H-infinity Control Research Articles

Nonlinear optimal control for wind power generators comprising a multi-mass drivetrain and a DFIG

The article proposes a nonlinear optimal (H-infinity) control method for a wind power generation system comprising a two-mass drivetrain and a Doubly-Fed Induction Generator (DFIG). Comparing to the 6-th order dynamic model of the DFIG, the state-space model of the considered power generation unit is extended after including in it the dynamics of the drivetrain. To solve the associated control problem, the dynamic model of the power generation unit undergoes approximate linearization around a temporary operating point which is recomputed at each time-step of the control algorithm. The linearization procedure relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space description of the power unit, an H-infinity controller is developed. This stands for the solution of the optimal control problem for the wind power system under model uncertainty and external perturbations. For the computation of the controller’s feedback gain an algebraic Riccati equation is repetitively solved at each iteration of the control method. Moreover, with the use of Lyapunov analysis the global asymptotic stability of the control scheme is proven. Finally, to implement state estimation-based control without the need to measure the entire state vector of the power unit, the H-infinity Kalman Filter is used as a robust observer.

Structured H-Infinity Controller for an Uncertain Deregulated Power System

A deregulated power system is considered to be a highly complex uncertain system due to the presence of multiple bilateral transactions. Load frequency control in such a system hence assumes significance because of the challenging nature of operation and therefore use of robust controllers is imperative. Conventional robust controller designs give higher order controllers and hence restricts its application in the industry. But the alternative is to use structured H-infinity controllers, which give sufficiently lower-order controllers and can be used in system with nonlinearities. In this paper, structured H-infinity controller has been designed for a deregulated power system considering the effect of nonlinearities like generation rate constraint, governor deadband, and time delay associated with communication network in the system from practical point of view. These physical constraints demand an electrical energy storage system. Hence, load frequency control is accomplished with a structured H-infinity controller supplemented with redox flow battery in each area of a two-area deregulated power system consisting of GENCOs of reheat thermal type.

H-Infinity Control for T-S Aero-Engine Wireless Networked System With Scheduling

H-Infinity Control for T-S Aero-Engine Wireless Networked System With Scheduling

Stabilizing Mixed Vehicular Platoons with Connected Automated Vehicles: An H-infinity Approach

Abstract This paper presents a car-following control strategy of connected automated vehicles (CAVs) to stabilize a mixed vehicular platoon consisting of CAVs and human-driven vehicles. This study first establishes a string stability criterion for a mixed vehicular platoon. Specifically, a mixed vehicular platoon is decomposed into “subsystems” that are all possible sequential subsets of the platoon. String stability is then defined as the “head-to-tail” string stability for all subsystems: the magnitude of a disturbance is not amplified from the first vehicle to the last vehicle of each subsystem. Based on this definition, distributed frequency-domain-based CAV control is proposed to increase the number of head-to-tail string stable subsystems and consequently dampen stop-and-go disturbances drastically. Specifically, an H-infinity control problem is formulated, where the maximum disturbance “damping ratios” in each subsystem is minimized within the predominant acceleration frequency boundaries of human-driven vehicles. Simulation experiments, embedded with real human-driven vehicle trajectories, were conducted, and results show that the proposed control can effectively dampen stop-and-go disturbances.

H-infinity Control of singular Takagi–Sugeno fuzzy systems with additive time-varying delays

This paper discusses the problem of delay-dependent H∞ control for fuzzy singular systems with additive time-varying delays. Our purpose is to design a state feedback controller, such that the resultant closed-loop system is regular, impulse free, and stable with H∞ performance constraint. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, numerical examples show that the proposed methods are less conservative than existing ones.

Nonlinear optimal control for a spherical rolling robot

The article presents a nonlinear H-infinity (optimal) control approach for the problem of the control of the spherical rolling robot. The solution of such a control problem is a nontrivial case due to underactuation and strong nonlinearities in the system’s state-space description. The dynamic model of the robot undergoes approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the system’s Jacobian matrices. For the linearized dynamics of the spherical robot an H-infinity controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation in solved at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, for the implementation of sensorless control for the spherical rolling robot, the H-infinity Kalman Filter is used as a robust state estimator.

Design of H∞ control for single-phase active power filter

ABSTRACTIn this work, an output feedback controller is designed based on H-infinity control theory to reduce the influence of parameter perturbation on the performance and robustness of active filters. The designed controller maintained the power current distortion rate below 2.9%, thus guaranteeing the stability of the active filter when parameter perturbation occurred. The simulation results demonstrated the new controller’s improved compensation performance and robustness compared to traditional hysteresis control.

Observer-Based H-infinity Controller for Nonlinear Singular Networked Control Systems

Observer-Based H-infinity Controller for Nonlinear Singular Networked Control Systems

Practical implementation of H-infinity control for fuel cell-interleaved boost converter

ABSTRACTThis paper presents a non-isolated DC–DC converter for fuel-cell electric vehicle applications. An H-infinity control, based on mixed sensitivity, applied to a three-phase interleaved boost converter, is proposed. This controller is intended for an outer voltage loop and an inner current loop, to ensure a high stability, especially of the dynamic responses, under any operating conditions. The proposed H-infinity controller for the fuel cell system is implemented in a digital signal processor, thus ensuring both excellent reference tracking and disturbance rejection properties.

Nonlinear optimal control for the synchronization of biological neurons under time-delays.

The article proposes a nonlinear optimal control method for synchronization of neurons that exhibit nonlinear dynamics and are subject to time-delays. The model of the Hindmarsh-Rose (HR) neurons is used as a case study. The dynamic model of the coupled HR neurons undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure relies on Taylor series expansion of the model and on computation of the associated Jacobian matrices. For the approximately linearized model of the coupled HR neurons an H-infinity controller is designed. For the selection of the controller's feedback gain an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The stability properties of the control loop are proven through Lyapunov analysis. First, it is shown that the H-infinity tracking performance criterion is satisfied. Moreover, it is proven that the control loop is globally asymptotically stable.

Bruce Francis and H-infinity Control [Historical Perspectives

I first came across Bruce Francis's work while reading his internal model principle paper [1] as an assistant professor at the University of Southern California. This demonstrated a very mature level of problem formulation together with very clear and precise results. When I moved to Cambridge in 1976, I was delighted to hear that Bruce would be a visiting postdoc for that academic year. At some point, Bruce suggested we look at the problem of bounded peaking, and we discussed it a bit. However, he did all of the heavy lifting but nevertheless generously included me as a coauthor [2]. This heavy lifting even became physical when he and Ian Postlethwaite helped my family move into the house where we have remained ever since.

Full State Feedback 𝐇𝟐 and H-infinity Controllers Design for a Two Wheeled Inverted Pendulum System

In this work, two robust controllers, which are full state feedback, 𝐻2 and full state feedback 𝐻∞ controllers are proposed for the two wheeled inverted pendulum system. The nonlinear equations for the two wheeled inverted pendulum system are developed using Euler – Lagrange equation. The system parameters changes are considered to show the effectiveness of the proposed robust controllers. These controllers are proposed not only to stabilize the pendulum in upright position but also to drive the position to track a given reference input. The results show that more desirable robustness and time response specifications can be achieved using the proposed controllers. The effectiveness of the proposed controllers is verified experimentally using real two wheeled inverted pendulum system.

A Nonlinear H-Infinity Control Approach to Stabilization of Distributed Synchronous Generators

This paper proposes a new nonlinear H-infinity control method for stabilization and synchronization of distributed interconnected synchronous generators. At first stage, local linearization of the distributed generators’ model is performed round its present operating point. The approximation error that is introduced to the linearized model is due to truncation of higher-order terms in the performed Taylor series expansion and is represented as a disturbance. The control problem is now formulated as a min–max differential game in which the control input tries to minimize the state vector's tracking error while the disturbances affecting the model try to maximize it. Using the linearized description of the distributed generators’ dynamics, an H-infinity feedback controller is designed through the solution of a Riccati equation at each step of the control algorithm. The inherent robustness properties of H-infinity control assure that the disturbance effects will be eliminated and the state variables of the individual power generators will converge to the desirable setpoints. The proposed method, stands for a reliable solution to the problem of nonlinear control and stabilization for interconnected synchronous generators. It is also a novel approach, comparing to control of synchronous generators based on global linearization methods. Its efficiency is further confirmed through simulation experiments.

Design of a controller for a rigid-flexible satellite using the H-infinity method considering the parametric uncertainty

Abstract In the design of the Attitude Control System (ACS) for a Rigid-flexible Satellite (RFS) it is important to take into account the influence of the structure’s flexibility, since its interaction with the satellite rigid motion during translational and/or rotational maneuver, can damage the ACS pointing accuracy. In the linearization and/or reduction of the RFS mathematic model, usually one loses some important information associated with the satellite true dynamical behavior. One way to recovery this information is to include in the ACS design the parametric and non parametric uncertainties of the system. The H infinity control methodology is able to take into account the parametric uncertainty in the control law design so as the controller becomes more robust. This paper presents the design of a robust controller using the H infinity control technique to control the attitude of a RFS which is represented by a flexible beam connected to a central rigid hub considering the set of parametric uncertainty. The results of the simulations have shown that the control law designed with the H-infinity control method was robust enough to support the action of uncertainties and control the RFS attitude and suppress its panel’s vibrations.

Offset‐free model predictive control of diesel engine by combined design of disturbance model and observer

The diesel engine is a typical multi-input multi-output system with strong couplings, actuator constraints, and fast dynamics. The objective is to operate the engine to meet driver's speed demand and reduce exhaust emissions of nitrogen oxides (NOx) during transient process. Interactions between the actuators and nonlinear behavior of the system make the problem difficult to handle using classical control design methods. Instead, we propose an offsetfree model predictive control system. It is based on the combined design of integrating disturbance model and state observer. The dynamic observer is designed by solving an H-infinity control problem aimed at minimizing the effect of unmeasured disturbances and model mismatch on the output prediction error. The proposed approach has a low computation requirement and is suitable for implementation in the engine control unit on board. The application of this system in continuous working process by using dSPACE MicroAutoBox verified its feasibility and effectiveness for achieving precise reference tracking of engine speed and reducing emissions.

Robust Finite-Time H-Infinity Control with Transients for Dynamic Positioning Ship Subject to Input Delay

This paper presents the problem of robust finite-time H∞ control with transients for ocean surface vessels equipped with dynamic positioning (DP) system in presence of input delay. The main objective of this work is to design a finite-time H∞ state feedback controller, which ensures that all states of ship do not exceed a given threshold over a fixed time interval, with better robustness and transient performance subject to time-varying disturbance. Based on a novel augmented Lyapunov-Krasovskii-like function (LKLF) with triple integral terms and a method combining the Wirtinger inequality and reciprocally convex approach, a less conservative result is derived. In particular, an H∞ performance index with nonzero initial condition is introduced to attenuate the overconservatism caused by the assumption of zero initial condition and enhance the transient performance of ship subject to external disturbance. More precisely, the controller gain matrix for the DP system can be achieved by solving the linear matrix inequalities (LMIs), which can be easily facilitated by using some standard numerical packages. Finally, a numerical simulation for a ship is proposed to verify the effectiveness and less conservatism of the controller we designed.

Output feedback Q-learning for discrete-time linear zero-sum games with application to the H-infinity control

Approximate dynamic programming techniques usually rely on the feedback of the measurement of the complete state, which is generally not available in practical situations. In this paper, we present an output feedback Q-learning algorithm towards finding the optimal strategies for the discrete-time linear quadratic zero-sum game, which encompasses the H-infinity optimal control problem. A new representation of the Q-function in the output feedback form is derived for the zero-sum game problem and the optimal output feedback policies are presented. Then, a Q-learning algorithm is developed that learns the optimal control strategies online without needing any information about the system dynamics, which makes the control design completely model-free. It is shown that the proposed algorithm converges to the optimal solution obtained by solving the game algebraic Riccati equation (GARE). Unlike the value function based approach used for output feedback, the proposed Q-learning scheme does not require a discounting factor that is generally adopted to mitigate the effect of excitation noise bias. It is known that this discounting factor may compromise the closed-loop stability. The proposed method overcomes the excitation noise bias problem without resorting to the discounting factor, and therefore, converges to the nominal GARE solution. As a result, the closed-loop stability is preserved. An application to the H-infinity autopilot controller for the F-16 aircraft is demonstrated by simulation.

Robust fault-tolerant controller design for aerodynamic load simulator

Load simulator is one of the main mechanisms for stability and performance evaluation of the rotational/translational actuators in the laboratory. The movement of (under testing) actuator generates a large disturbance on the load simulator known as “extraneous torque”. Elimination of this large surplus disturbance is the main concern of the dynamic load simulator design. The faults are unavoidable events in system operation. Sensor or actuator faults frequently occur in flight systems. The design method based on Quantitative Feedback Theory (QFT) can be used as a passive Fault-Tolerant Control (FTC) of the plants with sensor or actuator faults. In this paper, a QFT-FTC is proposed for the electric load simulator (ELS) in presence of sensor and actuator faults. For this purpose, a particular type of faults is used, which the sensor and actuator faults are considered as semi-deterministic jumps that occurring at random intervals with random amplitudes. In the first step, the faults are converted to parameter uncertainties and disturbance is transferred to the input and output of the plant. Then, a QFT controller is designed for this uncertain plant. Proposed QFT-FTC attenuates the large disturbance even if the control effort is limited. Under these circumstances, an adequate bandwidth is achieved. Furthermore, semi-deterministic jumping faults on sensor and actuator are applied during the simulations and high robust tracking performance is obtained in presence of the saturated control. Compared to H-infinity Controller, the proposed controller has a simpler structure and its tracking performance is better than H-infinity method.

Non-fragile mixed H-infinity and passivity control for neural networks with successive time-varying delay components

This paper is concerned with the problem of nonfragile mixed H∞ and passivity control for neural networks with successive time-varying delay components. We construct a suitable Lyapunov–Krasovskii function with triple and quadruple integral terms then utilizing Jensen's lemma and Wirtinger-type inequality technique. Some sufficient conditions are presented for the existence of nonfragile mixed H∞ and passivity performance criterions. The expressions for the nonfragile controller can be obtained by solving a set of linear matrix inequality. Finally, two numerical examples are presented to demonstrate the effectiveness of our proposed method.

Predictive Control for Linear and Hybrid Systems [Bookshelf

This book offers new insight in the realm of predictive control. The authors demonstrate how predictive control can be implemented in applications that were thought to be impossible when they started their collaboration about two decades ago. The book not only contains mature, and tried and tested, material but also the fundamentals necessary for understanding recent methods that have been receiving considerable interest in academia and industry. Depending on your perspective, predictive control can be seen as a subset or superset of classical optimal control or as something completely different. Here, predictive control is viewed as a modern optimal control method that builds on classical optimal control results, when possible. The main thesis in predictive control is that most practical control problems are naturally formulated as a sequence of infinite-dimensional, constrained, nonlinear optimal control problems, which are often impossible to solve. For example, in most applications, the optimal controller is not simply a linear, finite-dimensional dynamical system, as in proportional-integral-derivative, linear-quadratic Guassian, or H-infinity control, even if the model of the controlled system is linear and finite dimensional. The optimal control policy can be discontinuous, even if all the functions used to define the optimal control problem are smooth. Researchers in predictive control aim to understand these and other fundamental problems that naturally arise in applications, while finding practical and approximate solutions with appropriate guarantees. The book's emphasis is on the use of multiparametric programming to compute the explicit solution to the FHOCPs. It is divided into five parts: I) Basics of Optimization, II) Multiparametric Programming, III) Optimal Control, IV) Constrained Optimal Control of Linear Systems, and V) Constrained Optimal Control of Hybrid Systems. If readers started at the beginning and worked all the way to the end, they will have been introduced to a variety of fundamental and interesting topics in optimization, geometry, control, and dynamical systems theory that could be applied in a number of areas. In terms of a target audience, the book is suitable for both advanced undergraduate engineering students and in some cases, engineering postgraduates and above.