Static Anti-windup Compensator Research Articles

Static anti-windup compensator based on BMI optimisation for discrete-time systems with directional change in controls avoidance

In the paper, a design method of a static anti-windup compensator for systems with input saturations is proposed. First, an antiwindup controller is presented for system with cut-off saturations, and, secondly, the design problem of the compensator is presented to be a non-convex optimization problem easily solved using bilinear matrix inequalities formulation. This approach guarantees stability of the closedloop system against saturation nonlinearities and optimizes the robust control performance while the saturation is active.

Division Linearization Zero-Bias Current Control for AMBs–Rotor System With Uncertainties and Saturation

Traditional constant current sum (CCS) distribution strategy is always employed in the nonlinear active magnetic bearing (AMB) system control for linearization, but the bias current in CCS causes extra power consumption and limits the AMBs' capacity. In this paper, a division linearization zero-bias current (DLZBC) distribution strategy is proposed as a substitution for CCS strategy. Under this strategy, a linear active disturbance rejection controller (LADRC) with a static anti-windup compensator (SAWC) is applied to deal with model uncertainties and current saturation. For different types of AMB-supported machines, a partial normalized nonlinear model is established. Subsequently, the performance of the CCS strategy is analyzed, and a DLZBC strategy is presented to reduce the power consumption and transform the system into a linear plant with a lumped uncertain parameter. Afterward, a LADRC is designed to enhance robustness, whose parameters are chosen according to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu -$</tex-math></inline-formula> synthesis framework and are convenient for adjustment practically. For anti-saturation, a SAWC is developed to help the system escape quickly from current saturation and enlarge the stability domain of the saturated system. Comparative simulations and experiments results show that the proposed control method can significantly reduce power consumption and achieve good response in AMB-rotor system.

Static anti-windup compensator design for locally Lipschitz systems under input and output delays.

This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints.

Static anti-windup compensator based on BMI optimisation for discrete-time systems with cut-off constraints

Static anti-windup compensator based on BMI optimisation for discrete-time systems with cut-off constraints

A novel approach for static anti-windup compensation of one-sided Lipschitz systems under input saturation

This paper illustrates a new strategy for designing the local static anti-windup (AW) compensator for nonlinear systems with one-sided Lipschitz (OSL) nonlinearities under saturating actuators and exogenous disturbances. The static AW strategy is designed such that the resulting closed-loop system with OSL nonlinearity, actuator saturation, and exogenous disturbance is stable and the region of attraction can be maximized. Inequalities based conditions are formulated for the static AW gain design by using Lyapunov stability theory, sector condition, L2 gain reduction, OSL inequality, and quadratic inner-bounded (QIB) condition. The proposed AW technique is simpler to design, straightforward to implement and deals with a broader class of systems in contrast to conventional methods. An application example demonstrates that the proposed static AW can successfully mitigate the saturation consequences in OSL nonlinear systems.

Combined Static and Dynamic Anti-Windup Compensation for Quadcopters Experiencing Large Disturbances

This paper proposes a composite anti-windup design approach in which the anti-windup compensator features both dynamic and static components. The advantage of the extra static component is that it can be specially structured to limit classical integrator wind-up, which is useful in nonlinear systems that operate far from their design operating point. An approach to combining the static and dynamic elements is provided that ensures closed-loop stability, yet with the structure of the static compensator preserved. The work is motivated by the need to stabilize quadcopters subject to large disturbances, and excerpts from an extensive simulation campaign are reported. The simulations clearly indicate that the combination of dynamic and static anti-windup compensation provides stability for significantly larger disturbances than either static or dynamic anti-windup compensation alone.

Static anti-windup compensator for nonlinear systems with both state and input time-varying delays

In this work, the design on static anti-windup compensator (SAWC) for a class of nonlinear systems with saturation constraint is presented, in which both state time-varying delay and input one are involved. First, by utilizing an augmented Lyapunov–Krasovskii functional (LKF), sector condition, and L2 gain reduction for exogenous input, a sufficient condition on local stability is presented in terms of linear matrix inequalities (LMIs), which is later extended to the global stability issue. During the discussions, an improved dynamical Lyapunov method is initially proposed and it can fully utilize the individual and mutual information on both state and input delays. Especially, some effective techniques are utilized to given more tighter estimations on the LKF’s derivatives. In all, these treatments above can result in much less conservatism. Finally, some comparisons and simulations are presented in two numerical examples under the proposed SAWC.

Static anti-windup compensator design for nonlinear time-delay systems subjected to input saturation

In this paper, a novel technique for synthesizing static anti-windup compensator (AWC) is explored for dynamic nonlinear plants with state interval time-delays, exogenous input disturbance, and input saturation nonlinearity, by means of reformulated Lipschitz continuity property. A delay-range-dependent approach, based on Wirtinger-based inequality, is employed to derive a condition for finding the static AWC gain. By using the Lyapunov–Krasovskii functional, reformulated Lipschitz continuity property, Wirtinger-based inequality, sector conditions, bounds on delay, range of time-varying delay, and $$\mathcal {L}_2$$ gain reduction, several conditions are derived to guarantee the global and local stabilization of the overall closed-loop system. Further, when the lower time-delay bound is zero, the delay-dependent stabilization condition is derived for saturated nonlinear time-delay systems as a particular scenario of the suggested static AWC design approach. Furthermore, a static AWC design strategy is also provided when a delay-derivative bound is not known. An application to the nonlinear dynamical system is employed to demonstrate the usefulness of the proposed methodologies. A comparative numerical analysis with the existing literature is provided to show the superiority of the proposed AWC results.

A nonlinear modification for improving dynamic anti-windup compensation

This paper presents a simple modification which can be made to a pre-designed dynamic anti-windup scheme in order to improve its performance. Roughly speaking, the modification enables the dynamic anti-windup compensator to act more like a static anti-windup compensator in certain circumstances. In particular, the modification enables the output of the compensator to decay more quickly than if it were absent, thereby effecting a swifter recovery of linear behaviour. The modification is therefore suitable for – and indeed motivated by – applications where the original anti-windup compensator contains slow poles, resulting in a potentially lengthy recovery of linear behaviour. The paper describes in detail the modification and presents conditions under which it is able to preserve stability.

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.

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.

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.

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.

Anti-windup-based dynamic controller synthesis for lipschitz systems under actuator saturation

This paper presents a new method for simultaneous synthesis of dynamic controller and static anti-windup compensator for saturated Lipschitz systems. Thanks to the reformulated Lipschitz property, the Lipschitz systems can be transformed into LPV (linear parameter-varying) systems whose system matrices are affine in a parameter matrix. Based on the modified sector condition dealing with saturation nonlinearity, the design of a nonlinear anti-windup-based controller leads to the solvability of a set of bilinear matrix inequalities (BMI) on the vertices of a bounded convex set which can be solved by the so-called iterative linear matrix inequality (ILMI) algorithm. A numerical example is presented to illustrate the effectiveness of the proposed method.

An Improved Antiwindup Design Using an Anticipatory Loop and an Immediate Loop

We present an improved antiwindup design for linear invariant continuous-time systems with actuator saturation nonlinearities. In the improved approach, two antiwindup compensators are simultaneously designed: one activated immediately at the occurrence of actuator saturation and the other activated in anticipatory of actuator saturation. Both the static and dynamic antiwindup compensators are considered. Sufficient conditions for global stability and minimizing the inducedL2gain are established, in terms of linear matrix inequalities (LMIs). We also show that the feasibility of the improved antiwindup is similar to the traditional antiwindup. Benefits of the proposed approach over the traditional antiwindup and a recent innovative antiwindup are illustrated with well-known examples.

Dynamic anti-windup design for anticipatory activation: enlargement of the domain of attraction

Traditional anti-windup compensators are designed for activation immediately at the occurrence of actuator saturation. Recently, anti-windup compensators designed for actuation either after the saturation has reached a certain level or in anticipation of its occurrence. In the case of static anti-windup compensators, it has been shown that an anti-windup compensator designed for activation in anticipation of actuator saturation would lead to better performance than those designed for immediate or delayed activation could, both in terms of transient performance and the size of the domain of attraction. More recently, it has been shown that a dynamic anti-windup compensator designed for anticipatory activation would also result in better transient performance than those designed for immediate or delayed activation could. In this paper, we design dynamic anti-windup compensators for the enlargement of the domain of attraction. These compensators are designed respectively for immediate, delayed and anticipatory activation. We will show by simulation that a dynamic anti-windup compensator designed for anticipatory activation would result in a larger domain of attraction than a dynamic anti-windup compensator designed for immediate or delayed activation could.

Anti-windup-based dynamic controller synthesis for nonlinear systems under input saturation

This paper describes the design of dynamic controller and static anti-windup compensator (AWC) for Lipschitz nonlinear systems under input saturation. Global and local AWC-based control schemes for stabilization of the nonlinear systems are proposed, and necessary conditions for feasibility of the control approaches are investigated. A one-step approach for simultaneous design of H∞ controller and AWC by means of linear matrix inequalities (LMIs) is presented herein, which supports multi-objective synthesis to attain stabilization or tracking, robustness against disturbance and noise, and penalization of large and high frequency control signals. This multi-objective synthesis can be accomplished by incorporating design weights, as commonly used in the standard H∞ control theory, to design a performance-oriented anti-windup-based control scheme. LMIs for the global control of the nonlinear systems subject to input saturation are derived by application of a quadratic Lyapunov function, the Lipschitz condition, the global sector condition, L2 gain reduction, substantial matrix algebra and variable transformation. In order to cope with unstable and oscillatory nonlinear systems, LMI-based local results are established using a local sector condition. Additional conditions are derived, by incorporating properties of the saturation function, to ensure well-posedness of the controller. Two simulation examples are provided to show the effectiveness of the proposed control schemes for control of stable and chaotic nonlinear systems under input saturation.

Design of Anti-Windup Compensators for a Class of Nonlinear Control Systems with Actuator Saturation

This paper addresses the design of static anti-windup compensators for a class of nonlinear systems subject to actuator saturation. Considering that a (possibly nonlinear) dynamic output feedback control law has been previously designed disregarding the saturation, a method to compute a static anti-windup gain which ensures the local stability of the closed-loop system is proposed. The results are based on a differential algebraic representation of rational systems and on a modified version of the generalized sector condition to deal with the saturation effects. From these elements, an algorithm based on the solution of LMIs is proposed to calculate an anti-windup gain to enlarge the region of attraction of the closed-loop system. Moreover, extensions of the results are presented to deal with parameter uncertainty and the presence of energy bounded disturbances. A numerical example is presented to illustrate the proposed method.

On Immediate, Delayed and Anticipatory Activation of Anti-Windup Mechanism: Static Anti-Windup Case

This technical note examines the immediate, delayed and anticipatory activation of anti-windup mechanism. Traditional anti-windup compensators are designed for immediate activation. A recent innovation is to delay the activation of the anti-windup mechanism until the degree of saturation reaches to a certain level. By allowing the nominal controller to function undisturbed in the face of modest actuator saturation, delayed activation of the anti-windup mechanism has been shown to lead to improvement in the closed-loop performance. In this technical note, we propose to activate the static anti-windup compensation in anticipation of actuator saturation and show that such a “precautionary” approach has the potential of leading to further improvement in the closed-loop performance, in terms of both the transient quality in reference tracking and the region of stability.

Finite-gain L2 Stability of PID Set Position Control with Anti-windup Compensation for Euler-Lagrange Systems with Actuator Saturation

Finite-gain L2 stabilization is achieved locally for a system using a PID set position controller and a newly proposed static anti-windup compensation for Euler-Lagrange systems with actuator saturation and external disturbances. In a closed-loop nonlinear system with feedback and input saturation, L2 stability of the Euler-Lagrange systems is guaranteed based on the passivity of anti-windup compensation. The control performance to counter an external disturbance added for the purpose of input saturation is verified by numerical simulations and experiments using a two-link robot arm.