Control Input Saturation Research Articles

A separation principle for a class of non-UCO systems

This paper introduces a new approach to output feedback stabilization of single-input-single-output systems which, unlike other techniques found in the literature, does not use quasilinear high-gain observers and control input saturation to achieve separation between the state feedback and observer designs. Rather, we show that by using nonlinear high-gain observers working in state coordinates, together with a dynamic projection algorithm, the same kind of separation principle is achieved for a larger class of systems which are not uniformly completely observable. By working in state coordinates, this approach avoids using knowledge of the inverse of the observability mapping to estimate the state of the plant, which is otherwise needed when using high-gain observers to estimate the output time derivatives.

Polyhedral Robust Asymptotic Stability Regions of Discrete-Time Linear Systems with Saturating Controls

The estimation of the region of robust local asymptotic stability of uncertain discrete-time linear systems with saturating control inputs is performed constructing piecewise-affine Lyapunov functions. New necessary and sufficient conditions for piecewise-affine functions be Lyapunov functions are derived. Based on linear programming formulation of these conditions, an effective non homothetic expansion procedure is proposed for construction of such Lyapunov functions for estimation of the region of robust local asymptotic stability of closed-loop saturating systems. The results obtained are strictly less conservative than those obtained via construction of contractive polyhedral sets associated to Minkowski Lyapunov functions.

Piecewise-affine Lyapunov functions for discrete-time linear systems with saturating controls

This paper is concerned with piecewise-affine (PWA) functions as Lyapunov function candidates for stability analysis of time-invariant discrete-time linear systems with saturating closed-loop control inputs. Using a PWA model of saturating closed-loop system, new necessary and sufficient conditions for a PWA function be a Lyapunov function are presented. Based on linear programming formulation of these conditions, an effective algorithm is proposed for construction of such Lyapunov functions for estimation of the region of local asymptotic stability. Compared to piecewise-linear functions, like Minkowski functions, PWA functions are more adequate to capture the dynamical effects of saturation nonlinearities, giving strictly less conservative results. The complexity of the proposed approach is polynomial in state dimension and exponential in saturating control dimension, being hence appropriate for problems with large state dimension but with few saturating inputs.

A bilateral control scheme for 2-DOF telemanipulators with control input saturation

Abstract Since the dynamics of the telemanipulator consisting of high reduction ratio joints is likely to be much slower than that of the master manipulator, the control inputs of the telemanipulator are frequently saturated resulting in poor position control performance and deteriorated stability. This paper proposes a bilateral control scheme for 2-DOF telemanipulators with control input saturation, which can improve the position tracking performance while effectively compensating for saturation. A series of experiments show that the proposed scheme provides an excellent position control performance regardless of saturation.

Computation of contractive polyhedra for discrete-time linear systems with saturating controls

This paper deals with computational aspects of characterization and construction of polyhedral u -contractive sets with respect to discrete-time linear systems with saturating feedback control inputs. Using a piecewise-affine model of the saturating closed-loop system, new necessary and sufficient algebraic condition for convex closed polyhedra be u -contractive is derived. Based on linear programming formulation of this condition, an effective procedure is proposed for construction of as large as possible u -contractive convex polyhedra for estimation of the region of asymptotic stability of origin. The procedure starts with a u -contractive polyhedron, possibly contained in the region of linear control, and progressively expands it non-homothetically over the region of non-linear saturated control. The proposed approach is less conservative and computationally much more efficient than previously published ones.

Numerical analysis of optimal vehicle trajectories for emergency obstacle avoidance

Vehicle trajectories for emergency obstacle avoidance are analyzed from a viewpoint of optimal control. The performance function consists of integrals of longitudinal acceleration, lateral acceleration and control effort is defined to formulate the obstacle avoidance problem as an optimal control problem. A numerical optimization method called a direct optimization is applied to calculate the optimal steering program. Using a nonlinear vehicle model, physical constraints such as saturation of control input, inequality constraints for vehicle trajectories, and equality constraints for terminal vehicle states are taken into account. The solutions to the optimal control problem provide valuable insight into the vehicle maneuver at the obstacle avoidance situations.

Robust Adaptive Variable Structure Control of Spacecraft Under Control Input Saturation

In this paper we propose two globally stable control algorithms for robust stabilization of spacecraft in the presence of control input saturation, parametric uncertainty, and external disturbances. The control algorithms are based on variable structure control design and have the following properties: 1 ) fast and accurate response in thepresenceofbounded external disturbancesand parametricuncertainty;2 )explicit accounting forcontrol input saturation; 3 ) computational simplicity and straightforward tuning. We include a detailed stability analysis for the resulting closed-loop system. The stability proof is based on a Lyapunov-like analysis and the properties of the quaternion representation of spacecraft dynamics. It is also shown that an adaptive version of the proposed controller results in substantially simpler stability analysis and improved overall response. We also include numerical simulations to illustrate the spacecraft performance obtained using the proposed controllers.

Polyhedral Regions of Robust Local Stability for Linear Systems With Saturating Controls

The estimation of regions of robust local asymptotic stability of uncertain discrete-time linear systems with saturating control inputs is performed constructing robustly contractive polyhedral sets. New necessary and sufficient conditions for compact polyhedral sets be robustly contractive are derived. Based on linear programming formulation of these conditions, an effective non nomothetic expansion procedure is proposed for construction of robustly contractive potyhedral sets and consequent estimation of regions of robust local asymptotic stability of closed-loop saturated systems. The procedure starts with the supremal robustly contractive potyhedral set contained in the region of linear control arid progressively expands it over the region of nonlinear saturated control.

A Force Referenced Bilateral Control Scheme for Heavy-Duty Power Manipulators

This paper proposes a force referenced bilateral control scheme for heavy-duty power manipulators, which can compensate control input saturation. Also, design condition is presented for satisfying the stability of the proposed scheme. From the experimental results, it can be seen that the proposed scheme has an excellent tracking performance regardless of the saturated control input.

Dynamic anti-windup method for a class of time-delay control systems with input saturation

An anti-windup-based approach is newly attempted to deal with time-delay control systems with input saturation. Following the anti-windup paradigm, we assume that controllers have been designed beforehand for time-delay control systems based on existing design techniques which will show desirable performance. Then, an additional compensator is designed to provide graceful performance degradation under control input saturation. By taking the difference of controller states in the absence and presence of input saturation as a performance index, a dynamic compensator which minimizes it is derived. The resulting anti-windup compensator is expressed in plant and controller parameters. The proposed method not only provides graceful performance degradation, but also guarantees the stability of the overall systems. Illustrative examples are provided to show the effectiveness of the proposed method. Copyright © 2000 John Wiley & Sons, Ltd.

Robust PI stabilization of a class of chemical reactors

The aim of this letter is to study the stabilization of a class of continuous-stirred tank reactors in the face of control input saturations and uncertain chemical kinetics. A first-order compensator with modeling error compensation is designed, and its ability to stabilize the reactor temperature at an arbitrary setpoint is proven. It is shown that the resulting controller is equivalent to a standard PI compensator with antireset windup scheme.

Robust PI stabilization of a class of continuously stirred‐tank reactors

AbstractThis article deals with the stabilization of continuously stirred‐tank reactors in the face of control input saturations and uncertain chemical kinetics. Using ideas from modeling‐error compensation techniques, a first‐order compensator is designed, and its ability to stabilize the reactor temperature at an arbitrary setpoint is shown. The dynamic part of the proposed controller is interpreted as a type of robust integral action to accommodate the modeling error.

Dynamic compensator design method for a class of time-delay control systems with saturating actuators

A dynamic compensator design method for a class of time-delay control systems with saturating actuators is proposed. Under the assumption that a controller was designed for a time-delay control system based on existing design techniques which shows desirable nominal performance, an additional compensator is introduced to provide smooth performance degradation under control input saturation. By taking the difference of the controller states in the absence and presence of saturating actuators as a performance index, a dynamical compensator which minimizes it is derived. The resulting dynamical compensator is expressed explicitly in the plant and controller parameters. The proposed method not only provides smooth performance degradation, but also guarantees the total stability of the overall systems.

Dynamic behavior of a continuous stirred bioreactor under control input saturation

A continuous stirred bioreactor with open-loop periodic behavior is analyzed under closed-loop conditions, using the dilution rate as control input. In the absence of control input bounds, the limiting substrate concentration converges to set point. When stringent bounds on control input are imposed, it becomes permanently saturated; then a limit cycle is generated, and the substrate concentration oscillates around an equilibrium point induced by saturation (EPIS). Suitable conditions are developed to avoid the presence of this closed-loop limit cycle. When the above conditions are satisfied, numerical simulations show that the substrate concentration in the closed-loop bioreactor has no permanent oscillations, the EPIS disappears and the limiting substrate concentra-tion converges again to set point, in spite of the control input bounds. © 1998 SCI

An anti-wind-up controller design for rocket control systems with control input saturation

An anti-wind-up controller for the attitude control of a two-stage sounding rocket has been designed. Once the actuator comes up to saturation limits, a feedback signal is generated in this controller from the difference between the compensator output and the actuator control input, and is used to make the actuator work in linear ranges. When this type of controller was applied to the two-stage sounding rocket attitude control system, a remarkable improvement was made in the control performance as compared with the PID (proportional, integral, plus derivative) controller case. Since the performance of this anti-wind-up controller was sensitive to the variation of control gains, a modified anti-wind-up controller has been also proposed to compensate for this.

Stable adaptive control of a class of continuous‐flow bioreactors

AbstractA stable adaptive control strategy is suggested for a class of continuous‐flow bioreactor processes described by Monod kinetics with two unknown parameters, one of which appears nonlinearly. Similarly, as in the case of the previously reported adaptive controllers, the parametrization of the process model, in conjuction with the adaptive exponential feeding strategy and corresponding adaptive algorithms, results in a stable system in which the convergence of the output errors to zero is guaranteed. In the former, however, two major problems are encountered: (1) both output errors were used to adjust the controller parameters, which may yield unacceptable performance of the resulting adaptive system; (2) conditions under which the process output can assume only positive values are difficult to derive. Hence, a design of a stable adaptive controller is suggested, whose parameters are adjusted using only one of the output errors and that yields acceptable performance of the control system. With this method, conditions under which the process outputs can assume only positive values can be readily derived. These conditions in turn guarantee that the control input saturation at value zero cannot occur. In this context, two adaptive controllers are suggested, such that the resulting adaptive systems are stable and the control objective is met. The adaptive controller design relies on a convenient coordinate transformation, while the proof of stability is based on suitably chosen Lyapunov functions. The performance of the adaptive system is evaluated through computer simulations.

Control system design issues for unstable linear systems with saturated inputs

The paper studies stable setpoint tracking for linear open-loop unstable systems with saturated control input. A linear reference filter is introduced that allows the independent design of the prestabilising and setpoint tracking controllers in an internal model control configuration. A nonlinear reference conditioning filter is also proposed that avoids saturation in the main control loop, which remains stable thereafter. Rules of thumb giving bounds on amplitude and frequency for sinusoidal references are given that ensure stable saturated operation of the nonlinear reference filter.

Analysis and Control of Nonlinear Systems

This paper describes my work on nonlinear analysis and control over the last twenty years. The first part of the paper concerns the development of nonlinear analysis tools for predicting stability and forced response characteristics of high speed ground vehicles. The principal motivation was to develop an alternative to “brute force” time domain simulation. The developed tools were extensions of “describing function” or “equivalent linearization” methods for both periodic and stochastic excitation. The “statistical linearization” analysis tools were then extended and applied to design control laws for nonlinear stochastic regulators. The second part of the paper was motivated by control system design for highly nonlinear, multivariable systems, such as automotive powertrain control and aircraft flight control. For these classes of systems, statistical linearization procedures are computationally cumbersome and also provide no stability or robustness guarantees. A method which has proven extremely powerful, both theoretically and experimentally, is “sliding control.” This technique is a form of input/output linearization that directly incorporates model error information with stability and performance measures. My students and I found several difficulties in the direct application of this method to automotive and aircraft control. This paper describes our solutions to the problems of repeated model differentiation, differentiation of model error, undesirable “internal dynamics” and systems with saturating control inputs.

Synthesis of time-fuel-optimal control: a second-order example

Abstract The synthesis of controls which minimize a linear combination of time and fuel is considered. A second-order system with eigenvalues in simple ratio (with associated parameter λ) and a scalar saturable control input is treated using a transformation of variables approach (Fuller 1973, 1974). An explicit characterization of the optimal switch curves in state space is obtained in the cases of (i) a stable plant ( λ < 0) ; and (ii) an unstable plant ( λ > 0) for which the optimal solution exists only within a bounded region of controllability. For the case of λ = 0 the result reduces to the known optimal control synthesis for the double integrator system.

Quasi-Time-Optimal Feedback Control of Some Fifth-Order Systems

A quasi-time-optimal feedback control approach is proposed for certain fifth-order systems with a single saturable control input. A pure integrator system is treated initially and the suboptimal feedback control, which achieves finite-time transition to the state origin, is shown to be piecewise constant with at most seven switches in sign; the analysis is also valid for a system with negative real eigenvalues in simple ratio. The effectiveness of the approach is demonstrated by numerical example. An extension of the control, via a linear state transformation, to more general systems with real nonpositive eigenvalues is indicated.