Saturated State Feedback Research Articles

Robust bilinear tracking control of a parabolic trough solar collector via saturation

This paper investigates the problem of robust tracking control of heat transport in a Parabolic Trough Solar Collector (PTSC), where the output has to track a desired reference trajectory. In this work, the PTSC is modeled by state-space bilinear dynamics. The manipulated variable is the pump volumetric flow rate, and the source term, i.e., solar irradiance, is assumed to be unmeasured. In addition, the actuator’s physical constraints induce saturation bounds on the manipulated variable and need to be considered explicitly in the controller design. To deal with these challenges, we first propose a saturated state-feedback law that meets the control objectives. Then, we reconstruct the unknown time-varying source term using an adaptive estimator. Later, through Lyapunov stability analysis, we prove that the closed-loop system and the output tracking error are uniformly ultimately stable. Numerical simulations attest to the performance of the proposed control strategy.

Robust Regulation of a Power Flow Controller via Nonlinear Integral Action

This article considers a robust output set-point tracking problem for an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$</tex-math> </inline-formula> -terminal power flow controller (PFC) for meshed dc micro-grids. The PFC is a power electronics device used to control the power flow at a node in the meshed grid and may act as a dc circuit breaker. The system is modeled by state-space bilinear dynamics coupled with a polynomial output. In the proposed design, the plant is first extended with an integral action processing the regulation error. The cascaded model composed of the plant and the integrator is then stabilized using a saturated state-feedback law, designed with a forwarding approach. An anti-windup function is added to cope with transient saturations. A tuning method is proposed to set the controller gains along the available degrees of freedom with respect to a cost function. The stability of the closed loop is guaranteed for any compact set of initial conditions and for small parametric variations around the nominal set point. Experiments have been carried out and these properties are successfully assessed on a tenth-scale experimental setup.

Finite‐time tracking control of disturbed non‐holonomic systems with input saturation and state constraints: Theory and experiment

AbstractThis article investigates the finite‐time tracking control problem for disturbed non‐holonomic systems with input saturation and state constraints. Input saturation is ensured by utilizing saturated state feedback and designing auxiliary variables. A rigorous design procedure, which combines barrier Lyapunov function‐based backstepping and neural networks, is introduced to satisfy state constraints and overcome the influence of lumped disturbances. A finite‐time filter is developed to address the explosion of complexity problem. Together with relay switching, the designed saturated controller guarantees that the tracking errors converge to arbitrarily small neighbourhoods around zero within a finite time. Stability analysis indicates that all closed‐loop system signals maintain bounded, and the desired input and state constraints are not violated throughout the control process. To demonstrate the effectiveness of the proposed approach, simulation and experimental results on a wheeled mobile robot are presented.

Design of Saturating State Feedback With Sign-Indefinite Quadratic Forms

In this article, we propose a novel class of piecewise smooth Lyapunov functions leading to linear-matrix-inequality-based stability/performance analysis and control design for linear systems with saturating inputs. We provide conditions for global properties, and also conditions for local properties and guaranteed estimates of the basin of attraction. The backbone of our result consists in using quadratic forms with constant matrices that are not necessarily sign definite, thereby providing additional degrees of freedom. Using generalized sector conditions involving the dead-zone nonlinearity and its derivative, we formulate convex optimization conditions to verify their positivity in the region of interest. Several numerical examples with connections to existing results illustrate the potential behind our novel construction.

Güvenli Ulaşım Bakış Açısıyla Bir Kayıcı Teknenin Yalpa Hareketi İçin Kontrolcü Dizayni

The issue of safe navigation in the maritime sector is becoming more important day by day. This situation is valid not only in terms of passenger and cargo transportation, but also in different maritime operations. Based on this point, much equipment is used in order to perform safe navigation in ships for different sea states such as wind, wave, etc. This equipment is classified as active and passive systems and can be applied to different types of ships. Active stabilizer systems are frequently used, especially for ship types where speed and maneuverability are high, as instantaneous responses are important. Although there are many active systems used, active roll stabilizer fin systems are the most common. At this point, this paper describes an application of LMI (Linear Matrix Inequality) based robust and saturated H2 state feedback control to roll motion of the planing hull via the fin stabilizer. In the mathematical model, nonlinearities are expressed through damping and restoring terms. Based on the planing hull roll motion mathematical model, we also present a state space model suitable for simulation and control applications. Nondimensional lift coefficients of the fin stabilizer for different angles of attack are calculated with Star CCM+ package software. Both controlled and uncontrolled conditions are examined for the maximum lift coefficient. As a result, the efficiency of the proposed approach for safe transportation was demonstrated with the simulation results and an effective study was carried out by reducing the amplitudes of the roll motion to reasonable levels.

LMI-based synthesis of a robust saturated controller for an underactuated mechanical system subject to motion constraints

In this paper, we suggest a control synthesis approach for the robust stabilization of an underactuated mechanical system, the Inertial Wheel Inverted Pendulum (IWIP), with norm-bounded parametric uncertainties and subject to both motion constraints and actuator saturation. A state-feedback controller is adopted to achieve such robust stabilization of the IWIP at its upright position, while the problem of the motion constraints is addressed by considering the saturation effect of the control input. Our design methodology of the robust saturated state-feedback control law is realized within the framework of Linear Matrix Inequalities (LMIs). We show first that the synthesis problem of such controller is written in terms of Bilinear Matrix Inequalities (BMIs), which are hardly tractable numerically. Then, in order to overcome this obstacle, we use some judicious mathematical tools to convert these BMIs into LMIs. Moreover, we consider the problem of enlarging the domain of attraction by computing the largest attractive invariant ellipsoid for the uncertain constrained nonlinear dynamics of the underactuated IWIP under the saturated state-feedback control law. Simulation results demonstrate the effectiveness and the robustness of the proposed robust saturated state-feedback controller towards norm-bounded parametric uncertainties while constraints on the system motion and the control input are respected.

Robust Stabilization for Uncertain Saturated Time-Delay Systems: A Distributed-Delay-Dependent Polytopic Approach

This technical note investigates the robust stabilization problem for uncertain linear systems with discrete and distributed delays under saturated state feedback. Different from the existing approaches, a distributed-delay-dependent polytopic approach is proposed in this technical note, and the saturation nonlinearity is represented as the convex combination of state feedback and auxiliary distributed-delay feedback. Then, by incorporating an appropriate augmented Lyapunov-Krasovskii (L-K) functional and some integral inequalities, the less conservative stabilization and robust stabilization conditions are proposed in terms of linear matrix inequalities (LMIs). The effectiveness and reduced conservatism of the proposed conditions are illustrated by numerical examples.

State reference design and saturated control of doubly-fed induction generators under voltage dips

ABSTRACTIn this paper, the stator/rotor currents control problem of doubly-fed induction generator under faulty line voltage is carried out. Common grid faults cause a steep decline in the line voltage profile, commonly denoted as voltage dip. This point is critical for such kind of machines, having their stator windings directly connected to the grid. In this respect, solid methodological nonlinear control theory arguments are exploited and applied to design a novel controller, whose main goal is to improve the system behaviour during voltage dips, endowing it with low voltage ride through capability, a fundamental feature required by modern Grid Codes. The proposed solution exploits both feedforward and feedback actions. The feedforward part relies on suitable reference trajectories for the system internal dynamics, which are designed to prevent large oscillations in the rotor currents and command voltages, excited by line perturbations. The feedback part uses state measurements and is designed according to Linear Matrix Inequalities (LMI) based saturated control techniques to further reduce oscillations, while explicitly accounting for the system constraints. Numerical simulations verify the benefits of the internal dynamics trajectory planning, and the saturated state feedback action, in crucially improving the Doubly-Fed Induction Machine response under severe grid faults.

Finite‐time output feedback attitude stabilisation for rigid spacecraft with input constraints

This study deals with finite-time output feedback attitude stabilisation problem for rigid spacecraft systems subject to input constraints. First, a continuous saturated state feedback controller is proposed based on the homogeneous method, after which can guarantee the closed-loop system is global finite-time stable. Then, a switched saturated output feedback controller is developed under a state observer, after which can guarantee the closed-loop system is semi-global finite-time stable. Simulation results are given to demonstrate the effectiveness of the proposed method.

Saturated finite-time stabilization of uncertain nonholonomic systems in feedforward-like form and its application

This paper investigates the problem of finite-time stabilization by state feedback for a class of uncertain nonholonomic systems with inputs saturation. Comparing with the existing relevant literature, a distinguishing feature of the systems under investigation is that the x-subsystem is in feedforward-like form. Rigorous design procedure for saturated finite-time state feedback control is presented by using the adding a power integrator and the nested saturation methods. The development of saturated finite-time controller is also presented briefly for a class of dynamic nonholonomic systems in feedforward-like form. An application example for a kinematic hopping robot is provided to illustrate the effectiveness of the proposed approach.

Global Finite-Time Partial Stabilization for a Class of Nonholonomic Mobile Robots Subject to Input Saturation

In this paper, the global finite-time partial stabilization problem is discussed for a class of nonholonomic mobile wheeled robots with continuous pure state feedback and subject to input saturation. Firstly, for the mobile robot kinematic model, a “3 inputs, 2 chains, 1 generator” nonholonomic chained form systems can be obtained by using a state and input transformation. The continuous, saturated pure state feedback control law is proposed such that the special chained form systems can be stabilized to zero (except an angle variable) in a finite time, i.e., finite-time partial stabilization. Secondly, the rigorous stability analysis of the corresponding closed-loop system is presented by applying Lyapunov theorem combined with the finite-time control theory, and the angle variable can be proved to converge to a constant, moreover, its convergent limit may be accurately estimated in advance. Finally, the simulation results show the correctness and the validity of the proposed controller not only for the chained system but also for the original mobile robots system.

Event‐triggered Control of Linear Systems with Saturated Inputs

AbstractThis paper investigates the event‐triggered control of linear systems with saturated state feedback and saturated observer‐based feedback, respectively. The problem of simultaneously deriving stabilizing event‐triggered controllers and tackling saturation nonlinearity is cast into a standard linear matrix inequalities problem. Key topics are studied, such as event‐triggered observer design and event‐triggered saturated observer‐based feedback synthesis. Important issues are touched on, including the existence of the positive lower bound for inter‐event times, and self‐triggered algorithms.

Delay-Dependent Stabilizability of 2D Delayed Continuous Systems with Saturating Control

This paper deals with the problem of stability and stabilization of 2D delayed continuous systems with saturation on the control. An improved delay-dependent stability condition taken from the recent literature is first extended to the case of 2D systems. Second, a delay-dependent stabilizability condition is deduced. The synthesis of stabilizing saturating state feedback controllers for such systems is then given. A set of allowed delays for both directions of the state is computed. All involved conditions are given under LMI formalism. Examples are worked to show the effectiveness of the approach.

Global finite-time stabilisation using bounded feedback for a class of non-linear systems

In this study, the authors consider the problem of global finite-time stabilisation for a class of non-linear systems by bounded feedback control. First, we use the generalised adding a power integrator and the nested saturation methods to design a saturated homogeneous state feedback controller. Under this bounded controller, a class of non-linear systems comprised of a chain of power integrators perturbed by uncertain bounded non-linearities can be globally stabilised in a finite time. Second, as an application of previous developed results, a bounded finite-time output feedback controller is designed for a class of special non-linear systems, which is comprised by a chain of integrators plus known bounded non-linearities. To estimate the unknown states in a finite time, a finite-time convergent observer is constructed. By substituting the estimated states into the state feedback stabiliser, it can be guaranteed that the closed-loop system is globally finite-time stable.

Controller design for a class of nonlinear systems with input saturation using convex optimization

In this paper, we propose a new design strategy for nonlinear systems with input saturation. The resulting nonlinear controllers are locally asymptotically stabilizing the origin. The proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state-dependent input saturation. Linear saturating state feedback controllers and soft variable-structure controllers are developed based on this system formulation. The resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist. Polynomial approximation based on Legendre polynomials is used to extend the methodology to a more general class of nonlinear systems. To demonstrate the benefit of this design method, a stabilizing controller for a single link manipulator with flexible joint is developed.

Stability and Robust Regulation of Battery-Driven Boost Converter With Simple Feedback

This paper investigates the problem of regulating the output voltage of a battery-driven boost converter, where the load is uncertain or changes within a certain range. The battery is modeled with a second order circuit with two capacitors. A state-space approach is developed for estimating the parameters of the battery. By using the state-space averaging method, the open-loop system for regulating the output voltage is described as a sixth order differential equation with a bilinear term and input constraints. A simple saturated state feedback is designed by solving some optimization problem with linear matrix inequality constraints. The optimized controller is very close to an integrator feedback. Using the newly developed Lyapunov method, we analyze the stability and regulation of the closed-loop bilinear system including the battery dynamics. Computation shows that both the optimized state feedback and the integrator feedback can achieve practically global regulation in the presence of uncertain load and uncertain battery voltage. The results are validated by experimental systems. The effect of discontinuous conduction mode on transient response is discussed via simulation and experiment.

Global Finite-Time Stabilization of a Class of Nonlinear Systems via Bounded Output Feedback Controllers

AbstractIn this paper, we consider the problem of global finite-time stabilization for a class of nonlinear systems by bounded output feedback. First, we use the generalized adding a power integrator and the nested saturation methods to design a saturated homogeneous state feedback controller which globally finite-time stabilizes the nonlinear systems. Then, a finite-time convergent observer is constructed to estimate the unknown states in a finite time. Finally, by substituting the estimated states into the state feedback stabilizer, it can be guaranteed that the closed-loop system is globally finite-time stable, which leads to a design process satisfying the separation principle.

Decentralised state feedback design for large-scale linear systems subject to input saturation

This study considers the design of decentralised controllers for large-scale linear systems under actuator saturation. Saturation in the magnitude of the control input is first considered. For the closed-loop system under a saturating decentralised state feedback law, conditions are identified under which an ellipsoid is contractively invariant and thus within the domain of attraction, or the restricted ℒ2 gain from the disturbance to the output is less than or equal to a pre-specified value γ. Based on these conditions, the designs of decentralised state feedback laws that achieve large domains of attraction or low ℒ2 gains can be formulated as optimisation problems with bilinear matrix inequality (BMI) constraints. Numerical algorithms are developed to solve these BMI problems. These developments are also extended to the situation where the inputs are subject to nested saturation, such as simultaneous actuator magnitude and rate saturation. Throughout the study, numerical examples are used to demonstrate the effectiveness of the proposed design method.

Asymptotic Stability Problem for Discrete-time Delay Systems with Saturated State Feedback

摘要: 讨论具有饱和状态反馈的离散时滞线性系统的渐近稳定性问题. 给出了在一定假设下, 判断系统全局渐近稳定和局部渐近稳定的充分条件, 并通过数值算例验证了所给出的条件是有效的. 关键词: 离散时滞线性系统 / 饱和状态反馈 / 全局(局部)渐近稳定 / 不变吸引椭球体 / 饱和函数

구동기포화를 갖는 불확실한 시스템의 H2제어

This paper presents an LMI-based method to design a saturated state-feedback <TEX>$H_2$</TEX> controller for uncertain systems with actuator saturation. Specifically, the paper proposes a sufficient condition such that the system under norm-bounded uncertainties and actuator saturation is asymptotically stable and the <TEX>$H_2$</TEX>-norm of the system has an upper-bound. The resulting condition is further utilized to solve a convex optimization problem specified in the context of <TEX>$H_2$</TEX>-norm minimization, whose solution yields a saturated <TEX>$H_2$</TEX> controller. A numerical example is presented to show the effectiveness of the proposed method.