Robust State Feedback Controller Research Articles

Robust local stabilization of discrete time-varying delayed state systems under saturating actuators

This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three convex sets allowing less conservative estimates. Through two numerical examples, we compare our approach with others in the literature and illustrate the better behavior of the proposed methods.

New iterative linear matrix inequality based procedure for H2 and H∞ state feedback control of continuous‐time polytopic systems

SummaryThis article provides new linear matrix inequality (LMI) sufficient conditions for a generalized robust state feedback control synthesis problem for linear continuous‐time polytopic systems. This generalized problem includes the robust stability, H2‐norm, and H∞‐norm problems as special cases. Using a novel general separation result, which separates the state feedback gain from the Lyapunov matrix but with the state feedback gain synthesized from the slack variable, then allows the formulation of LMI sufficient conditions for the generalized problem. Compared to existing parameterized LMI based conditions, where auxiliary scalar parameters are introduced in order to include the quadratic stability conditions (ie, assuming a constant Lyapunov matrix) as a special case, the proposed new conditions are true LMIs and contain as a particular case the optimal quadratic stability solution. Utilizing any initial solution derived by the quadratic or some existing methods as a starting solution, we propose an algorithm based on an iterative procedure, which is recursively feasible in each update, to compute a sequence of nonincreasing upper bounds for the H2‐norm and H∞‐norm. In addition, if no feasible initial solution can be found for some uncertain systems using any existing methods, another algorithm is presented that offers the possibility of obtaining a robust stabilizing gain. Numerical examples from the literature demonstrate that our algorithms can provide less conservative results than existing methods, and they can also find feasible solutions where all other methods fail.

Randomized probabilistic approach for parametric uncertainties in unmanned helicopters

SummaryParametric uncertainties and the problems associated with the design of robust state feedback control tends to be a major concern for achieving stable operation of nonlinear systems. To overcome these drawbacks, this article provides a perspective on a randomized algorithm based probabilistic control for nonlinear systems. The control approach aims at development of randomized algorithms for control of unmanned helicopters which are subjected to uncertainties. A controller gain is synthesized by developing a robust probabilistic approach using sequential randomized algorithm with the two degree of freedom helicopter system. Subsequently, the stability and reachability for the action of developed controller is validated with the help of Lyapunov asymptotic stability and reach tube analysis, and the corresponding results were analyzed. A comparative assessment of simulation and real‐time control results of projected approaches on helicopter model are presented for validation of the controller response.

Functional observer–controller method for unmeasured premise variables Takagi-Sugeno systems with external disturbance

A functional observer–controller design problem of Takagi-Sugeno fuzzy systems with unmeasured premise variables and external disturbance is investigated in this paper. First, robust state feedback controller is designed based on a relaxed fuzzy Lyapunov approach. With an estimation membership functions of transformation technique, a fuzzy functional observer is introduced to estimate the unmeasured premise variables and system control input. By using a robust separation principle, the observer and controller errors system is proved to be stable and robust to external disturbance. Finally, the estimation and control effects of the proposed method are verified through several engineering examples.

Non‐fragile control for a class of fractional‐order uncertain linear systems with time‐delay

This study addresses the non-fragile controller design of a class of fractional-order (FO) linear delayed systems assumed to have structured uncertainties in both the plant and the controller. By using the linear matrix inequality method, singular value decomposition and FO Razumikhin theorem, the delay-dependent and order-dependent robust non-fragile state feedback controller and non-fragile observer-based robust state feedback controller are synthesised, respectively, based on whether the states are available or not. Three examples are presented to verify the effectiveness of the proposed schemes.

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.

Non-fragile memory feedback control for uncertain time-varying delay switched fuzzy systems with unknown nonlinear disturbance

Currently, the feedback control rate of most nonlinear systems is realised by the memoryless state feedback controller which cannot affect the impact of time delay on the systems, and the general processing method of the Lyapunov–Krasovskii functional for the time-varying delay switched fuzzy systems (SFS) is more conservative. Therefore, this paper addresses the problem of non-fragile robust and memory state feedback control for switched fuzzy systems with unknown nonlinear disturbance. Non-fragile memory state feedback robust controller which has two controller gains different from each other, and switching law are designed to keep the proposed systems asymptotically stable for all admissible parameter uncertainties. Delay-dependent less conservative sufficient conditions are obtained through using the Lyapunov–Krasovskii functional method and free-weighting matrices depending on Leibniz–Newton, guaranteeing that the SFS can be asymptotically stable. A numerical example is given to illustrate the proposed controller performs better than the classic memoryless state feedback controller.

Systematic Design of Robust Event-Triggered State and Output Feedback Controllers for Uncertain Nonholonomic Systems

This article studies the event-triggered control problem for nonholonomic systems in the chained form with disturbances and drift uncertain nonlinearities. Both the cases of state-feedback and output-feedback are investigated. To address the effects of nonholonomic constraints in event-triggered control, a new systematic design integrating a state-scaling technique and set-valued maps are proposed. A crucial strategy is to transform the event-triggered control system into an interconnection of multiple input-to-state stable systems, to which the cyclic-small-gain theorem is applied for event-based controller synthesis. It is shown that the cyclic-small-gain-based design scheme leads to Zeno-free event-triggered controllers. For the output-feedback case, a new nonlinear observer is designed to deal with the sampling errors. Interestingly, the obtained results are new even if the plant model is disturbance-free. Both numerical and experimental results validate the efficiency of the proposed cyclic-small-gain-based event-triggered control methodology.

Design of a Robust H2 State Feedback Temperature Controller for a Steel Slab Reheating Furnace

This article addresses the design of a robust H2 state feedback controller (H2-SFC) for the effective temperature control in the heating zone of the steel slab reheating furnace. Based on the available field data and system identification procedures, a mathematical model of the heating zone is derived, which presents autoregressive-moving average with exogenous input (ARMAX) structure and fourth order. The design of an H2-SFC controller for the effective control of the heating zone temperature of the slab reheating furnace under study is developed. The simulation results of the designed control system showed its high effectiveness compared to the conventional PID control.

Robust stability and stabilization of networked control systems with stochastic time-varying network-induced delays

This paper investigates the robust stability analysis and state feedback controller design of networked control systems (NCSs). A stochastic network-induced delay in given interval with known lower and upper bounds is considered. Therefore, the NCS is modeled as linear system with probabilistic time-varying delay distribution. Then, the Lyapunov-Krasovskii functional (LKF) is formulated using probabilistic informations of both lower and upper bounds of the time-varying network-induced delay, and Wirtinger-based integral inequalities are used to estimate the accuracy of the resulting time derivatives and also to reduce conservatism by introducing some new cross terms. Afterwards, stability condition based on [Formula: see text] disturbance attenuation level is expressed in terms of a set of linear matrix inequalities (LMIs), and Finsler’s lemma is used to relax it by adding slack decision variables and decoupling the systems matrices from those of Lyapunov-Krasovskii. This procedure makes the state feedback controller design as simple as a variables change. Finally, a maximum allowable upper bound of the network-induced delay and state feedback controller gains are calculated by resolving the above relaxed LMIs’ convex optimization problem. Practical numerical examples are provided to validate the proposed approach; the results show that the negative effects of the unpredictable network-induced delays are compensated and the stability of NCSs with high disturbance attenuation level is guaranteed. A comparative study with other results in recent researches is also given and the superiority of the proposed method in terms of robustness and conservatism reduction is shown.

Finite-time optimized robust control with adaptive state estimation algorithm for autonomous heavy vehicle

Structured and unstructured uncertainties coupled with external disturbances usually pose considerable challenges in realizing heavy vehicle automatic lane guidance control. This paper presents a novel solution paradigm for the lateral control of autonomous heavy vehicle. The proposed control framework consists of an adaptive state estimator and a finite-time optimized ℋ∞ state feedback regulator. Firstly, based on the dual extended Kalman filter (DEKF) technique, which can estimate model time-varying parameters and unknown states at the same time, the adaptive state estimation algorithm is proposed and investigated to improve state estimation adaptivity against uncertain time-varying general front/rear axle cornering stiffnesses. Then, using zero-sum dynamic game theory as the general framework, we analyze the minimax controller design problem and introduce the finite-time optimized robust regulator design method. The autonomous heavy vehicle automatic lane guidance controller is designed in the framework of robust optimal state feedback control to make it robust against external disturbance. Finally, results of various driving scenarios from both simulation and hardware-in-loop (HIL) implementation show that the proposed finite-time optimized robust and adaptive state estimation control paradigm can robustly obtain satisfactory automated lateral control performance for heavy vehicle when the control system is characterized by both time-varying model parameters and uncertain external energy-bounded disturbance. A comparative study is also conducted to investigate cases to show its effectiveness when the adaptive state estimation is used and when it is not.

Fuzzy Observer-controller Design in Finite Frequency Domain: Application to Wind Turbine

This work presents the generalized Kalman Yakubovich-Popuv (gKYP) combined with the Takagi Sugeno (T-S) fuzzy model to design a fuzzy robust state feedback controller and a fuzzy robust observer-based in finite frequency (FF) domain. T-S fuzzy model is well known for its efficiency to control complex nonlinear systems. However, for wind generator system, the unknown parts are large and produce disturbances parameters. In order to attenuate, the level of the disturbances parameters observer based is utilized to estimate the unknown parts of the wind system. The control design method is based on Lyapunov function, the generalized gKYP with projection lemma, a PDC (Parallel Distributed Compensation) structure and the finite frequency (FF) technique. The proposed approach is formulated linear matrix inequalities (LMIs) to prove the asymptotic stability in (FF) domain. Finally, an example of wind turbine is show the validity of the proposed new approach.

Design Procedure Combining Linear Matrix Inequalities and Genetic Algorithm for Robust Control of Grid-Connected Converters

This article proposes a design procedure for $\mathcal {H}_{\infty }$ current controllers suitable for application in grid-connected converters (GCCs) subject to disturbances and uncertain parameters. Linear matrix inequalities provide robust state feedback controllers from a set of design parameters automatically tuned with the help of a genetic algorithm, oriented by a suitable objective function. Such strategy allows to overcome the problem of $\mathcal {H}_{\infty }$ high control gains, ensuring a good tradeoff between performance and robustness against uncertain grid parameters. The proposal contributes to improve the effective use of metaheuristics for automated control tuning in GCCs, avoiding time-consuming human–machine interaction in the design stage. A case study with experimental results is presented, demonstrating the viability and the superior performance of the proposed controllers with respect to similar techniques, and also the compliance with the IEEE 1547 Std for grid currents.

Consensus in networked multi-robot systems via local state feedback robust control

In the article, the consensus problem is considered for networked multi-robot systems, in which the dynamical equation of all robots is non-holonomic and nonlinear systems. In the multi-robot systems, each robot updates its current states and receives the states from the neighboring robots. Under the assumption that if the network graph is bidirectional, a local information-based state feedback robust controller is designed to make sure the convergence of the individual robots’ states to a common value. Finally, the effectiveness of the presented method is illustrated by the simulation results of a group of four mobile robots.

State-Estimator-Integrated Robust Adaptive Tracking Control for Flexible Air-Breathing Hypersonic Vehicle With Noisy Measurements

In this paper, a novel state-estimator-integrated robust adaptive tracking control law is proposed for flexible air-breathing hypersonic vehicle (FAHV), with consideration of noisy measurements, parametric uncertainties, and unknown flexible dynamics. First, to reconstruct the states contaminated by the measurement noises, a continuous-model-based state estimator is designed, which can avoid severe phase lag problem brought by low-pass filter and greatly improve the estimation accuracy in the transition process. Then, based on noise-free measurements, an ideal state feedback robust adaptive tracking controller is formulated to deal with the parametric uncertainties as well as unknown flexible dynamics, where interval type-2 fuzzy logic systems are employed to approximate the unknown dynamics of FAHV online. Lyapunov theorem is utilized to analyze the stability properties of the state estimator and the ideal state feedback tracking controller. By synthesizing the above two parts, the whole state-estimator-integrated robust adaptive tracking control law is finally developed. Comparative numerical simulations of four scenarios demonstrate the effectiveness and superiority of the proposed integrated control law.

Robust Stabilization in LMI Regions for Constrained Input Systems

Stabilization of constrained uncertain linear systems in LMI regions is studied. Robustness is in demand and exact pole assignment is no longer suitable for uncertain systems. Therefore, LMI region pole assignment encompasses the exact one preserving time domain performances in the presence of uncertainties. Robust constrained state feedback controllers are designed such that asymptotic stability and desired performances are achieved. Constraints are assumed symmetric and the LMI regions are closed under complex conjugacy. Hence, LMI’s are deduced such that robust pole assignment is obtained and constraints on the input are respected. Namely, two design strategies are treated: the unsaturating and the saturating case. Optimization problem for enlarging the initial conditions set is also achieved. Simulation examples are given to show the application and the ease of the proposed approach. Comparison with different approaches for both given examples is also presented.

LFT-Structured Uncertainty State-Space Modeling for State Feedback Robust Control of the Ultra-Precision Wafer Stage

This paper presents linear-fractional-trans-formation (LFT)-structured uncertainty state-space modeling for robust control of the multiple-input multiple-output (MIMO) ultra-precision wafer stage with flexible structures to meet the challenges of vibration-dependent model uncertainties. Specifically, based on the modal MIMO state-space model, a parametric uncertainty model related with flexible modes is presented, and the uncertainty parameters are structured to a diagonal matrix with the LFT method. Meanwhile, a multiplicative uncertainty model is employed to express the uncertainty in high frequency with respect to ignored high-order modes. Thus, the final uncertainty model is structured with uncertainty parameters and high-frequency uncertainty. Based on the proposed uncertainty model, a comprehensive robust control scheme is proposed. Specifically, the weighting function matrixes are designed by the loop-shaping approach, and a $\mu$ analysis is employed to achieve a nonconservative solution with respect to the structured uncertainty. A standard stability criterion of a $\bf{M} \boldsymbol{\Delta}$ structure system is then utilized to determine the system stability by the largest structure singular value. Comparative experiments on a developed ultra-precision wafer stage are finally conducted, and the results validate that the proposed method achieves significant improvements on control performance, robustness, and robust stability in all exposure fields.

An LMI-based design of a robust state-feedback control for the master-slave tracking of an impact mechanical oscillator with double-side rigid constraints and subject to bounded-parametric uncertainty

In this paper, a Linear Matrix Inequality- (an LMI-) based approach for designing a robust state-feedback controller for a 1-DoF, periodically forced, impact mechanical oscillator subject to double-side rigid barriers/constraints and under bounded parametric uncertainties to track another impact oscillator, as a master or reference system, is proposed. The dynamics of such impact oscillator is defined by a hybrid non-autonomous system with impulsive effects, for which the impulsive event occurs when the system state encounters the two barriers and the oscillation motion is limited between them. The main idea in the synthesis of the stability conditions lies in the use of the S-procedure Lemma and the Finsler Lemma in order to only consider the regions inside which the master-slave tracking error evolves. We show that the stability conditions of the tracking error are reformulated by a set of Bilinear Matrix Inequalities (BMIs). Via the Schur complement Lemma and the Matrix Inversion Lemma, a linearization procedure is realized to transform these BMIs into LMIs where the admissible maximum bounds of the parametric uncertainties are maximized. The effectiveness of the proposed feedback controller towards uncertainties is illustrated through simulation results.

Design of nonlinear active noise control earmuffs for excessively high noise level.

When exposed to high levels of noise, earmuffs are often used to avoid hearing loss. However, active noise control earmuffs may exhibit nonlinearities under excessive levels of noise, due to their low-power characteristics of the loudspeakers, and thus nonlinear control algorithms are required to improve the control performance. In this paper, an analytical model of a nonlinear active noise control earmuff is investigated. Based on this model, a robust state feedback control law is designed in the framework of linear matrix inequalities with respect to the parametric uncertainties of the loudspeaker and the limitation of control input. Then the backstepping approach is adopted to force the nonlinear part of the loudspeaker to track the derived state feedback signal and estimate the unknown parameters. Both recorded vehicle noise and multi-frequency noise are used to test the effectiveness of the proposed controller and the control performance is compared with that of a widely accepted nonlinear generalized functional link artificial neural network algorithm. Simulation results demonstrate that the proposed controller is capable of attenuating the interior noise and reducing harmonic and intermodulation distortions significantly.

ISS Robust Stabilization of State-Delayed Discrete-Time Systems With Bounded Delay Variation and Saturating Actuators

We address the problem of robust input-to-state stabilization of parameter-varying discrete-time systems with time-varying state delay, saturating actuators, and subject to $\ell _2$ -limited disturbance. It is assumed that the delay belongs to a known interval and its maximum variation between two consecutive instants is taken into account. The proposed convex delay-dependent conditions for the synthesis of robust state feedback controllers ensure local input-to-state stability of the closed-loop system for a set of initial conditions and for energy-bounded disturbance signals. However, the computed controllers do not require the real-time knowledge of the delay. The approach is based on the rewriting of the saturating and delayed system in terms of a switching uncertain augmented delay-free system with a dead-zone nonlinearity and on the application of the generalized sector condition. To illustrate the efficiency of our approach, we compare it by means of numerical examples with others found in the literature.