Presence Of Control Saturation Research Articles

Robust finite-time guidance against maneuverable targets with unpredictable evasive strategies

This paper presents a robust finite-time guidance (RFTG) law to a short-range interception problem. The main challenge is that the evasive strategy of the target is unpredictable because it is determined not only by the states of both the interceptor and the target, but also by external un-modeled factors. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. The design of this integrated strategy has two points: 1) effect of a target maneuver is modeled as disturbance and then is estimated by the second-order homogeneous observer; 2) the finite-time stabilizer is actively coupled with the observer. Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. Numerical comparison studies demonstrate the guidance performance.

Effect of Control Saturation on the Tracking of Longitudinal States of an Aircraft

Abstract This paper addresses the effect of elevator saturation on asymptotically stable tracking of a desired flight path angle of an aircraft. The desired reference trajectory is computed using a non-linear kino-dynamic model of the longitudinal states of the aircraft incorporating control bounds. Next, based on a linearised model about the reference states, a state-feedback controller is designed to track the reference trajectory in the presence of deviations. Using results from the polytopic approach, which indicate that in the presence of control saturation, the magnitudes of the allowable deviations reduce as the eigenvalues of the open-loop system move from the left to the right of the complex plane. By estimating the volumes of these so-called regions of asymptotic stability, which is based on solving a set of Linear Matrix Inequalities, the results presented in this paper aid in the selection of appropriate trajectories that enable asymptotically stable tracking in the presence of deviations and control saturation. Simulation results are used to illustrate this concept.

Framework for reducing digital-to-analogue converter quantisation error in servo control systems

A framework for reducing the digital‐to‐analogue convertor (DAC) quantisation effect in servo control systems is proposed. In the framework, two compensators are used to shape the spectrum of the DAC quantisation noise. One compensator, which is an anti-windup-based compensator, not only filters out the high-frequency part of the quantisation noise, but also provides stability and performance in the presence of control saturation. The other compensator, which is a quantisation error feedback compensator, provides effective reduction of the low-frequency noise and can account for the spectral distribution of DAC quantisation noise by an optimal choice of some parameters. Theorems concerning the solvability and the stability are given. Systematic procedures to design the compensators for single-input-single-output (SISO) and multi-input-multi-output (MIMO) plants are also suggested. To validate the performance of the framework, servo control of an optical disc head is considered. Experiments indicate that the output error caused by DAC quantisation is significantly reduced.

Non-rational dynamic output feedback for time-delay systems with saturating inputs

This paper addresses the synthesis of stabilizing non-rational dynamic output feedback controllers for time-delay systems in the presence of control saturation. Based on Lyapunov–Krasovskii functionals, the use of a modified sector condition, and a classical change of variables, theoretical LMI conditions that allow to simultaneously design the controller and a static anti-windup loop are derived. Two synthesis objectives are considered: the maximization of an estimate of the basin of attraction of the system; and the guarantee that the trajectories of the system are bounded in the presence of bounded disturbances, while ensuring an overbound on the gain from the disturbance to the regulated output.

Solutions for handling control magnitude bounds in adaptive dynamic inversion controlled satellites

Traditional adaptive control assumes full control authority and lacks an adequate theoretical treatment for control in the presence of actuator saturation limits. The adaptive dynamic inversion control methodology, which uses dynamic inversion to calculate the control and adaptation to compensate for errors in the inversion due to model uncertainties, also lacks an adequate theoretical treatment for saturation. This paper investigates the problems introduced in adaptive dynamic inversion control schemes due to bounds on the control, and develops a three component control scheme to overcome them. The main contribution of the paper is determination of the maximum possible domain of attraction with respect to the control position limit, and development of a control switching strategy to contain the plant within the maximum possible domain of attraction. This strategy ensures boundedness of the state by restricting it within the Domain of Control Authority. A direction consistent control constraint mechanism was also developed, to maintain the resultant direction of the rate of change of state to be the same as that of the desired, even in the presence of control saturation. Finally, a modified adaptation mechanism was implemented to prevent incorrect adaptation arising from trajectory errors due to control saturation. Mathematical development of the control laws and the adaptation mechanisms is presented, along with proofs for convergence of the tracking error and stability of the overall control scheme. To demonstrate the control scheme, two different numerical simulations for rigid spacecraft attitude tracking with uncertain inertias and saturated controls are presented. Results show that the control scheme successfully handles adaptive dynamic inversion control of systems with dynamics that are nonlinear in terms of the state, with uncertain parameters that appear linearly, in the presence of initial condition errors and control position bounds, and nonlinear saturation constraints on the components of the control.

STABILIZATION OF NEUTRAL SYSTEMS WITH SATURATING INPUTS

This paper focuses on the stabilization problem of neutral systems in the presence of control saturation. Based on a descriptor approach and the use of a modified sector condition, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions allow to consider systems presenting time-varying delays and are formulated directly as linear matrix inequalities (LMIs). Optimization problems are proposed with the aim of computing stabilizing state feedback control laws.

Suppression of wing rock of slender delta wings using a single neuron controller

Wing rock is a highly nonlinear phenomenon in which the aircraft undergoes limit cycle roll oscillations at high angles of attack. A single neuron control scheme for suppression of wing rock of slender delta wings is presented. The effectiveness of the control scheme is demonstrated through software simulation and real-time control experiments in a wind tunnel on a 80/spl deg/ swept back wing. The suppression of the limit cycle is achieved in presence of control saturation. The robustness of the scheme is demonstrated by the suppression of the wing rock at various initial conditions and different angles of attack.

Some new results on closed-loop stability in the presence of control saturation

Some new sufficient conditions for determining global asymptotic stability of an equilibrium point under control saturation are presented. For an open-loop stable system, we show that there exists a class of linear time invariant state feedback matrices which globally stablizes an equilibrium under control saturation. In addition, we show that for open-loop unstable plants, an equilibrium can never be globally stabilized using a certain class of saturated linear time invariant state feedback. Finally, we extend the stability results to nonlinear systems whose nonlinearities are globally Lipschitz.