Linear State Feedback Control Research Articles

Flight envelope estimation for helicopters under icing conditions via the zonotopic reachability analysis

This paper presents a new approach to estimating a flight envelope for a helicopter flying under clean and icing conditions based on a zonotopic reachability analysis. The helicopter is stabilized with a state-feedback linear controller to maintain its attitude around a trim point. Given the sets of possible initial conditions and disturbance inputs, and control effectiveness indices, this analysis results in reachable sets of state variables of the helicopter for a finite time interval. The reachability analysis is thus useful for predicting whether or not the helicopter evolves into an unsafe flight condition when it undergoes degraded control effectiveness ensued from the icing condition. The merit of this approach is shown through a case study about the Raptor-90 unmanned helicopter stabilized with either the linear quadratic regulator (LQR) or the H∞ controller in a hover-flight mode. This helicopter is considered to be affected by both symmetric and asymmetric icing conditions. The case study shows that the H∞ controller outperforms the LQR controller as the former is able to cope with greater loss of control effectiveness caused by the icing conditions. Moreover, as compared to the longitudinal control input, the lateral and directional control inputs are more susceptible to adverse effects of the icing conditions. These results verify not only the effects of ice contamination upon the helicopter dynamics and control, but also the capability of the proposed approach for flight envelope estimation.

Memoryless linear feedback control for a class of upper-triangular systems with large delays in the state and input

This paper studies the problem of global asymptotic stabilization for a class of upper-triangular systems with large delays in the state and input. Using the idea of feedback domination, we develop a Lyapunov-Krasovskii method for the design of time-invariant, memoryless linear state and output feedback controllers, achieving global asymptotic stabilization of the closed-loop systems under a linear growth condition. The resulting controllers are different from predictor-based or delay-dependent controllers in the sense that they are delay-free and easier to be implemented due to the nature of “memoryless” feedback. Two examples are presented to demonstrate the effectiveness of the proposed delay-free state and output feedback control strategies.

Stabilization of a new commensurate/incommensurate fractional order chaotic system

AbstractIn the current article, agreeing on the stability theory of fractional order systems, the conditions for the asymptotic stability of nonlinear fractional order systems are presented. We discuss the stabilization of new fractional order chaotic system where the state equations contain the same or different fractional orders. Then we design a control strategy for stabilization of new fractional order chaotic system. Our aim is to stabilize the unstable equilibrium points of fractional order chaotic systems by planning a fit linear state feedback controller. In the following, a comparison between linear state feedback controller and sliding mode control for commensurate and incommensurate new fractional order chaotic systems is conducted. Numerical simulations approve the validity of the presented results.

Robust Control for Stable and Safe Performance of a Two Wheeled Human Transporter

A personal, electric human transportation vehicle is a promising invention for pollution and congestion free future. A two wheeled human transporter (TWHT) characterizes an inherently unstable system due to which its control for safe operation is a challenge. This paper proposes a higher order sliding mode control (HOSMC) for stable and safe performance of the TWHT system. A reduced order model is considered for control development. Unmeasurable states are estimated using higher order sliding mode differentiator. The proposals are validated in simulation and also compared with linear state feedback controller (SFC) to show its efficacy. The robust property of HOSMC is tested by considering variations in rider’s weight.

Robust H∞ Control for PWM Boost Converters Subject to Aging Capacitor Conditions

Electrolytic capacitors are extensively used in DC-DC power converters and consist of a major source of concern about system reliability. Although these components are heavily affected by aging, conventional modelling and control design for converters often disregard the uncertainty on capacitor parameters. In this paper, the robust control problem for boost converters is addressed with the derivation of a more comprehensive model. Although the modelling complexity is higher, the simplicity of linear state feedback control is preserved and the synthesis algorithm is performed by a LMI-based optimization problem. Moreover, the proposed control scheme requires state estimation, which is performed online as part of an identification system. Simulation results are presented and indicate the validity of the proposed concept.

Modelling, design and control of non-isolated single-input multi-output Zeta-Buck-Boost converter

In this article, we focus on the analytical modeling of nonisolated single-input multiple-output (SIMO) dc–dc converters governed by linear differential algebraic equations (DAEs). The modeling challenge in nonisolated SIMO converters arises due to the switching among multiple DAEs governing the circuit. Averaged models of such converters, described by an ordinary differential equation, are derived using the notion of quasi-Weierstrass transformation. Using this technique, we derive the averaged model for a nonisolated Zeta–Buck–Boost (ZBB) converter. It is observed that the dynamics of the state variable corresponding to the algebraic constraint is uncontrollable and eliminating this state leads to a fourth-order completely controllable averaged model. This model is used to design a linear state-feedback controller for line regulation. In the case of bipolar SIMO converters, ZBB being an example, regulation of the two outputs can be achieved using any one of the two output integral states. Although the state-feedback controller successfully rejects the disturbance asymptotically, it is found that the deviations from the set point in the transient phase can be large. To see if smaller deviations can be achieved by appending the linear controller with a nonlinear term, we explore a nonlinear controller based on the Lyapunov redesign technique. Smaller deviations with complete disturbance rejection are possible if the disturbance is matched. When it is unmatched, small deviations are achieved at the expense of steady-state errors, whose estimate is explicitly found. The proposed model and control scheme are verified through a laboratory built hardware prototype.

State Estimation and Stabilization of Discrete-Time Systems with Uncertain Nonlinearities and Disturbances

Nonautonomous discrete-time control systems with uncertain nonlinearities and bounded external disturbances are considered. Based on the method of matrix comparison systems and the technique of difference linear matrix inequalities, an approach to solve the problems of state estimation, finite time boundedness with respect to given sets, the suppression of initial deviations and uncertain disturbances using a linear state feedback controller is developed. A method to design a controller with variable coefficients that guarantees the transition from one given ellipsoid to another under any disturbances bounded by the L∞ norm is proposed.

Extended-Order High-Gain Observer-Based Feedback Control Law for Tracking the Longitudinal Dynamics of a Mini UAV

The paper presents extended-order high-gain observer (EHGO)-based robust control design for longitudinal dynamics of a mini UAV. The multi-input, multi-output nonlinear dynamic model of the UAV is transformed by dynamic extension to achieve well-defined relative degree. State feedback linearization control is then designed for the transformed model. The system states and uncertainties are estimated by EHGO. Simulations of the closed-loop system with the proposed control methodology exhibit robustness to perturbations. Performance comparison of feedback linearizing control with state feedback, high-gain observer-based control and EHGO-based control in the presence of perturbations is also presented.

Vibration control of micro-scale structures using their reduced second order bilinear models based on multi-moment matching criteria

This paper deals with vibration control of micro-scale structures; i.e. MEMS devices. For modeling of the structures, finite element method which is a distinguished and accurate technique will be used. This method, however, leads to a model with high number of degrees of freedom which may cause computational costs especially for control problems. Hence, we will apply the second order Krylov subspace method based on multi-moment matching to obtain a reduced order model which is in the form of a second order bilinear system. For vibration suppression of the corresponding micro-structure, a quadratic feedback controller and also a linear state feedback controller using linear matrix inequality (LMI) will be designed. Finally, a micro-cantilever beam will be considered as a practical case study and simulation results of applying the proposed method will be presented.

Nonlinear/Linear Switched Control of Inverted Pendulum System: Stability Analysis and Real-Time Implementation

This paper treats the problems of stability analysis and control synthesis of the switched inverted pendulum system with nonlinear/linear controllers. The proposed control strategy consists of switching between backstepping and linear state feedback controllers on swing-up and stabilization zones, respectively. First, the backstepping controller is implemented to guarantee the rapid convergence of the pendulum to the desired rod angle from the vertical position. Next, the state feedback is employed to stabilize and maintain the system on the upright position inherently unstable. Based on the quadratic Lyapunov approach, the switching between the two zones is analyzed in order to determine a sufficient domain in which the stability of the desired equilibrium point is justified. A real-time experimentation shows a reduction of 84% of the samples below the classical scheme when using only the backstepping control in the entire operating region. Furthermore, the reduction percentage has become 92% in comparison with the composite linear/linear controller.

Multi Objective Modulated Model Predictive Control of Stand-Alone Voltage Source Converters

This paper introduces a novel model predictive control (MPC) strategy for stand-alone voltage source converters (VSCs) with constant switching frequency. Multiple control targets are incorporated in a single cost function. This allows fulfilling all the requirements for an uninterruptible power supply (UPS) inverter in terms of fast dynamic response, elimination of steady-state error, and harmonic compensation capability. The control output vector is determined as an analytical solution that corresponds to the minimum value of the cost function. The space vector modulation (SVM) is then used to synthesize the corresponding switching sequence. Therefore, this control strategy is equivalent to the linear state feedback control, which allows the usage of linear theory for tuning the parameters. The superior characteristics of this control strategy compared to cascaded linear control and finite control set MPC are, finally, demonstrated experimentally.

An LVRT Scheme for Grid Connected DFIG Based WECS Using State Feedback Linearization Control Technique

This paper primarily focuses on an advance control strategy to enhance the low voltage ride through (LVRT) capability in doubly fed induction generator (DFIG) based wind energy conversion system (WCES). In the proposed control strategy, the captured wind energy during grid faults circumstances is stored timidly in the rotor’s inertia kinetic energy. Though a minimal amount of energy is available in the grid, stator current and DC-link voltage are set beneath the perilous levels. However, both the required stator voltage and stator current are kept within a tolerable range of rotor side converter (RSC), through state feedback linearization technique for maintaining the accurate control to suppress the overvoltage and overcurrent. Furthermore, stator current oscillations are significantly suppressed during fault transient. The input mechanical energy from the wind turbine can be resumed after the fault clearance. In spite of being dissipated in the resistors of crowbar circuit, as in the conventional LVRT assemblies, torque balancing among electrical and mechanical measures is attained; DC-link voltage instabilities and rotor speed inconsistencies are substantially reduced. As a result, a noticeable reduction in the requirement of reactive power and swift restoration of terminal voltage on fault clearance is acquired successfully. Correspondingly, several tests are conducted to validate the effectiveness and enhancement in the performance of the DFIG based wind farms, when the proposed control strategy is implemented over it during numerous fault ride-through circumstances.

Design and experimentation of an LPV extended state feedback control on Electric Power Steering systems

This paper deals with Column-type Electric Power Steering systems. An H∞ state feedback Linear Parameter-Varying controller is developed considering a parameter-dependent Lyapunov function. For practical implementation, an H∞∕H2 Proportional Integral observer is added for state and driver torque estimation. The whole observer-based control has been implemented in real-time using dSpace/MicroAutobox on a test car. Some driving tests have been carried out on a test track, and promising results are achieved regarding both estimation and control performances.

Effect of Asymmetric Control Constraints on Fixed-Wing UAV Trajectories

Reference trajectories, for the longitudinal states of a fixed-wing unmanned aerial vehicle subjected to asymmetric control constraints, are distinguished using the characteristics of regions of asymptotic stability calculated as ellipsoidal domains by solving linear matrix inequalities. These domains are used to determine the maximum allowable deviations from the reference, for which stable closed-loop tracking can be ensured. Constraints are imposed on a linear state feedback controller with the saturation modeled as a sector nonlinearity.

DESAIN SISTEM KENDALI UMPAN BALIK STATE PADA KASUS KONTINYU UNTUK MEJA KERJA CNC

Fakhruddin Mangkusasmito, Tsani Hendro Nugroho in this paper explain that One of the important control system in the manufacturing industry is the position control. Mainly in the Computer Numerical Control (CNC) machine, work-table motion control system is used to regulate work-table movements when the machine process a workpieces on it. On standard machines, work-table movements are two axes (X-Y), which is driven by a motor and lead-screw. The discussion in this research only focus on one axis assuming that the systems on both axes are the same and independent. In this research, MATLAB is used to describe the behaviour of the system and also to design appropriate control system in continuos system using state feedback linear controller such as pole placement , tracking system, full order compensator and reduced order compensator. The goal is to obtain a fast response with a rapid rise time and settling time to a step command, while not exceeding an overshoot of 5%. The specification are than a percent overshoot equal to1%, 0,05s settling time and 0,03s rise time. The performance of each control methods are simulated and analyzed to decide the best suit control method for the systems with such criteria. And the result verify that using tracking system controller method achieve such specification with 0% overshoot, 0,04s settling time and 0,028s rise time.

Switching tracking control for linear time‐invariant systems without overshoot: a positive systems method

In this study, the authors study the issue of how to design controllers to asymptotically track a constant signal without overshoot for linear time-invariant systems. Using the theory of positive systems, they obtain the non-negative invariant set of the output for the autonomous systems. Then, a linear state feedback controller is designed to ensure the non-overshooting tracking when the initial state is in some region. Furthermore, for a single-input single-output system, the problem of global non-overshooting tracking control is solved by a switching control law. For multi-input multi-output systems, they also obtain the non-overshooting response under some assumptions. A numerical example is given to illustrate the effectiveness of the proposed theory.

Enhanced Global Asymptotic Stabilization Criteria for Delayed Fractional Complex-valued Neural Networks with Parameter Uncertainty

This paper addresses the global asymptotic stabilization of delayed fractional complex-valued neural networks (FCVNNs) subject to bounded parameter uncertainty. The problem is proposed for two reasons: 1) The available methods for uncertain dynamical systems may be too conservative; 2) The existing algebraic conditions will lead to huge computational burden for large-scale FCVNNs. To surmount these difficulties, the delayed FCVNNs with interval parameters are transformed into a tractable form at first. Then, a simple and practical controller–linear state feedback controller is designed to achieve the global asymptotic stabilization. By constructing different Lyapunov functions and utilizing the fractional-order comparison principle and interval matrix method, two sufficient global asymptotic stabilization criteria expressed in LMI forms, are established. The obtained results in this paper improve and extend some previous published results on FCVNNs. Finally, two numerical examples are provided to illustrate the correctness of the theoretical results.

Exponential Synchronization and L2 -Gain Analysis of Delayed Chaotic Neural Networks Via Intermittent Control With Actuator Saturation.

By using an intermittent control approach, this paper is concerned with the exponential synchronization and L2 -gain analysis for a class of delayed master-slave chaotic neural networks subject to actuator saturation. Based on a switching strategy, the synchronization error system is modeled as a switched synchronization error system consisting of two subsystems, and each subsystem of the switched system satisfies a dwell time constraint due to the characteristics of intermittent control. A piecewise Lyapunov-Krasovskii functional depending on the control rate and control period is then introduced, under which sufficient conditions for the exponential stability of the constructed switched synchronization error system are developed. In addition, the influence of the exogenous perturbations on synchronization performance is constrained at a prescribed level. In the meantime, the intermittent linear state feedback controller can be derived by solving a set of linear matrix inequalities. More incisively, the proposed method is also proved to be valid in the case of aperiodically intermittent control. Finally, two simulation examples are employed to demonstrate the effectiveness and potential of the obtained results.

On sensor quantization in linear control systems: Krasovskii solutions meet semidefinite programming

Abstract Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization-free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solution to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples.

Semitrailer Steering Control for Improved Articulated Vehicle Manoeuvrability and Stability

Abstract Articulated heavy vehicles have some specific performance limitations and safety risks due to their special dynamic characteristics. They show poor manoeuvrability at low speeds and may lose their stability in different manners at high speeds. In this study, the potential of active steering control of the semitrailer on manoeuvrability and stability of tractor-semitrailer combinations is investigated. A linear bicycle model and a nonlinear version are used for controller design and vehicle dynamic simulation in MATLAB environment. The Linear Quadratic Regulator optimal state feedback control is used to minimise the tracking error at low-speed, and regulate Rearward Amplification ratio and roll at high-speed. Quantum Particle Swarm Optimisation is used for optimising the weighting factors. Three different control algorithms are introduced and it is demonstrated through simulations that the vehicle with the proposed steering control exhibits desirable improvements compared to the baseline vehicle.