Input Rate Saturation Research Articles

Switching Anti-windup Synthesis for Linear Systems Subject to Asymmetric Input Magnitude and Rate Saturation: Application to Aircraft Engines

Switching Anti-windup Synthesis for Linear Systems Subject to Asymmetric Input Magnitude and Rate Saturation: Application to Aircraft Engines

Asymmetric integral barrier Lyapunov function-based three-dimensional integrated guidance and control design with field-of-view constraint and input saturation

This paper proposes an adaptive integrated guidance control (IGC) scheme for the flight vehicle intercepting the maneuvering target with asymmetric field-of-view angle constraint, input magnitude and rate saturation, and system uncertainties. A novel nonlinear three-dimensional IGC model is established in the body line-of-sight (LOS) coordinate system by employing the dual-integral control law. Based on this model, the input magnitude and rate saturation for the conventional IGC system can be converted to the limitations of the new augmented states. Asymmetric integral barrier Lyapunov function and dynamic surface control approach are applied to deal with the asymmetric state constraints of the proposed IGC model, and adaptive control laws are designed to compensate for model uncertainties. Furthermore, based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are bounded while the constrained states are not violated. Finally, the effectiveness and robustness of the proposed IGC scheme are illustrated with numerical simulations.

Optimal non-fragile control design for linear systems under amplitude and rate saturation: An LMI approach

In this paper, the problem of optimal non-fragile guaranteed cost control design for linear systems subject to input amplitude and rate saturation is addressed. Sufficient conditions for the existence of a non-fragile state feedback are obtained by Lyapunov stability theory. The designed controller not only guarantees the asymptotic stability of the overall closed-loop system with a minimum upper bound of a cost function, but also ensures the actuator saturation avoidance. This problem is transformed into an optimization problem with linear matrix inequality (LMI) constraints. The proposed method guarantees that the control input amplitude and rate remain within the allowable ranges and do not exceed the considered bounds. The simulation results illustrate the effectiveness and superiority of the proposed theoretical results.

Distributed observer‐based tracking of multi‐agent systems with bounded input amplitudes and rates

SummaryThis work solves the distributed tracking problem for multi‐agent systems with bounded inputs over directed networks. Unlike existing results focusing only on the input amplitude saturation, both input amplitude and input rate saturation are taken into account, which are more challenging due to the coupled evolutions of input amplitudes and input rates. Firstly, relative disturbance observers are developed using relative state measurements to estimate the relative disturbances, where the estimation errors converge to zero within a finite time horizon. Subsequently, distributed tracking error observers are proposed by means of a novel bounded function to estimate the tracking errors, where the estimation errors will converge to zero. Then, an observer‐based saturated control strategy is designed to achieve the distributed tracking objective. Finally, simulations of DC‐DC buck converters tracking and vehicles formation are provided to verify the effectiveness of the control scheme.

Adaptive Flight Control in the Presence of Limits on Magnitude and Rate

Input constraints as well as parametric uncertainties must be accounted for in the design of safe control systems. This paper presents an adaptive controller for multiple-input-multiple-output (MIMO) plants with input magnitude and rate saturation in the presence of parametric uncertainties. A filter is introduced in the control path to accommodate the presence of rate limits. An output feedback adaptive controller is designed to stabilize the closed loop system even in the presence of this filter. The overall control architecture includes adaptive laws that are modified to account for the magnitude and rate limits. Analytical guarantees of stable adaptation, bounded trajectories, and satisfactory tracking are provided. Three flight control simulations with nonlinear models of the aircraft dynamics are provided to demonstrate the efficacy of the proposed adaptive controller for open loop stable and unstable systems in the presence of uncertainties in the dynamics as well as input magnitude and rate saturation.

Online Feedback-based Optimization with Multi-input Direct Constraint Control

The starting point of this paper is to solve a steady-state optimization problem with simple feedback controllers using the Primal-Dual approach. However, this approach controls the constraint indirectly and on a slow time scale by manipulating the Dual variables (Lagrange multipliers). This control strategy may lead to unacceptable dynamic violations. The main contribution of this paper is to reduce the violations by introducing direct constraint control on the fast time scale using a selector. To get consistency with the steady-state optimization, we need to change the constraints in the Primal-Dual approach to involve the input used for direct constraint control. As a further refinement of this idea, we propose a multi-input direct constraint control for cases where many inputs affect the constraint value, and where pairing with a single input may lead to input rate saturation. The proposed control structure is applied to a subsea oil production network, showing that the proposed approach can minimize the dynamic violation during transient, and can achieve optimal steady-state conditions using simple feedback controllers.

Robust command filtered control for course tracking of ships under actuator dynamics with input magnitude and rate saturation

This article investigates the course tracking of ships subject to parametric uncertainties and environmental disturbances. Particularly, the actuator dynamics with input magnitude and rate saturation is also considered. When including the actuator dynamics, the ship course tracking system becomes a mismatching system, which brings a great difficulty to the control design. A novel robust command filtered control strategy is presented by incorporating a disturbance observer and an auxiliary anti-saturation system into the command filtered backstepping control architecture. The disturbance observer is designed to compensate for the mismatched lumped disturbance. The auxiliary anti-saturation system is introduced to tackle the effects of input magnitude and rate saturation. It is strictly proved that all the closed-loop error signals under the proposed controller are uniformly ultimately bounded and the course angle tracking error can converge to the adjustable small region around the origin. Moreover, the proposed controller is computationally simple and has the strong robustness against uncertainties and disturbances. The effectiveness and advantages of the proposed control strategy are verified through simulations and comparisons.

Adaptive finite time attitude tracking control of a rigid spacecraft considering input magnitude and rate saturations

This article investigates the attitude tracking control problem of a rigid spacecraft under the modeling inaccuracy, environmental disturbance, and input magnitude and rate saturations. A robust controller is proposed based on several nonlinear control methods, including the integral terminal sliding mode control, adaptive control, backstepping control, auxiliary system, and nonlinear observer methods. Within the control framework, a new integral terminal sliding mode surface (ITSMS) is first designed which integrates the fast nonsingular terminal sliding mode surface (FNTSMS) with a first-order filter to achieve the finite time stability without the input singularity problem. And adaptive laws are employed to compensate for the modeling inaccuracy and environmental disturbance with no prior knowledge. To satisfy the input magnitude and rate saturation constraints, a dynamic model in the form of a first-order filter is built up to restrict the dynamics of the actuators, which is then associated with the auxiliary system. Meanwhile, a nonlinear observer is used to avoid calculating the derivative of the expected virtual control signal. Semi-globally uniformly ultimate bounded stability is proved for the closed-loop system, and the tracking errors can converge to small regions around the expected equilibrium in finite time. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed controller.

Observer-based tracking control for single machine infinite bus system via flatness theory

In this research, we aim to use the flatness control theory to develop a useful control scheme for a single machine connected to an infinite bus (SMIB) system taking into account input magnitude and rate saturation constraints. We adopt a fourth-order nonlinear SMIB model along an exciter and a turbine governor as actuators. According to the flatness-based control strategy, first we show that the adopted nominal SMIB model is a flat system. Then, we develop a full linearizing state feedback as well as an outer integral-type loop to ensure suitable tracking performances for the power and voltage as well as the angular velocity outputs. We assume that only the angular velocity of the generator is available to be measured. So, we provide a linear Luenberger observer to estimate the remaining states of the system. Also, the saturation nonlinearities are transferred to the linear part of the system and they are canceled out using their estimations. The efficiency and usefulness of the proposed observer-controller against faults are illustrated using simulation tests in Eurostag and Matlab. The results show that the clearing critical time of the introduced methodology is larger than the classical control approaches and the proposed observer-based flatness controller exhibits over much less control energy compared to the classic IEEE controllers.

Pitch autopilot design for an autonomous aerial vehicle in the presence of amplitude and rate saturation

In this article, a new composite anti-windup (AW) compensator scheme is proposed to tackle the rate and amplitude saturations in an autonomous aerial vehicle (AAV). The actuator input saturation is a practical and critical challenge in the controller design of autonomous vehicles. Nowadays, modern anti-windup compensators are presenting practical remedies to cope with input amplitude and rate saturation. Meanwhile, Riccati-based compensators can be a suitable choice due to their high performance and simplicity. Therefore, this article proposes an integrated approach by combining the anti-windup amplitude and rate methods to deal with the aforementioned problems. First, the basic controller function on the linear model is examined. It is shown that this controller behaves well so long as there is no saturation. However, when saturation occurs, its performance is decreased and even becomes unstable. By modifying the controller via the proposed method, the controller efficiency is increased significantly. The proposed method has been implemented on an autonomous aerial vehicle with 6-degrees of freedom (6DOF). Through various simulation scenarios, it is shown that the proposed method can show proper behavior in the case of a nonlinear and close-to-reality model of the system. In addition, the proposed controller efficacy has been investigated in a comprehensive Monte Carlo simulation and it is shown that the proposed method keeps its efficiency against the practical uncertainties of the system behavior.

Finite-time spacecraft attitude control under input magnitude and rate saturation

This paper addresses attitude-stabilizing control for rigid spacecraft with actuator magnitude and rate saturation (MRS). Firstly, a continuous dynamical system is introduced to model the actuator MRS. Rigorous analysis is given to demonstrate that the model’s output can always meet the MRS constraints if the control scheme applied to the model derived here is continuous. Then, by using the proposed MRS model and the homogeneity property, two attitude-stabilizing control laws are presented. The measurement of angular velocity is required in the implementation of the first control law, but this requirement is unnecessary in the second one. The local finite-time stability of the resulting closed-loop system is ensured by employing the Lyapunov approach. Finally, several simulation examples are presented to validate the efficiency of the proposed method.

Disturbance Observer-Based Attitude Control for Spacecraft With Input MRS

This paper considers the problem of attitude tracking control for uncertain rigid spacecraft subject to control input magnitude and rate saturation (MRS). First, a smooth input MRS model is proposed. Then, a robust attitude tracking control scheme is designed based on the backstepping and finite-time disturbance observer techniques. Finally, the effectiveness of the control scheme derived here is illustrated by numerical simulations.

Robust predictive sliding mode control for input rate-constrained discrete-time system

AbstractThis paper investigates a class of uncertain linear discrete-time systems subject to input rate saturation. A predictive sliding mode control approach is proposed which guarantees the control inputs remain bounded in the input rate saturation. Furthermore, the disturbance observer is developed to compensate for the system uncertainty and disturbance. Finally, the simulations demonstrate the effectiveness of the proposed predictive sliding mode control scheme.

Adaptive sliding mode control for a general nonlinear multicompartment lung model with input pressure and rate saturation constraints

SummaryIn this article, we develop an output feedback adaptive sliding mode controller for a general multicompartment lung mechanics model with nonlinear resistance and compliance respiratory parameters. Specifically, for a given clinically plausible reference volume pattern, we develop an adaptive sliding mode controller that accounts for input pressure and rate saturation constraints to automatically adjust the applied input pressure by the mechanical ventilator so that the total lung volume tracks the given reference pattern. The pressure due to lung muscle activity is also considered in the controller design. A Lyapunov‐based approach is presented to show convergence of the closed‐loop system, and the proposed control framework is applied to a two‐compartment lung model to show the efficacy of the proposed control method. Copyright © 2015 John Wiley & Sons, Ltd.

An LMI-based decoupling control for electromagnetic formation flight

Electromagnetic formation flight (EMFF) leverages electromagnetic force to control the relative position of satellites. EMFF offers a promising alternative to traditional propellant-based spacecraft flight formation. This novel strategy is very attractive since it does not consume fuel. Due to the highly coupled nonlinearity of electromagnetic force, it is difficult to individually design a controller for one satellite without considering others, which poses challenges to communications. This paper is devoted to decoupling control of EMFF, including regulations, constraints and controller design. A learning-based adaptive sliding mode decoupling controller is analyzed to illustrate the problem of existing results, and input rate saturation is introduced to guarantee the validity of frequency division technique. Through transformation, the imposed input rate saturation is converted to state and input constraints. A linear matrix inequalities (LMI)-based robust optimal control method can then be used and improved to solve the transformed problem. Simulation results are presented to demonstrate the effectiveness of the proposed decoupling control.

Adaptive Filtering Backstepping for Ships Steering Control without Velocity Measurements and with Input Constraints

We consider the problem of course tracking for ships with uncertainties and unknown external disturbances, in the presence of input magnitude and rate saturation. The combination of approximation-based adaptive technique and radial basis function (RBF) neural network allows us to handle the unknown disturbances from the environment and uncertain ship dynamics. By employing the adaptive filtering backstepping, the full-state feedback controller is first derived. Then the output feedback controller is designed with the unmeasurable state estimated by using a high-gain observer. In order to cope with the input constraints, an auxiliary system is introduced to the output feedback controller, and the semiglobal uniform boundedness of the modified control solution is verified. Simulation results are presented for the course tracking of a cargo ship, which are demonstrative of the excellent performance of the proposed controller.

A magnitude and rate saturation model and its use in the solution of a static anti-windup problem

In this paper we address the anti-windup design problem for linear control systems with strictly proper controllers in the presence of input magnitude and rate saturation. Using generalized sector condition, we provide an LMI-based procedure for the construction of a linear anti-windup gain acting on the controller state equation such that regional closed-loop stability is guaranteed and suitable performance measures are optimized. The approach is successfully illustrated on a simulation example.

STATIC LINEAR ANTI-WINDUP DESIGN FOR STRICTLY PROPER CONTINUOUS TIME CONTROL SYSTEMS WITH MAGNITUDE AND RATE SATURATION 1

In this paper we address the anti-windup design problem for linear control systems with strictly proper controllers in the presence of input magnitude and rate saturation. Using generalized sector conditions, we provide an LMI-based procedure for the construction of a linear anti-windup gain acting on the controller state equation such that regional closed-loop stability is guaranteed and suitable performance measures are optimized. The approach is successfully illustrated on a simulation example.

Design for Feedback Systems With Plant Input Amplitude and Rate Saturation

In this paper, a method of compensation for feedback systems subject to simultaneous plant input amplitude and rate saturation is presented. It applies to uncertain, stable plants of a type greater than or equal to 1. Founded on Horowitz’s original idea for amplitude saturation compensation (Horowitz, I., 1983, Int. J. Control, 38(1), pp. 169–197) and extensions developed in (Wu, W., and Jayasuriya, S., 1999, Proceedings of American Control Conference, San Diego, CA, pp. 3046–3050; Wu, W., and Jayasuriya, S., 2001, ASME J. Dyn. Syst., Meas., Control, 123(2), pp. 225–232; Wu, W., 2000, Ph.D. dissertation, Texas A&M University), a synthesis method that explicitly takes into account input amplitude and rate saturation is further developed. In the case of simultaneous amplitude and rate saturation, approaches developed separately for amplitude alone, and rate alone saturation (Wu, W., 2000, Ph.D. dissertation, Texas A&M University), respectively, are integrated into one method, and results in a 4DOF(degrees of freedom) feedback system with two extra compensators to deal with two saturation nonlinearities. Design constraints for saturation compensation are developed and expressed as frequency domain bounds. Synthesis of the two additional compensators follows from loop shaping methods, such as QFT. This approach guarantees input/output stability for the class of plants considered. Examples are given to illustrate the application of this approach.

Design of Feedback Systems With Plant Input Rate Saturation via QFT Approach

In this paper, a synthesis approach for input rate saturation compensation of feedback systems is presented. Uncertain, stable plants of type greater than or equal to 1 are considered. Based on Horowitz’s original design for input amplitude saturation (Horowitz, I., 1983) and extensions developed in (Wu, W., and Jayasuriya, S., 1999; Wu, W., and Jayasuriya, S., 2001; Wu, W., 2000) an independent loop around the rate saturating element is introduced for saturation compensation by means of the third DOF (degree of freedom) saturation compensator, H(s). First, the structure of the additional loop transmission is constructed to generate the desired response behavior on a systems recovery from saturation. Second, robust stability and robust performance under the addition of H(s) are investigated. The circle criterion, describing function, and nonovershooting conditions are utilized to generate design constraints. In the end, all design constraints involving saturation compensation are expressed as frequency domain bounds, and the synthesis of saturation compensator H(s) follows from loop shaping methods such as QFT. The proposed approach guarantees input/output stability under saturation for the plant class considered.