Saturated Feedback Control Research Articles

Saturated Feedback Stabilizability to Trajectories for the Schlögl Parabolic Equation

It is shown that there exist a finite number of indicator functions, which allow us to track an arbitrary given trajectory of the Schlögl model, by means of an explicit saturated feedback control input whose magnitude is bounded by a constant independent of the given targeted trajectory. Simulations are presented showing the stabilizing performance of the explicit feedback constrained control. Further, such performance is compared to that of a receding horizon constrained control minimizing the classical energy cost functional.

Nested saturated feedback control of an electro-hydrodynamic jet printer

This paper investigates design of a nested saturated feedback control for an electro-hydrodynamic jet (E-jet) printer. The closed-loop control of this system is vital due to high dependency of product quality on the various system parameters. Typically, this printer is controlled by adjusting the voltage between the nozzle and substrate to regulate the height of the cone-jet to a desired value. This helps to manipulate size of droplets as an indicator of print quality. The proposed controller is simulating along with a widely-used PID controller in order to evaluate its overall performance. Then, this controller is implemented in COMSOL software, which emulates a more realistic model of the system, in order to mimic an experimental set up. Both studies show that the proposed controller could produce desired transient as well as steady-state responses in the presence of external disturbances.

Asynchronous Impulsive Protocols With Asymmetric Feedback Saturation on Leader-Based Formation Control of Multiagent Systems.

Saturation phenomena often exist due to limited system resources, and impulsive protocols can lead to a reduction in communication cost. From these issues, this article investigates a leader-based formation control problem of multiagent systems via asynchronous impulsive protocols with saturated feedback. General linear system models with and without finite time-varying time delays under asymmetric saturated feedback control are concurrently considered. The asynchronous impulsive protocols only permit communication at impulsive instants and each agent has its own communication instants independently. Moreover, to improve system performance, an offset only containing desired formation information is introduced. Finally, because the feedbacks are saturated, admissible regions are proved to exist, which are also estimated by a mean of optimization. Numerical simulations are presented to demonstrate the validity of the proposed schemes.

Local Stabilization of an Unstable Parabolic Equation via Saturated Controls

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities. We show that our results can be used with distributed as well as scalar boundary control, and with different types of saturations. The efficiency of the proposed method is demonstrated by means of numerical simulations.

Bounded control of feedforward nonlinear systems subject to input time‐delay

SummaryThis article is concerned with the global stabilization problem of a family of feedforward nonlinear time‐delay systems whose linearized system consists of multiple distinct oscillators. To fully utilize the delayed information and maintain the state decoupling property in the controller design, the considered nonlinear feedforward system is first transformed into a new system which contains time delays in both its input and states based on a novel model transformation containing time delays, and then the stabilizing saturated controller for the transformed system is designed based on the recursive design method. Meanwhile, explicit stability conditions are also provided. When the linearized system is a cascade of multiple oscillators and multiple integrators, a modified saturated feedback control utilizing not only the current state but also the delayed state is also established for the corresponding global stabilization problem. Two examples, including a practical one, are given to show the effectiveness and superiority of the proposed approaches.

On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control

This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L2([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L∞ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.

Saturated Feedback Control to Improve Ride Comfort for Uncertain Nonlinear Macpherson Active Suspension System With Input Delay

A robust saturation control approach is developed for input-time delay Macpherson active suspensions, subject to dynamical uncertainties, exogenous disturbances, and road excitations. The proposed control method comprises of a linear combination of two smooth saturation functions of a filtered signal and a regulation error, hence the control law is smooth and bounded by a known and adjustable constant bound. An auxiliary signal involving a finite integral over the delayed time interval of past control values is exploited to convert the delayed system into a delay-free system, and Lyapunov–Krasovskii (LK) functionals are constructed to eliminate the residual delayed terms in a Lyapunov-based analysis. The vertical displacement and velocity of the sprung mass are proven to uniformly ultimately bounded regulating to improve the ride comfort, despite model uncertainties, additive disturbances and the input delay. Several simulations are performed to verify the improvement in the ride comfort under different road profiles, while the tire deflection and suspension deflection are within an admissible limitation in comparison with two other suspensions.

Dynamics Analysis and Control of a Bird Scale Underactuated Flapping-Wing Vehicle

In this paper, the dynamics modeling, analysis, and control of bird scale flapping-wing vehicles (FWVs) are investigated. On the basis of quasi-steady-state aerodynamic theory, the dynamics model of the FWV with flat plate wings is presented. By qualitatively analyzing the properties of the dynamics and quantitatively analyzing the relationships between the inputs and outputs of the FWV, a saturated feedback controller based on dynamic compensators is proposed. By theoretical analysis, numerical simulations, and prototype experiments, the modeling method and the stability of the presented controller have been verified.

Motion planning and control for endoscopic operations of continuum manipulators

This paper presents a novel coordinated motion planning method for solving the inverse kinematic problems of endoscopic operations of continuum manipulators. For safe and stable control of the continuum manipulators in complex constrained environments, a saturated feedback controller is proposed. The global stability of the controller is analyzed. Some numerical simulations also demonstrate that the proposed motion planning method and the control approach are feasible under certain conditions.

Design of saturated controls for an unstable parabolic PDE

We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume Lyapunov stability of the uncontrolled system, and consider general unstable systems. Using Lyapunov methods, we provide estimates for the region of attraction for the closed-loop system, given in terms of linear and bilinear matrix inequalities. We show that our results can be used with distributed as well as scalar boundary control. The efficiency of the proposed method is demonstrated by means of a numerical simulation.

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

SummaryFor the global stabilization of a family of feedforward nonlinear time‐delay systems whose linearized systems consist of a chain of identical oscillators, a saturated feedback control is established based on a special canonical form. The proposed control laws use not only the current states but also the delayed states for feedback, which helps maintain the decoupling property in the recursive design. Moreover, explicit conditions guaranteeing the stability of the closed‐loop system are provided. When the nonlinear terms vanish and even the oscillators are distinct, a modified saturated feedback control can still be established for the corresponding global stabilization problem. Two numerical examples are given to illustrate the effectiveness of the proposed approaches.

On Bounded Control of A Class of Feedforward Nonlinear Time-Delay Systems

For the global stabilization of a family of feedforward nonlinear time-delay systems with linearized identical oscillators, a saturated feedback control is established based on a special canonical form for the considered system. The proposed control laws use not only the current states but also the delayed states for feedback, and, moreover, contain some free parameters. These advantages can help to improve the transient performance of the closed-loop system significantly. A numerical example is given to illustrate the effectiveness of the proposed approaches.

Output Feedback Passification of Switched Continuous-Time Linear Systems Subject to Saturating Actuators

This paper is concerned with the output feedback passification of switched continuous-time linear systems with actuation saturation. A switching law and saturated output feedback controllers with t...

Mixed H2/H∞ robust model predictive control with saturated inputs

In this paper, we investigate the mixed H2/H∞ robust model predictive control (RMPC) for polytopic uncertain systems, which refers to the infinite horizon optimal guaranteed cost control (OGCC). To fully use the capability of actuators, we adopt a saturating feedback control law as the control strategy of RMPC. As the saturating feedback control law can be effectively represented by the convex hull of a group of auxiliary linear feedback laws, the auxiliary feedback laws allow us to design the actual feedback control law without consideration of the input constraints directly to achieve the improved performance. Moreover, we suggest the relative weights on the actual and auxiliary feedback laws to the RMPC, which in turn improves the closed-loop system performance. Furthermore, an off-line design of the proposed RMPC is also developed to make it more practical. Numerical studies demonstrate the effectiveness of the proposed algorithm.

One-Dimensional Constrained Coulomb Structure Control with Charge Saturations

A Coulomb structure is a cluster of free-flying satellites which maintains its shape through inter-vehicle electrostatic forces. These Coulomb forces are generated using on-board charge emission devices. This paper investigates the 1-D restricted motion of a 3-craft cluster. Two charge feedback strategies are discussed where the charge saturation limitation is considered. First a continuous formation shape feedback control strategy is presented. Next a saturated control strategy is developed to arrest any relative velocities of the Coulomb structure. If the structure can be brought to rest, then the continuous charge control can be engaged to achieve the desired virtual structure. The saturated feedback control is developed using Lyapunov's direct method and can control the separation rates between the satellites by changing the signs of the three saturated charge products. Implementable real-charge solutions are ensured through scaling the Lyapunov function rate. The control is shown to be Lyapunov stable. Because of the limitations of the control charge magnitudes, certain initial conditions will not lead to the desired zero relative motion rates. Conditions under which the relative motion of the Coulomb structure can be stabilized are analyzed through investigating the total energy of the system in the symmetric motion assumption. The general convergence areas are illustrated numerically in various state planes. Simulations demonstrate the performance of the control.

Objective function design for robust optimality of linear control under state-constraints and uncertainty

We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations. © 2009 EDP Sciences, SMAI.

An Improved Fuzzy Predictive Control Algorithm and Its Application to an Industrial CSTR Process

A finite horizon predictive control algorithm, which applies a saturated feedback control law as its localcontrol law, is presented for nonlinear systems with time-delay subject to input constraints. In the algorithm, N free control moves, a saturated local control law and the terminal weighting matrices are solved by a minimization problem based on linear matrix inequality (LMI) constraints online. Compared with the algorithm with a nonsaturated local law, the presented algorithm improves the performances of the closed-loop systems such as feasibilityand optimality. This model predictive control (MPC) algorithm is applied to an industrial continuous stirred tank reactor (CSTR) with explicit input constraint. The simulation results demonstrate that the presented algorithm is effective.

Strong stability of elastic control systems with dissipative saturating feedback

We will consider, with a focus on saturating feedback control laws, two problems associated with damping in a bounded acoustic cavity Ω⊂ R 3 . Our objective is to verify (compare (Discrete Continuous Dynamical Systems 7 (2001) 319, Math. Control Signals Systems 2 (1989) 265) that these are strongly stable: for every finite-energy solution, the acoustic energy goes to zero as t→∞. We will, in each case, formulate the problem in terms of a contraction semigroup of nonlinear operators on an appropriate Hilbert space and compare this with the corresponding semigroups without saturation—following Avalos and Lasiecka (Semigroup Forum 57 (1998) 278) in using the spectral methods of Arendt and Batty (Trans. Amer. Math. Soc. 8 (1988) 837) to show strong stabilization for those linear semigroups.

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.

Estimation of Stabilisation Domains for Program Motions of Affine Systems

The stabilization problems are considered for program motion of affine systems. To solve these problems we transform affine system into canonical form in a neighborhood of program trajectory. The stabilising control is designed by the method of feedback linearization. The closed loop system is linear one and we can fix the Lyapunov function. Then we consider saturated feedback control and corresponding closed loop system. To estimate the stabilisation domain of program trajectory under saturated control we use the fixed Lyapunov function for linear system.