LMI solutions for H-two and H-infinity decentralized controllers applied to an aerothermic process

In this paper, we present a linear matrix inequality (LMI)-based solution to implement H-two and Hinfinity decentralized robust control strategies. Appropriate parametrization of optimal H-two and H-infinity controllers is used. The general formulation of the decentralized control design leads to the optimal determination of both the state feedback gains and the observer gains of the decentralized controllers. This formulation is two folds: first, a centralized controller is obtained, and then, a simplified decentralized solution is derived by optimizing only the observer gains. The mathematical determination of these gains is formulated as an LMI optimization problem that can be easily solved using LMI solvers. As an experimental evaluation of these controllers, a real time application to an aerothermic process is carried out. A continuous-time model of the process obtained with a suitable direct continuous-time identification approach is elaborated. Results illustrating the real performance obtained from the H-two and H-infinity decentralized controllers are discussed and compared with the centralized ones.     

基于观测器的不确定T-S模糊系统鲁棒镇定

为带有参数不确定性的T-S模糊控制系统提出了新的基于观测器的鲁棒输出镇定条件. 该条件用来设计模糊控制器和模糊观测器. 为了设计模糊控制器和模糊观测器, 用T-S模糊模型来表示非线性系统, 并运用平行分布补偿观念. 充分条件基于二次Lyapunov函数, 通过将模糊系统的鲁棒镇定条件表述为一系列矩阵不等式, 比以往文献中列出的条件具有更小的保守性. 该不等式为双线性矩阵不等式, 可分两步骤先后解得使T-S模糊系统镇定的控制器增益和观测器增益. 最后, 通过对一个具有不确定性的连续时间非线性系统控制的例子证明了提出方法比以往方法更宽松.     

Stability and performance of current harmonic controllers for multiphase PMSMs

Multiphase electric machines can provide significant benefits over conventional three-phase machines. A drawback to multiphase machines is that they are known to have problems with stator current harmonics. The harmonics can be eliminated by various current harmonic control methods. However, there appears to be no clear agreement on the most suitable method for multiphase machines. This paper aims to compare different current harmonic controllers in terms of stability and performance under model uncertainty. A detailed theoretical analysis of the harmonic controllers is given by taking a modern multi-input multi-output approach based on a structured singular value analysis. Further, the performance of the harmonic controllers is studied with experimental results from a dual three-phase permanent magnet synchronous machine. The analysis and results of this paper show how to design robust high-performance current harmonic controllers for multiphase machines.     

Backstepping approach for design of PID controller with guaranteed performance for micro-air UAV

Flight controllers for micro-air UAVs are generally designed using proportional-integral-derivative (PID) methods, where the tuning of gains is difficult and time-consuming, and performance is not guaranteed. In this paper, we develop a rigorous method based on the sliding mode analysis and nonlinear backstepping to design a PID controller with guaranteed performance. This technique provides the structure and gains for the PID controller, such that a robust and fast response of the UAV (unmanned aerial vehicle) for trajectory tracking is achieved. First, the second-order sliding variable errors are used in a rigorous nonlinear backstepping design to obtain guaranteed performance for the nonlinear UAV dynamics. Then, using a small angle approximation and rigorous geometric manipulations, this nonlinear design is converted into a PID controller whose structure is naturally determined through the backstepping procedure. PID gains that guarantee robust UAV performance are finally computed from the sliding mode gains and from stabilizing gains for tracking error dynamics. We prove that the desired Euler angles of the inner attitude controller loop are related to the dynamics of the outer backstepping tracker loop by inverse kinematics, which provides a seamless connection with existing built-in UAV attitude controllers. We implement the proposed method on actual UAV, and experimental flight tests prove the validity of these algorithms. It is seen that our PID design procedure yields tighter UAV performance than an existing popular PID control technique.     

Robust PI controller design for nonlinear systems via fuzzymodeling approach

The design problem of proportional and proportional-plus-integral (PI) controllers for nonlinear systems is studied. First, the Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties is used to approximate the nonlinear systems. Then a numerically tractable algorithm based on the technique of iterative linear matrix inequalities is developed to design a proportional (static output feedback) controller for the robust stabilization of the system in T-S fuzzy model. Next, we transform the problem of PI controller design to that of proportional controller design for an augmented system and thus bring the solution of the former problem into the configuration of the developed algorithm. Finally, the proposed method is applied to the design of robust stabilizing controllers for the excitation control of power systems. Simulation results show that the transient stability can be improved by using a fuzzy PI controller when large faults appear in the system, compared to the conventional PI controller designed by using linearization method around the steady state     

Online Learning Control for Harmonics Reduction Based on Current Controlled Voltage Source Power Inverters

Nonlinear loads in the power distribution system cause non-sinusoidal currents and voltages with harmonic components. Shunt active filters (SAF) with current controlled voltage source inverters (CCVSI) are usually used to obtain balanced and sinusoidal source currents by injecting compensation currents. However, CCVSI with traditional controllers have a limited transient and steady state performance. In this paper, we propose an adaptive dynamic programming (ADP) controller with online learning capability to improve transient response and harmonics. The proposed controller works alongside existing proportional integral (PI) controllers to efficiently track the reference currents in the d -q domain. It can generate adaptive control actions to compensate the PI controller. The proposed system was simulated under different nonlinear (three-phase full wave rectifier) load conditions. The performance of the proposed approach was compared with the traditional approach. We have also included the simulation results without connecting the traditional PI control based power inverter for reference comparison. The online learning based ADP controller not only reduced average total harmonic distortion by 18.41 %, but also outperformed traditional PI controllers during transients.      

Robust Control of Positive Fractional‐Order Interconnected Systems with Heterogeneous Delays

The problem of robust decentralized control of positive fractional‐order interconnected systems with heterogeneous time‐varying delays is studied in this paper. Necessary and sufficient conditions are first derived for internal positiveness of the system. By exploiting the monotonicity induced from positivity of the system, robust stability conditions subject to uncertain system parameters are derived. The derived stability conditions are then utilized to address the controller synthesis problem. The design conditions for obtaining controller gains of stabilizing decentralized controllers are formulated using linear programming, which can be effectively solved by various convex optimization algorithms. Finally, the effectiveness of the obtained results is validated by two numerical examples.     

Robust control for voltage and transient stability of power grids relying on wind power

Common practice in stabilization of power grids is to refer to different stability categories (transient stability, voltage stability, rotor angle stability) and to address these by designing dedicated controllers separately based on models linearized around nominal operation points. Furthermore, the controllers of a generating unit contained in the grid are usually synthesized without considering other grid nodes. This work, in contrast, proposes a scheme for unified synthesis of controllers which conjunctively address rotor angle stability and voltage stability for grids containing synchronous generators as well as wind energy conversion systems based on doubly-fed induction generators. First, a procedure is proposed to describe the generating units by linear-parameter-varying (LPV) systems, in which fluctuations imposed by the grid or the wind are mapped into time-varying model parameters. For appropriate ranges of these parameters, decentralized robust controllers can be synthesized by semidefinite-programming, such that the power grid is stabilized for the considered fluctuations and disturbances. The effectiveness of the approach is demonstrated for a multi-bus benchmark system, where the grid oscillations are well damped and the LPV-controller stabilizes the grid after permanent changes.     

Multivariable PID control with set-point weighting via BMI optimisation

The paper focuses on the design of multivariable PID controllers with set-point weighting. The advantage of this PID structure is that the responses of the system to disturbances and to changes in the set-point can be adjusted separately. The proposed design methods rely on the transformation of the tuning of the controller gains into a static output feedback (SOF) problem. Hence, multivariable PID controllers can be designed by solving an optimisation problem with bilinear matrix inequalities (BMIs). The paper addresses the design of both time-invariant and gain-scheduled robust controllers. All of the tuning methods discussed through the paper are based on a PID structure with filtered derivative term, thus guaranteeing the well-posedness of the closed loop system.     

Observers for stabilization of systems with matched uncertainty

In this article, we study the design of observer-based robust linear feedback controllers. The uncertainty, which can enterA, and either theB orC matrices, is assumed to satisfy certain matching conditions. Lyapunov techniques are used to establish sufficient conditions for stability, given an uncertainty bound. In particular, sufficient conditions are obtained that, if met, result in stabilizing controllers regardless of the size of the uncertainty entering the system matrix, as long as the standard constraints on the uncertainty entering the input or output matrices are met. As with the case of more general forms of uncertainty, the resulting observers often have high gains. To study performance, the problem of disturbance rejection is considered. Sufficient conditions are presented for obtaining control laws that stabilize the closed loop system, regardless of the size of the uncertainty entering the system matrix, while simultaneously guaranteeing arbitrarily small infinity norm for the transfer function from the plant disturbances to the outputs.     

Intelligent-controlled doubly fed induction generator system using PFNN

An intelligent-controlled doubly fed induction generator (DFIG) system using probabilistic fuzzy neural network (PFNN) is proposed in this study. This system can be applied as a stand-alone power supply system or as the emergency power system when the electricity grid fails for all sub-synchronous, synchronous, and super-synchronous conditions. The rotor side converter is controlled using the field-oriented control to produce three-phase stator voltages with constant magnitude and frequency at different rotor speeds. Moreover, the grid side converter, which is also controlled using field-oriented control, is primarily implemented to maintain the magnitude of the DC-link voltage. Furthermore, an intelligent PFNN controller is proposed for both the rotor and grid side converters to improve the transient and steady-state responses of the DFIG system at different operating conditions. The network structure, online learning algorithm, and convergence analyses of the PFNN are introduced in detail. Finally, the feasibility of the proposed control scheme is verified using some experimental results.     

Nonlinear controller synthesis based on inverse describing function technique in the MATLAB environment

In this research, a new software based on a systematic nonlinear controller design technique for nonlinear systems is developed. This software is in the MATLAB environment, and it is based on inverse describing functions in order to arrive at nonlinear gains of the controller. The software may be used to synthesize nonlinear controllers for nonlinear systems without restriction on system order, the number, type, and arrangement of nonlinear terms. The goal is to design an output feedback system that is a solution to a robust design such that sensitivity of the feedback control system with respect to amplitude of the excitation signal and the operating regimes would be at a minimum.     

Identification and control — Closed-loop issues

An overview is given of some current research activities on the design of high-performance controllers for plants with uncertain dynamics, based on approximate identification and model-based control design. In dealing with the interplay between system identification and robust control design, some recently developed iterative schemes are reviewed and special attention is given to aspects of approximate identification under closed-loop experimental conditions.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

Simulation and control of electrode position controllers for electric arc furnaces

A comparative study is made of the dynamic performance of the main types of electrode position controllers used with industrial arc furnaces, consisting essentially of direct actuators employing hydraulic servosystems and indirect actuators operating a winch system. The overall system models include single- and three-phase power system representations and are used for the design of existing conventional analogue controllers to give improved short-term dynamic performance. Direct digital control of the electrode position servomechanism, incorporating conventional four mode algorithms and also suboptimal control based on a reduced-order linear model for controlling a non-linear plant model, is investigated. The study illustrates that improved long- and short-term dynamic performance of electrode position can be obtained by improved control system design.     

An intelligent coordinator design for GCSC and AGC in a two-area hybrid power system

This study addresses the design procedure of an optimized fuzzy fine-tuning (OFFT) approach as an intelligent coordinator for gate controlled series capacitors (GCSC) and automatic generation control (AGC) in hybrid multi-area power system. To do so, a detailed mathematical formulation for the participation of GCSC in tie-line power flow exchange is presented. The proposed OFFT approach is intended for valid adjustment of proportional–integral controller gains in GCSC structure and integral gain of secondary control loop in the AGC structure. Unlike the conventional classic controllers with constant gains that are generally designed for fixed operating conditions, the outlined approach demonstrates robust performance in load disturbances with adapting the gains of classic controllers. The parameters are adjusted in an online manner via the fuzzy logic method in which the sine cosine algorithm subjoined to optimize the fuzzy logic. To prove the scalability of the proposed approach, the design has also been implemented on a hybrid interconnected two-area power system with nonlinearity effect of governor dead band and generation rate constraint. Success of the proposed OFFT approach is established in three scenarios by comparing the dynamic performance of concerned power system with several optimization algorithms including artificial bee colony algorithm, genetic algorithm, improved particle swarm optimization algorithm, ant colony optimization algorithm and sine cosine algorithm.     

Robust non-fragile guaranteed cost control of uncertain large-scale systems with time-delays in subsystem interconnections

In this paper, the robust non-fragile guaranteed cost-control problem is studied for a class of uncertain linear large-scale systems with time-delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design a state feedback control law such that the closed-loop system is asymptotically stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.     

Bidirectional active control of structures with type-2 fuzzy PD and PID

Proportional-derivative and proportional-integral-derivative (PD/PID) controllers are popular algorithms in structure vibration control. In order to maintain minimum regulation error, the PD/PID control require big proportional and derivative gains. The control performances are not satisfied because of the big uncertainties in the buildings. In this paper, type-2 fuzzy system is applied to compensate the unknown uncertainties, and is combined with the PD/PID control. We prove the stability of these fuzzy PD and PID controllers. The sufficient conditions can be used for choosing the gains of PD/PID. The theory results are verified by a two-storey building prototype. The experimental results validate our analysis.     

Robust adaptive fault tolerant control for a process with actuator faults

This paper studies design and implementation of an enhanced multivariable adaptive control scheme for an uncertain nonlinear process exposed to actuator faults. For adaptive fault compensation, a model reference adaptive control (MRAC) strategy is utilized as main controller. A new adaptation algorithm making possible to improve transient performance of adaptive control is integrated to the controller. With the help of further modifications, some restrictive conditions on multivariable adaptive design are relaxed so that the system requires less plant information. The resulting controller has a simpler structure than the other matrix factorization based controllers. At the final stage of design, a robust adaptive control scheme is obtained with consideration of practical implementation problems such as sensor noises, external disturbances and unmodeled​ system dynamics. It is proved that the controller guarantees closed-loop signal boundedness and asymptotic output tracking. Real-time experiment results acquired from quadruple tank benchmark system are presented in order to exhibit the effectiveness of the proposed scheme.     

Digital tracker with output feedback: application to aircraft controls

A linear-quadratic output-feedback approach is given for designing digital servo-control systems of specified structure. The result is digital controllers that have a sensible structure based on classical control theory, in contrast to standard LQR design using state feedback plus an observer. The correct initial conditions for determining the LQ tracker output-feedback gains are not uniformly distributed as is traditionally assumed, but are shown to be explicitly given in terms of the step command magnitude. Both pole and zero placement are used to optimize the performance index. Arbitrary systems are treated, not only those with integrators in the forward paths, by adding a term to the performance index that weights the steady-state error. The approach works even if the system is non-minimum-phase. Necessary conditions are derived that may be used in a gradient-based routine to determine the optimal digital control gains. The approach does not rely on redesign of a continuous control system using techniques like the bilinear transformation, but uses direct discrete-time design. An aircraft digital command augmentation system is included as a sample design.