsmooth generalized switched filter is also investigated. By introducing the anti-windup compensator and the generalized switched filter into the adaptive fuzzy control torque design, a novel finite-time controller is developed. By using the multiple Lypaunov–Krasovskii functionals method, the resulting closed-loop system is state-independent input-to-output practical stable (SIIOpS) and based on this, it is proved to be finite-time SIIOpS. It is shown that the asymptotic convergence of the adaptive estimation errors and the finite-time convergence of the position tracking errors are obtained, whether the robots contact with the human operator/environment or not. Finally, the effectiveness is demonstrated by the simulation results.

Active Vibration Control Based on Static Anti-windup Compensator and Unknown Input Observation

In this paper, the windup problem is addressed for disturbance rejection control (DRC) based on an unknown input observer (UIO). The proposed combination aims at dealing with actuator input nonlinearities in active vibration control (AVC) to provide a useful tool for systems under unknown environmental stimuli. Accordingly, first, assuming the governing dynamics of the plant to be smooth and differentiable around the equilibrium points, a UIO is designed such that the two transfer functions from disturbance/control input to observation residuals are null. By aiming at rejecting the external perturbations in the plant output and the observation error dynamics, an improved form of the bounded real lemma is employed. Then, based on the Lipschitz condition and considering independent input disturbance signal (mismatch case) and measurement noise, DRC synthesis is formulated in linear matrix equality/inequality framework. To address the saturation of actuators, the developed controller is then augmented with a static anti-windup (AW) compensator in a linear fractional transformation (LFT) form. The proposed combination can be used as a low order yet effective method in model-based AVC of arbitrary mechanical/civil structures.

Switching Antiwindup Design on Enlarging the Domain of Attraction for a Supercavitating Vehicle Subject to Actuator Saturation

This paper presents a new switching antiwindup compensation design to maximize the domain of attraction for a supercavitating vehicle subject to actuator saturation. The dive-plane dynamics of the vehicle are considered. By applying the linear differential inclusion expression of saturated feedbacks, conditions under which the compensator locally stabilizes the closed-loop system are then derived. The design of antiwindup gains on maximizing the system's domain of attraction is finally formulated and solved as an iterative optimization problem with linear matrix inequality constraints. Simulations are conducted for systems with magnitude and rate limits to evaluate the effectiveness of the proposed method.

Adaptive neural network automatic parking constrained control via anti-windup compensator

In this article, an adaptive proportional–integral–derivative–type neural network constrained control method based on radial basis function neural network model identifier is presented for automati...

Application of Lyapunov matrix inequality based unsymmetrical saturated control to a multi-vectored propeller airship

The problem of the design of a controller for a multi-vectored propeller airship is addressed. The controller includes anti-windup that takes into account unsymmetrical actuator constraints. First, a linear transformation is applied to transform the unsymmetrical constraints into symmetric constraints with an amplitude-bounded exogenous disturbance. Then, a stability condition based on a quadratic Lyapunov function for the saturated closed-loop system is proposed. The condition considers both amplitude-bounded and energy-bounded exogenous disturbances. Thus, the controller design problem is transformed into a convex optimization problem expressed in a bilinear matrix inequality form. Two controller design methods were applied: one-step controller and traditional anti-windup controller. The one-step method obtains the controller and the anti-windup compensator in one step while the anti-windup controller method separates this process into the linear controller design and the compensator design. Simulation results showed that both controllers enlarge the stability zone of the saturation system and have good tracking performance. It is shown that the anti-windup controller design method not only has a larger region of stability, but the demanded actuator output exceeds the constraints less and has a smaller anti-windup coefficient matrix compared to the one-step method.

Robust Linear Static Anti-Windup With Probabilistic Certificates

In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed static anti-windup analysis and robust performance synthesis correspond to several optimization goals, ranging from minimization of the nonlinear input/output gain to maximization of the stability region or maximization of the domain of attraction. We also introduce a novel paradigm accounting for uncertainties in the energy of the disturbance inputs. Due to the special structure of linear static anti-windup design, wherein the design variables are decoupled from the Lyapunov certificates, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is of independent interest for similar robust synthesis problems involving parameter-dependent Lyapunov functions. We demonstrate that the scenario with certificates robust design formulation is appealing because it provides a way to implicitly design the parameter-dependent Lyapunov functions and to remove restrictive assumptions about convexity with respect to the uncertain parameters. Subsequently, to reduce the computational cost, we present a sequential randomized algorithm for iteratively solving this problem. The obtained results are illustrated by numerical examples.

Data-driven robust control of the plasma rotational transform profile and normalized beta dynamics for advanced tokamak scenarios in DIII-D

A control-oriented, two-timescale, linear, dynamic, response model of the rotational transform ι profile and the normalized beta βN is proposed based on experimental data from the DIII-D tokamak. Dedicated system-identification experiments without feedback control have been carried out to generate data for the development of this model. The data-driven dynamic model, which is both device-specific and scenario-specific, represents the response of the ι profile and βN to the electric field due to induction as well as to the heating and current drive (H&CD) systems during the flat-top phase of an H-mode discharge in DIII-D. The control goal is to use both induction and the H&CD systems to locally regulate the plasma ι profile and βN around particular target values close to the reference state used for system identification. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed-sensitivity robust control design problem is formulated based on the dynamic model to synthesize a stabilizing feedback controller without input constraints that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is then augmented with an anti-windup compensator, which keeps the given controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop system unmodified when no saturation is present. The proposed controller represents one of the first feedback profile controllers integrating magnetic and kinetic variables ever implemented and experimentally tested in DIII-D. The preliminary experimental results presented in this work, although limited in number and constrained by actuator problems and design limitations, as it will be reported, show good progress towards routine current profile control in DIII-D and leave valuable lessons for further advancements in the field.

Research on the Digital Hydraulic Cylinder Nonlinear Robust Controlling Methods with Input Saturation

First, the nonlinear model of the digital hydraulic cylinder and the controller are constructed, then the nonlinear problem is translated into the solving of a linear matrix inequality. Finally the anti-windup compensator is designed. Simulation results show that the proposed controller and compensator guarantee the robustness and good dynamic behavior of the system.

Positive [formula omitted] modification as an anti-windup mechanism

This paper proposes a simple anti-windup mechanism for a model reference adaptive control scheme subject to saturation constraints. The anti-windup compensator has, in essence, the same structure as positive μ modification for the same class of systems. It is shown how this structure can, under certain circumstances, display characteristics similar to anti-windup schemes proposed for linear control systems. In particular, it is shown that if the (unknown) ideal control signal eventually lies within the control constraints, then the response of the adaptive control system will converge to that of the reference system—provided certain conditions are satisfied. The paper illustrates the challenge of designing anti-windup compensators for model-reference adaptive control systems.

Guaranteed Cost Anti-windup Stabilization of Discrete Delayed Cellular Neural Networks

This paper studies the problem of guaranteed cost anti-windup stabilization of discrete delayed cellular neural networks. Saturation degree function is initially presented and the convex hull theory is applied to handle the saturated terms of discrete delayed cellular neural networks. Accordingly, after choosing a common quadratic performance function, the paper designs a guaranteed cost stabilization controller in the absence of input saturation on the basis of Lyapunov–Krasovskii theorem and linear matrix inequality formulation. Then a static state feedback anti-windup compensation is derived, which guarantee a guaranteed cost and the estimation of the asymptotic stability region for the closed-loop system. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed design technique.

Model reference adaptive autopilot with anti-windup compensator for an autonomous underwater vehicle: Design and hardware in the loop implementation results

In this paper, a novel model reference adaptive controller with anti-windup compensator (MRAC_AW) is proposed for an autonomous underwater vehicle (AUV). Input saturations and parametric uncertainties are among the practical problems in the control of autonomous vehicles. Hence, utilizing a proper adaptive controller with the ability to handle actuator saturations is of a particular value. The proposed technique of this paper incorporates the well-posed model reference adaptive control with integral state feedback and a modern anti-windup scheme to present an appropriate performance in practical conditions of an AUV. Stability of the proposed method is analyzed by Lyapunov theory. Then, the proposed controller is implemented in the hardware in the loop simulation of AUV. For this purpose, the introduced method is implemented in an onboard computer to be checked in a real-time dynamic simulation environment. Obtained results in the presence of real hardware of system, actuators, computational delays and real-time execution verify the effectiveness of proposed scheme.

Anti‐windup for a class of partially linearisable non‐linear systems with application to wave energy converter control

This paper studies the anti-windup (AW) problem for a certain class of non-linear systems, in which the plant is globally quadratically stable and also partially linearisable by a suitably chosen non-linear feedback control law. Three types of AW compensators are proposed for this type of non-linear system: the first one is a non-linear extension of the popular linear internal model control (IMC) scheme; the second one has a similar structure to the IMC AW compensator yet is of reduced order and has entirely linear dynamics; and the third one is again a linear AW compensator, but can endow the closed-loop system with some sub-optimal performance properties. All three AW compensators are able to provide global exponential stability guarantees for the aforementioned class of systems. This work was inspired by a wave energy application whose dynamics fall into the class of systems studied in this study. Simulation results show the efficacy of the three AW compensators when applied to the wave energy application.

Data-driven automatic parking constrained control for four-wheeled mobile vehicles

In this article, a novel data-driven constrained control scheme is proposed for automatic parking systems. The design of the proposed scheme only depends on the steering angle and the orientation angle of the car, and it does not involve any model information of the car. Therefore, the proposed scheme-based automatic parking system is applicable to different kinds of cars. In order to further reduce the desired trajectory coordinate tracking errors, a coordinates compensation algorithm is also proposed. In the design procedure of the controller, a novel dynamic anti-windup compensator is used to deal with the change magnitude and rate saturations of automatic parking control input. It is theoretically proven that all the signals in the closed-loop system are uniformly ultimately bounded based on Lyapunov stability analysis method. Finally, a simulation comparison among the proposed scheme with coordinates compensation and Proportion Integration Differentiation (PID) control algorithm is given. It is shown that the proposed scheme with coordinates compensation has smaller tracking errors and more rapid responses than PID scheme.

Decentralized Approaches to Antiwindup Design With Application to Quadrotor Unmanned Aerial Vehicles

This paper considers the design of structured antiwindup (AW) compensators for open-loop stable plants that themselves have a particular structure: a diagonal dynamic part cascaded with a static invertible part. Two approaches to the design of such compensators are proposed. The first one is a pseudodecentralized AW compensator that is a direct extension of a similar scheme in the literature. The second approach allows the AW compensators to be designed individually for each control channel and, provided that a certain linear program is satisfied, allows the compensators to be implemented in such a way that the nonlinear closed loop is asymptotically stable. The design approaches are applied to a quadrotor UAV, which inspired the work, and results from both simulations and flight tests are reported.

Stability analysis and anti-windup design of switched systems with actuator saturation

The stability analysis and anti-windup design problem is investigated for two linear switched systems with saturating actuators by using the single Lyapunov function approach. Our purpose is to design a switching law and the anti-windup compensation gains such that the maximizing estimation of the domain of attraction is obtained for the closed-loop system in the presence of saturation. Firstly, some sufficient conditions of asymptotic stability are obtained under given anti-windup compensation gains based on the single Lyapunov function method. Then, the anti-windup compensation gains as design variables are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Two numerical examples are given to show the effectiveness of the proposed method.