Discrete‐time polynomial systems approach to combined fault monitoring and control

The combined fault monitoring and control problem is discussed, using an H₂ optimization framework. The main aim is to investigate the frequency‐domain and pole‐zero properties of the combined control and fault estimation compensator. The solution of the LQG stochastic optimal multivariable control and fault estimation problem is obtained using a polynomial matrix systems approach. The combined control and fault estimation problem involves a performance index including the usual regulating error and control weighting terms and also fault estimation error terms. The system model includes input disturbances, reference, coloured noise signals and actuator/sensor fault signals. The proposed numerical algorithm has common polynomial terms, so that the computation of the fault estimates and control law, is not significantly more difficult than the calculation of the control law alone. Copyright © 2003 John Wiley & Sons, Ltd.     

Design of an optimal feedback linearizing‐based controller for an experimental flexible‐joint robot manipulator

This paper presents the design of an optimal non‐linear position tracking controller for a two‐link flexible joint robot manipulator. The controller is designed based on the concept of exact feedback linearization and LQG/LTR techniques. It is shown that the non‐linear robot model is feedback linearizable and a characterization of the set, over which the linearizing transformation is diffeomorphic, is provided. The proposed control approach reduces the number of required measurement sensors and takes into account the effects of measurement noises. A new method for computing the non‐linear state estimate is also presented. It takes advantage of the linear structure of the transformed system. Simulation results demonstrate the potential benefits of the proposed control approach in reaching the desired performance with minimum control effort. Copyright © 1999 John Wiley & Sons, Ltd.     

Reduced‐order LQG/LTR procedure for the plant output side

It is commonly believed that reduced‐order observers, including reduced‐order Kalman filters, cannot be used in the loop transfer recovery (LTR) design of the plant output side. In contrast to common understanding, we show that, at least for nonminimum‐phase plants, the reduced‐order Kalman filter can be used in the linear‐quadratic‐Gaussian (LQG)/LTR design of the plant output side with clear meaning in systems theory. The key concept is to regard a reduced‐order Kalman filter as a high‐gain full‐order Kalman filter. For the reduced‐order LQG controller, we examine the asymptotic property achieved by applying the recovery procedure used in the full‐order LQG/LTR design. Using the equivalent full‐order Kalman filter, we find that the sensitivity property of the reduced‐order LQG controller is asymptotically equivalent to that of a high‐gain partial output injection system. Motivated by this result, we propose the reduced‐order LQG/LTR procedure taking the high‐gain partial output injection system as a target. Some target properties are discussed to clarify the difference from the full‐order design. A multivariable design example is presented to show that the procedure provides a systematic design of a reduced‐order controller with optimality consideration.     

Robust satisfactory fault‐tolerant control of continuous‐time interval systems with time‐varying state and input delays

With the performance constraints on exponential stability, H_∞ norm of disturbance attenuation and upper bound of quadratic cost performance, the satisfactory and passive fault‐tolerant control problem is investigated for a class of interval systems with time‐varying input and state delays in the case of possible actuator faults. The bounded‐varying dynamics of actuator faults is described by interval matrix, which is more general and can be dealt with by the interval system theory. The delay‐dependent satisfactory fault‐tolerant controller design is developed based on multi‐objective optimization strategy. The results are derived in the forms of linear matrix inequalities, which is convenient to be solved in practice. Simulative example is presented to illustrate the effectiveness and necessity of the proposed fault‐tolerant control strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

Sensorless DC motor drive via optimal observer‐based servo control

This paper proposes an alternative design of a sensorless DC motor drive via optimal observer‐based servo control. Without the speed sensor, the extended Luenberger observer is implemented to estimate the rotor speed of the DC motor in the presence of the disturbance torque. With this knowledge of the speed estimated from the observer, the servo state‐feedback controller can drive such a rotor speed to follow the desired one. The stability and performance of the DC drive system can be guaranteed by the optimal control which minimizes the H₂ norm of the closed‐loop feedback control and observer system. The simulation and experiment studies are demonstrated for the effectiveness of the proposed control methodology in a practical approach for the sensorless DC drive. Copyright © 2002 John Wiley & Sons, Ltd.     

Reduced‐order observer‐based fault estimation and fault‐tolerant control for a class of discrete Lipschitz nonlinear systems

This paper addresses an issue on reduced‐order observer‐based robust fault estimation and fault‐tolerant control for a class of uncertain nonlinear discrete‐time systems. By introducing a nonsingular coordinate transformation, a new nonlinear reduced‐order fault estimation observer (RFEO) is proposed with a wide application range in order to achieve an accurate estimation of both states and faults. Next, an improved algorithm is given to obtain the optimal estimation by using a novel iterative linear matrix inequality technique. Furthermore, an RFEO‐based output feedback fault‐tolerant controller, which is independent of the RFEO, can maintain the stability and performance of the faulty system. Simulation results of an aircraft application show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust internal model‐based LQG design for active noise control of a one‐dimensional acoustic duct system

A control design method is proposed to design controllers to achieve global sound pressure attenuation for noise of narrow‐band frequencies in a one‐dimensional acoustic duct system. This method combines a linear‐quadratic‐gaussian (LQG) theory with an internal model principle to design internal model‐based active noise controllers so that noise of a specific (target) frequency in a duct can be reduced. The designed controller is, nevertheless, hyper sensitive to the perturbation of the target noise frequency. A reduced parameter sensitivity technique is further incorporated to improve robustness such that noise of narrow‐band frequencies can be attenuated. Computer simulation shows the effectiveness of robustness improvement for the proposed design method. In addition, global sound pressure attenuation along the duct is achieved. Experimental results also demonstrate frequency robustness improvement and global sound pressure attenuation despite the fact that the dynamic effects of the actuator are not considered in the control design. Both simulation and experimental results support the feasibility of the proposed design method. Copyright © 1999 John Wiley & Sons, Ltd.     

Adaptive rejection of unmatched input disturbances for output tracking using a control separation LQ method

In this paper, an adaptive disturbance rejection scheme is developed for output tracking of multivariable nonminimum‐phase systems in the presence of uncertain unmatched input disturbances. Using a new cost function, a control separation–based LQ control framework is established for desired disturbance rejection and output tracking. The finite‐time and infinite‐time control separation–based LQ solutions are derived in an explicit composite controller structure, which has enhanced disturbance compensation and output tracking properties, as compared with a traditional LQ solution. An adaptive parameter update algorithm is used for estimation of uncertain disturbances, based on which an adaptive control separation–based LQ control solution is developed for plants in the presence of uncertain disturbances. Simulation results are presented to verify the desired adaptive disturbance rejection control system performance.     

Modified whale optimization algorithm for fractional‐order multi‐input SSSC‐based controller design

In this paper, the design of a fractional‐order (FO) multi‐input–single‐output (MISO)–type static synchronous series compensator (SSSC) is proposed with a goal to improve the power system stability using modified whale optimization algorithm (MWOA). The proposed MWOA achieves an appropriate balance between exploitation and exploration stages of the original whale optimization algorithm. The performance of MWOA is validated by employing the benchmark test functions and further contrasted with whale optimization algorithm and other heuristic algorithms like gravitational search algorithm, particle swarm optimization, differential evolution, and fast evolutionary programming algorithms to demonstrate its strength. The proposed FO MISO SSSC controller is optimized by the MWOA technique and tested under single‐machine infinite bus system and further extended to a multi‐machine framework. To demonstrate the superiority of MISO‐type SSSC controller, the results obtained from it are compared with particle swarm optimization and differential evolution–based conventional single‐input–single‐output structured SSSC controllers. The comparison of results of MWOA with that of other methods validates its superiority in the present context.     

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

This paper develops a new optimal linear quadratic observer‐based tracker with input constraint for the linear unknown system with a direct transmission term from input to measured output. The off‐line observer/Kalman filter identification method is used to determine the linear sampled‐data model with a direct feed‐through term. On the basis of this model, a high‐gain optimal linear quadratic analog observer‐based tracker is proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction‐based digital redesign method is utilized to obtain a relatively low‐gain and implementable observer and digital tracker from the theoretically well‐designed high‐gain analog observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high‐gain property to fit the requirement of the input constraint, the modified linear quadratic analog tracker is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much. Copyright © 2014 John Wiley & Sons, Ltd.     

Feasibility of disturbance-accommodating control in steering of a large tanker

The feasibility of applying disturbance-accommodating control (DAC) techniques to the problem of steering control of a large tanker in a seaway is examined. A performance criterion representative of propulsion losses related to steering is used as a basis for the design of course-keeping controllers. The development of disturbance state models to take advantage of the short-term regularity of the seaway within a DAC framework is presented. Comparisons are made between the performance resulting from the DAC approach and previous LQG approaches to the problem using computer simulation results. On this basis, it is shown that controller design within a DAC framework may be a viable alternative to existing Kalman filter estimation/control schemes used in autopilot design.     

Discrete‐time proportional and integral observer and observer‐based controller for systems with both unknown input and output disturbances

In this paper, a novel discrete proportional and integral observer is proposed for estimating the system state, input and output disturbances at the same time. Compared with the previous results, the proposed observer has an advantage in handling output disturbances. A simulated numerical example is given to demonstrate the efficiency. By using the estimates of the state and disturbance, an observer‐based controller with disturbance accommodation is designed to ensure the system stability and to satisfy the specified performance index. A simulated study of a reduced‐order gas turbine discrete model is given to illustrate the design approach, and encouraging simulation results are obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

On the synthesis of time‐varying LQG weights and noises along optimal control and state trajectories

A general approach to control non‐linear uncertain systems is to apply a pre‐computed nominal optimal control, and use a pre‐computed LQG compensator to generate control corrections from the on‐line measured data. If the non‐linear model, on which the optimal control and LQG compensator design is based, is of sufficient quality, and when the LQG compensator is designed appropriately, the closed‐loop control system is approximately optimal. This paper contributes to the selection and computation of the time‐varying LQG weighting and noise matrices, which determine the LQG compensator design. It is argued that the noise matrices may be taken time‐invariant and diagonal. Three very important considerations concerning the selection of the time‐varying LQG weighting matrices are turned into a concrete computational scheme. Thereby, the selection of the time‐varying LQG weighting matrices is reduced to selecting three scalar design parameters, each one weighting one consideration. Although the three considerations seem straightforward they may oppose one another. Furthermore, they usually result in time‐varying weighting matrices that are indefinite, rather than positive (semi) definite as required for the LQG design. The computational scheme presented in this paper addresses and resolves both problems. By two numerical examples the benefits of our optimal closed‐loop control system design are demonstrated and evaluated using Monte Carlo simulation. Copyright © 2005 John Wiley & Sons, Ltd.     

A partitioning approach for H∞ control of singular time‐delay systems

This paper presents a new approach for delay‐dependent H_∞ stability analysis and control synthesis for singular systems with delay. By constructing an augmented Lyapunov–Krasovskii functional with a triple‐integral term, and using the partitioning technique, a bounded real lemma is presented to ensure the singular state‐delay system to be regular, impulse free and stable with γ‐disturbance rejection. The proposed result leads to significant performance improvement in system analysis and synthesis. Based on the criterion obtained, a homotopy‐based iterative LMI algorithm is developed to design a static output feedback controller. The feasibility and the effectiveness of theoretical developments are illustrated through numerical examples.Copyright © 2012 John Wiley & Sons, Ltd.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

High‐order observers‐based LQ control scheme for wind speed and uncertainties estimation in WECSs

Tip speed ratio control is a popular method in wind energy conversion systems in order to capture the maximum power. This method, however, requires wind speed information, which is difficult in practice to accurately measure it. Therefore, estimation methods are usually applied, where a high‐precision estimate leads to a high‐efficient system. Based on the fact that the wind speed varies in a random way, this paper proposes a generalized high‐order observer to estimate the aerodynamic torque and the wind speed accordingly. This observer algorithm releases the assumption that the wind speed should be slowly varying, which is required in previous observer designs. Moreover, two other generalized high‐order observers are also applied to estimate the uncertainties, which depend on state variables and cannot be considered as slow‐varying disturbances. Using the outputs of these observers, a robust high‐performance optimal control system is developed for the rotor speed to keep the optimal tip speed ratio. The stability analysis of the designed control system is fully presented. The effectiveness of the proposed technique is validated via simulation studies.     

Control‐relevant parameter estimation application to a model‐based PHEV power management system

Explicit model predictive control approach is a promising approach to fulfill automotive real‐time controls requirements. A key factor in the performance and real‐time capabilities of a predictive model‐based controller is the accuracy of the control‐oriented model. The control‐oriented model should capture the essential dynamics of the real plant and be adequately simple to make the controller implementable on a commercial hardware with limited memory and computational capabilities. In this study, control‐relevant parameter estimation is used to find a control‐oriented model for a real‐time predictive power management system for a plug‐in hybrid powertrain. Simulations, which are conducted using an equation‐based model of the powertrain, demonstrate a significant improvement of the power management system performance by improving the control‐oriented model with no effect on real‐time capabilities of the controller.     

Model predictive and linear quadratic Gaussian control of a wind turbine

Model Predictive and linear quadratic Gaussian controllers are designed for a 5MW variable‐speed pitch‐regulated wind turbine for three operating points – below rated wind speed, just above rated wind speed, and above rated wind speed. The controllers are designed based on two different linear dynamic models (at each operating point) of the same wind turbine to study the effect of utilising different control design models (i.e. the model used for designing a model‐based controller) on the control performance. The performance of the LQG controller is enhanced by improving the robustness, achieved by replacing the Kalman filter with a modified Luenberger observer, whose gain is obtained to minimise the effect of uncertainty and disturbance. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust reliability method and reliability‐based performance optimization for non‐fragile robust control design of dynamic system with bounded parametric uncertainties

An efficient robust reliability method for non‐fragile robust control design of dynamic system with bounded parametric uncertainties is presented systematically, in which the uncertainties existing in the controlled plant and controller realization are taken into account simultaneously in an integrated framework. Reliability‐based design optimization of non‐fragile robust control for parametric uncertain systems is carried out by optimizing the H₂ and H_∞ performances of the closed‐loop system, with the constraints on robust reliabilities. The non‐fragile robust controller obtained by the presented method may possess a coordinated optimum performance satisfying the precondition that the system is robustly reliable with respect to the uncertainties existing in controlled plant and controller. Moreover, the robustness bounds of uncertain parameters can be provided. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. It is demonstrated by a numerical example that the presented method is effective and feasible. Copyright © 2016 John Wiley & Sons, Ltd.     

Euler‐Lagrange equation: Case of energy‐optimal approach for induction machine

The optimal control problem that hinges on the Euler‐Lagrange equation can be applied to electric‐machine drives and the necessary and sufficient optimality conditions around the system control and the control variables can be designed in a congruent way. In this paper, a variational problem is proposed to minimize energy consumption by an Induction Motor (IM) under a Rotor Field–Oriented Vector Drive (RFOVD) during torque and speed transients. The optimal stimulus is to take into account real applications, like perturbed load torques, and an abrupt speed input. The approach consists of an off‐line algorithm that minimizes a cost functional or integral of the weighted sum of IM energy/power under the dynamic stress of the rotor flux and of rotation speed. The variational problem leads to a nonlinear differential equation known as the Euler‐Lagrange equation. A new method is suggested to run out an analytical solution and results in a time‐varying rotor flux considered as the optimal state variable of the dynamic IM model that saves energy of the IM drive under RFOVD. This solution provides loss‐minimization in steady‐state operations at an infinite horizon and performs adaptive suboptimal minimum‐energy consumption for torque transients. Simulation and experimental results are fully performed on 1.5‐kW laboratory IM, and prove the validity of the proposed method for both steady‐state and transient‐IM drive operations.