Linear Robust Control Research Articles

Robust Linear Quadratic Sliding-Mode Control for BLDC Motor Positioning System

The brushless dc motor position tracking system to be controlled includes a friction and a backlash as disturbances. In this paper, we propose a robust linear quadratic sliding-mode controller for precision positioning in a brushless dc motor system. The control algorithm includes a linear quadratic control for an optimal feedback gain and an integral nonlinear sliding-surface based on a new reaching law to remove the reaching phase. It has robust performance against parameter variation which causes an oscillation in case of linear quadratic control. Simulation results show that the proposed controller gives an improved accurate driving tracking result and is robust to plant parameter variation and load torque disturbances.

Robust Active Disturbance Rejection Control Approach to Maximize Energy Capture in Variable-Speed Wind Turbines

This paper proposes an alternative robust observer-based linear control technique to maximize energy capture in a 4.8 MW horizontal-axis variable-speed wind turbine. The proposed strategy uses a generalized proportional integral (GPI) observer to reconstruct the aerodynamic torque in order to obtain a generator speed optimal trajectory. Then, a robust GPI observer-based controller supported by an active disturbance rejection (ADR) approach allows asymptotic tracking of the generator speed optimal trajectory. The proposed methodology controls the power coefficient, via the generator angular speed, towards an optimum point at which power coefficient is maximum. Several simulations (including an actuator fault) are performed on a 4.8 MW wind turbine benchmark model in order to validate the proposed control strategy and to compare it to a classical controller. Simulation and validation results show that the proposed control strategy is effective in terms of power capture and robustness.

Design and experimental validation of linear and nonlinear vehicle steering control strategies

This paper proposes the design of three control laws dedicated to vehicle steering control, two based on robust linear control strategies and one based on nonlinear control strategies, and presents a comparison between them. The two robust linear control laws (indirect and direct methods) are built around M linear bicycle models, each of these control laws is composed of two M proportional integral derivative (PID) controllers: one M PID controller to control the lateral deviation and the other M PID controller to control the vehicle yaw angle. The indirect control law method is designed using an oscillation method and a nonlinear optimisation subject to H ∞ constraint. The direct control law method is designed using a linear matrix inequality optimisation in order to achieve H ∞ performances. The nonlinear control method used for the correction of the lateral deviation is based on a continuous first-order sliding-mode controller. The different methods are designed using a linear bicycle vehicle model with variant parameters, but the aim is to simulate the nonlinear vehicle behaviour under high dynamic demands with a four-wheel vehicle model. These steering vehicle controls are validated experimentally using the data acquired using a laboratory vehicle, Peugeot 307, developed by National Institute for Transport and Safety Research – Department of Accident Mechanism Analysis Laboratory's (INRETS-MA) and their performance results are compared. Moreover, an unknown input sliding-mode observer is introduced to estimate the road bank angle.

Electrical energy quality: Modeling and H∞ control of a three-phase shunt active filter

The main contribution of the paper is the modeling approach used to describe a pure threephase shunt active filter, and the application of the H∞ control design tool in order to improve the quality of electrical energy. Advanced power electronics devices have widely contributed to the degradation of power quality due to the injection of non-sinusoidal currents into the utility system. Therefore, it is essential to use an active compensator which can attenuate current harmonics to an acceptable level on the line side of the power source. In this work, a three-phase active filter connected in parallel to a supply system feeding a non-linear load is described, in a complex framework, by a linear multivariable state space representation in order to guarantee that the system is mathematically decoupled and therefore to simplify the controller design. This representation includes a sensor to measure perturbations, and allows one to calculate a linear robust control law. The originality of this paper is that a Linear Matrix Inequality based H∞ synthesis is performed to design a static state feedback controller with complex-valued parameters. The robustness of this controller with respect to network impedance uncertainties is investigated. Moreover, simulation and experimental results are given to reveal the effectiveness of the synthesized control law.

Robust and Resilient Finite-Time Control of a Class of Continuous-Time Nonlinear Systems

Finite-time state-feedback stabilization of a class of continuous-time nonlinear systems with conic type nonlinearities, bounded feedback control gain perturbations, and additive disturbances is presented. Sufficient conditions for the existence of a robust and resilient linear finite-time state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, solutions for the controller gain and the upper bound on the gain perturbations are obtained. The developed controller is robust for all unknown nonlinearities lying in a hyper-sphere and all admissible disturbances. Furthermore, it is resilient against any bounded perturbations that may modify the controller's gain by at most a prescribed amount. We conclude the paper with a numerical example illustrating the applicability of the main result.

A Robust Kalman Conjecture For First-Order Plants

A robust Kalman conjecture is defined for the robust Lur'e problem. Specifically, it is conjectured that the nonlinearity's slope interval for which robust absolute stability is guaranteed corresponds to the robust interval of the uncertain plant. We verify this robust Kalman conjecture for first-order plants perturbed by various norm-bounded unstructured uncertainties. The analysis classifies the appropriate stability multipliers required for verification in these cases. Robust control of Lur'e-type nonlinear systems satisfying this novel conjecture can therefore be designed using linear robust control methods.

Nonlinear Control Techniques for the Heart Rate Regulation in Treadmill Exercises

It has been recently shown in the literature that a robust output feedback controller for the heart rate regulation can be designed for an experimentally validated second order nonlinear model of the human heart rate response during long-duration treadmill exercises: It is based on piecewise linear approximations of the original nonlinear model and involves (local) robust linear control techniques. In this letter, we resort to recent nonlinear advanced control techniques in order to illustrate the existence of a nonlocal and nonswitching control which guarantees heart rate regulation with no exact knowledge of model parameters and nonlinearities: It simply generalizes to the nonlinear framework the classical proportional-integral control design for linear models of heart rate response during treadmill exercises. Simulation and experimental results demonstrate the effectiveness of the proposed approach in typical training exercises involving warm up/holding/cool down phases.

Linear fractional transformation gain-scheduling flight control preserving robust performance

In this article, a gain-scheduling flight controller design based on a blending/interpolating methodology and an optimal linear fractional transformation (LFT)-based control technique is proposed to achieve robust performances over a wide range of aircraft operating conditions. Representing the non-linear system dynamics into an uncertain LFT system form, our gain-scheduling strategy designs a limited number of robust linear controllers covering the whole range of operating conditions. Using these fixed controllers in a robust performance control set-up, we derive a blending/interpolating scheduling controller, which achieves the desired performance for the entire flight envelope. Our approach offers the benefit of facilitating controller design and provides proofs of robust stability and performance through an uncertain LFT robust performance formulation. In addition, tools analysing the robustness of the closed-loop gain-scheduling system are also provided. Non-linear simulations based on our proposed approach for a B1 flexible aircraft for a limited flight but reasonable flight envelope show very good performance results in both time and frequency domain responses.

A Nonlinear Control Method Based on ANFIS and Multiple Models for a Class of SISO Nonlinear Systems and Its Application

This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.

Indirect self-tuning control using multiple models for non-affine nonlinear systems

In this article, for a class of discrete time non-affine nonlinear systems, a multiple-model-based indirect self-tuning control method is developed. The indirect self-tuning control method is composed of a linear robust indirect self-tuning controller, a nonlinear neural network indirect self-tuning controller and a switching mechanism. By introducing a modified Clarke index, the indirect self-tuning control method can tolerate properties of non-minimum phase and open-loop instability of the controlled system and attenuate the disturbance caused by the higher order nonlinear term. By resorting to the time-varying operation, it is proved without the assumption on the boundedness of the nonlinear term or its differential term that the proposed multiple-model-based nonlinear indirect self-tuning control method can guarantee the bounded-input–bounded-output stability of the closed-loop system and improve the system performance simultaneously. To illustrate the effectiveness of the proposed method, simulations for a synthetic nonlinear system and a realistic nonlinear system are conducted.

Robust Wide Area Measurement System-Based Control of Inter-area Oscillations

The application of phasor measurement unit (PMU) measurements and a robust linear matrix inequality-based control based on a polytopic model of the system used to damp inter-area oscillations is investigated. The closed-loop eigenvalues are excluded from a region of the complex plane, guaranteeing that low-frequency modes must be damped. A 68-bus 16-generator system is used as a test system. Three DC lines, three static var compensators, and remote PMU frequencies as added inputs to selected power system stabilizers are used as the example control. Ten different system conditions are used as the vertices of the polytope. The system size is reduced using selective modal analysis.

Robust Control Design and Simulation for Cantilever-Typed Inverted Pendulum

In order to solve the problem of the control cantilever-typed inverted pendulum, the second order mathematic model for cantilever-typed inverted pendulum is built in this paper. Using the theory of Linear Robust Optimal Control, the systematic linear robust optimal controller is designed for the stability of this pendulum under the closed loop state. Compared to traditional Linear Quadratic Optimal Control, the final result shows that the robust optimal method has better effects by using Matlab simulation technique.

Robust and Resilient Finite-Time Control of a Class of Discrete-Time Nonlinear Systems

AbstractIn this paper, we address the finite-time state-feedback stabilization of a class of discrete-time nonlinear systems with conic type nonlinearities, bounded feedback control gain perturbations, and additive disturbances. Sufficient conditions for the existence of a robust and resilient linear state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, a solution for the controller gain is obtained. The developed controller is robust for all unknown nonlinearities lying in a hyper-sphere and all admissible disturbances. Moreover, it is resilient against any bounded perturbations that may alter the controller's gain by at most a prescribed amount. We conclude the paper with a numerical example showcasing the applicability of the main result.

Memoryless Linear Adaptive Robust Controllers of Uncertain Systems with Nonlinear Time-Varying Delayed State Perturbations

Memoryless Linear Adaptive Robust Controllers of Uncertain Systems with Nonlinear Time-Varying Delayed State Perturbations

Combined Nonlinear Tokamak Plasma Current Profile Control System Design and Simulation with Input Constraints

AbstractThe paper presents the design and simulation results of the combined multivariable control system with the plant input constraints for a plasma current profile in a tokamak. The plasma kinetic model was used in terms of the Grad-Shafranov plasma equilibrium equation and the poloidal magnetic flux diffusion equation. The model is square specifically contains 5 inputs and 5 outputs. Actuators are external current drive sources. Output is plasma current density measured at five points of the minor radius. A set of linear models for controller design was obtained by a state subspace identification approach. A set of H∞ controllers was synthesized by a loop shaping methodology at various values of the plasma electron temperature on the magnetic axis. Controllers designed were applied by the numerical simulation to the original model to change the current profile from one state to another. In the presence of plant input constraints a special logic block was developed in addition to the linear robust controller and used when plant inputs saturated. The plasma current profile control system designed showed its operability in the tokamak plasma electron temperature range on the magnetic axis from 0.1 to 18 keV.

Fully Autonomous Preload‐Sensitive Control of Implantable Rotary Blood Pumps

A pulsatility-based control algorithm with a self-adapting pulsatility reference value is proposed for an implantable rotary blood pump and is to be tested in computer simulations. The only input signal is the pressure difference across the pump, which is deduced from measurements of the pump's magnetic bearing. A pulsatility index (PI) is calculated as the mean absolute deviation from the mean pressure difference. As a second characteristic, the gradient of the PI with respect to the pump speed is derived. This pulsatility gradient (GPI) is used as the controlled variable to adjust the operating point of the pump when physiological variables such as the systemic arterial pressure, left ventricular contractility, or heart rate change. Depending on the selected mode of operation, the controller is either a linear controller or an extremum-seeking controller. A supervisory mechanism monitors the state of the system and projects the system into the region of convergence when necessary. The controller of the GPI continuously adjusts the reference value for PI. An underlying robust linear controller regulates the PI to the reference value in order to take into account changes in pulmonary venous return. As a means of reacting to sudden changes in the venous return, a suction detection mechanism was included. The control system is robustly stable within a wide range of physiological variables. All the clinician needs to do is to select between the two operating modes. No other adjustments are required. The algorithm showed promising results which encourage further testing in vitro and in vivo.

Nonlinear Control Design for an Active Suspension using Velocity-Based Linearisations

The conflict between ride comfort and safety is well-known for vehicle suspension systems. This work presents a control design concept which tries to ease this conflict for a fully active nonlinear suspension system using velocity-based linearisations. Within the corresponding velocity-based design framework, any nonlinear system can be approximated by a family of local linear subsystems which facilitates classical linear control design and analysis methods. In case of the active suspension system, first two robust linear controllers for good comfort and safety, respectively, are determined by numerical optimization. Then the velocity-based design framework is used to identify an adequate, locally stable way of continuously interpolating between those two controllers with scheduling variables. By that, a nonlinear controller is gained which is aimed at high performance and which avoids unnecessary restrictive slow-variation requirements on the scheduling variables. Finally the nonlinear controller is tested and evaluated in simulations with a realistic quarter-car model of a quad vehicle.

Robust backstepping output tracking control for SISO uncertain nonlinear systems with unknown virtual control coefficients

The output tracking controller design problem is dealt with for a class of nonlinear strict-feedback form systems in the presence of nonlinear uncertainties, external disturbance, unmodelled dynamics and unknown time-varying virtual control coefficients. A new method based on signal compensation is proposed to design a linear time-invariant robust controller, which consists of a nominal controller and a robust compensator. It is shown that the closed-loop control system with a controller designed by the proposed method has robust asymptotical practical tracking property for any bounded initial conditions and robust tracking transient property if all initial states are zero.

Robust linear object control by indirect measurements

We study the problem of designing a robust surveillance system for a linear object whose input and output is subject to various external uncontrolled disturbing influences, and regulating variables cannot be measured. We offer a control algorithm that provides satisfaction of target surveillance conditions by reference signals and compensating parametric and exogenous disturbances with the necessary precision. We show numerical examples and results of computer modeling.

A design method for robust and quadratic optimal MIMO linear controllers

In this paper a design method was formulated to deal with robustness and performance specifications for any MIMO linear controller. The controller tuning procedure was expressed as an optimization problem in which novel time-domain integrals of the weighted squared error and weighted squared control signals, with initial state zero and inputs not necessarily defined over the Lebesgue normed space ( L 2 + ) , were minimized. The control robustness is achieved by constraining the minimization such that the maximum complex/real ratio of the closed-loop control system eigenvalues was lower than one. The proposed tuning method was applied in the design of linear controllers with PID structure for a CSTR with disturbance noise and a nonlinear CSTR with control signal saturations, both reported in literature. The results show that the proposed control systems surpass the performance and robustness characteristics of the controllers designed with other reported methods.