Linear Quadratic Design Research Articles

An Objective Holographic Feedback Linearization Based on a Sliding Mode Control for a Buck Converter with a Constant Power Load

As a typical load, the constant power load (CPL) has negative impedance characteristics. The stability of the buck converter system with a mixed load of CPL and resistive load is affected by the size of the CPL. When the resistive load is larger than the CPL, the buck converter with the output voltage as an output function is a non-minimum phase nonlinear system, because its linear approximation has a right-half-plane pole. The non-minimum phase characteristic limits the application of many control techniques, but the objective holographic feedback linearization control (OHFLC) method is a good control strategy that can bypass the non-minimum phase system and make the system stable. However, the traditional OHFLC method, in designing the controller, generally uses a linear optimal quadratic design method to obtain a linear feedback control law. It requires a state quantity component with a one-order relative degree to the system. But it is not easy to find such a suitable state quantity with a one-order relative degree to the system. In this paper, an improved OHFLC method is proposed for Buck converters with a mixed loads of CPL and resistive loads, using the sliding mode control (SMC) theory to design the controller, so that the output state quantity components with different relative degrees to the system can be used in the holographic feedback linearization method. Finally, the simulation and experimental results also demonstrate that this method has the same, or even better, dynamic response performance and robustness than the traditional OHFLC method.

Optimal Sliding Mode Preview Repetitive Control for Three-Phase Z-Source Inverters

Aiming at high output voltage and obvious current fluctuation of the off grids inverters with unbalanced and nonlinear loads, a compound control strategy of sliding mode controller and optimal preview controller based on Z-source inverter (ZSI) is proposed. ZSI can boost the pressure and improve the system energy conversion rate through by combining the state with the linear quadratic design method of optimal control. The preview controller is introduced in the feedforward compensation link. With the help of difference operator, an extended state error system covering the target value signal and lag link feedback is designed. The optimal preview repetitive control (PRC) is transformed into a linear quadratic regulation matter of the discrete systems. Furthermore, a preview repetitive controller is obtained by using the Lyapunov method, linear matrix inequality, and the design method of optimal controller, which can realize sliding mode control, state feedback, repetitive control, and preview compensation. Finally, a 10 kV A prototype is built to verify the effectiveness of the proposed strategy.

Adaptive Compensation of Persistent Actuator Failures Using Control-Separation-Based LQ Design

Persistent actuator failures can cause uncertain system dynamics mutation including minimum and nonminimum phase switching, which motivates us to develop a robust adaptive control scheme using a control-separation-based linear quadratic (LQ) design. It is shown that such a system can be expressed by a parameterized time-varying input–output model plus an actuator failure dependent signal and a persistent signal which captures the effect of the system dynamics mutation. A control-separation LQ design has the specific desired functions for output regulation and failure compensation as well, and is applied and analyzed for solving the persistent actuator failure compensation problem. Both nominal control design for system known and adaptive control design for system unknown are developed. The desired control performance is ensured by a robust adaptive control technique and is fully characterized in terms of a small in the mean output regulation, that is, the mean value of the system output is bounded by the average number of actuator failures over time and the average actuator failure value. Such desired system performance is shown by a complete analytical study and demonstrated by an illustrative simulation study.

Centralized and Distributed Linear Quadratic Design for Flight Formations

This paper focuses on the analysis of the particularities of control for multi-agent systems. The design method is based on an optimal control approach which requires the solution of Linear Quadratic Regulator problem (LQR). The characteristics of the two types of control (centralized and distributed) for unmanned aerial vehicles flight formations are highlighted by the case studies. The dynamics of an UAV (Unmanned Aerial Vehicle) is used for the longitudinal motion. The flight formation considered as a case study consists of four identical agents.

Robustness evaluation and robust design for proportional-integral-plus control

ABSTRACTProportional-integral-plus (PIP) control provides a logical extension to conventional two- or three-term (proportional-integral-derivative) industrial control, with additional dynamic feedback and input compensators introduced when the process has second order or higher dynamics, or time delays. Although PIP control has been applied in a range of engineering applications, evaluation of closed-loop robustness has generally relied on empirical methods. In the present article, expressions for the norm of two commonly used PIP control implementations, the feedback and forward path forms, are used, for the first time, to quantify closed-loop robustness. It is shown that the forward path form is not robust for unstable plants. Additional expressions for the norm that encompass frequency weightings of generalised disturbance inputs are also determined. Novel analytical expressions to minimise the norm are derived for the simplest plant, while simulation results based on numerical optimisation are provided for higher order examples. We show that, for certain plants, there are (non-unique) sets of PIP control gains that minimise the norm. The norm is introduced in these cases to determine the controller that balances performance with robustness. Finally, the norm is used as a design parameter for a practical example, namely control of airflow in a 2 m by 1 m by 1 m forced ventilation chamber. The performance of the new PIP controller is compared to previously developed PIP controllers based on pole placement and linear quadratic design.

Optimal tracking control for a class of boundary controlled linear coupled hyperbolic PDE systems: Application to plug flow reactor with temperature output feedback

This work addresses an optimal linear quadratic (LQ) boundary output regulator design problem for the plug flow reactor described by hyperbolic partial differential equations (PDEs), with actuation applied only at the inlet of the reactor. By applying the weak variational approach, the necessary optimality conditions are provided and then an optimal state feedback controller is presented. In particular, the time-varying state feedback gain is determined by solving Riccati-type PDEs and this work extends the linear quadratic regulator design to the class of boundary controlled hyperbolic PDE systems. Along the line of the LQ design, an optimal boundary tracking regulator is designed such that the output of the considered reaction process tracks the desired reference signal generated by an exosystem. A simulation example is included to show performance of the proposed approach.

Towards probabilistic synchronisation of local controllers

ABSTRACTThe traditional use of global and centralised control methods fails for large, complex, noisy and highly connected systems, which typify many real-world industrial and commercial systems. This paper provides an efficient bottom-up design of distributed control in which many simple components communicate and cooperate to achieve a joint system goal. Each component acts individually so as to maximise personal utility whilst obtaining probabilistic information on the global system merely through local message-passing. This leads to an implied scalable and collective control strategy for complex dynamical systems, without the problems of global centralised control. Robustness is addressed by employing a fully probabilistic design, which can cope with inherent uncertainties, can be implemented adaptively and opens a systematic rich way to information sharing. This paper opens the foreseen direction and inspects the proposed design on a linearised version of coupled map lattice with spatio-temporal chaos. A version close to linear quadratic design gives an initial insight into possible behaviours of such networks.

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

ABSTRACTIn this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.

A Linear Quadratic Integral Design Approach for the Automatic Control System of a Launch Vehicle

This paper presents a design approach for the automatic flight control system of a launch vehicle using a linear quadratic integral technique together with a fixed gain Kalman filter. Its purpose is to analyse the stability and tracking robustness performances of the control system designed via this approach when atmospheric disturbances, modeling uncertainties and structural flexible modes of the launcher are taken into account.

Optimal LQ feedforward tracking with preview: Practical design for rigid body motion control

For reference-tracking motion control, preview-based linear quadratic (LQ) design methods provide an effective means to balance tracking performance with available actuation capacity. This paper considers a control structure for which the optimal feedforward controller is independent of the feedback controller. In this way, explicit implementation formulas for feedforward controllers are derived that can be applied to a range of rigid-body motion systems. Key aspects of the optimal LQ solutions are identified, particularly how the choice of design weightings affect steady-state error for polynomial tracking. A redesign procedure for finite preview-time is proposed that preserves exact polynomial tracking properties and control bandwidth of the optimal solutions. Comparative experimental results are presented for a motor-driven linear motion stage.

Disturbance Elimination of Buck-Converter with Resonant LPF via ILQ Servo-System

The proposed optimal control on the basis of both current and voltage of the buck-converter is designed to be based on Inverse Linear Quadratic (ILQ) design method with the resonant low pass filter, which eliminates the disturbance by appended disturbance compensator. The designed scheme is composed of the state equation, an optimal ILQ solution, the ILQ servo-system with the disturbance elimination, the optimal basic gain, the optimal condition, the transfer functions and the disturbance compensator. Our results show the proposed strategy is the stability and robust control and has been made to improve ILQ control for the disturbance elimination of the output response, which guarantees the optimal gains on the basis of polynomial pole assignment.

Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.

Application of adaptive controllers to a DC-motor

This paper presents the application of adaptive control strategy to a separately excited DC motor SEDCM. An experimentally validated physical model for the SEDCM is first presented. Recursive identification of this model structure is carried out using a single-input single-output SISO parameter estimation algorithm to obtain an equivalent discrete-time state space model of the SEDCM system. Linear quadratic Gaussian LQG design is implemented on the estimated model with the objectives of reference tracking and disturbance rejection. Simulation studies are presented to demonstrate the effectiveness of the proposed scheme.

LQG Servo Controller for the Current Control of $LCL$ Grid-Connected Voltage-Source Converters

This paper presents a current control scheme for a voltage-source converter connected to the grid through an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$LCL$</tex></formula> filter. The proposed current control is based on the linear quadratic (LQ) Gaussian (LQG) servo controller technique, which combines the LQ regulator and the Kalman filter (KF). The use of the KF instead of a Luenberger estimator improves the quality of the estimation of state variables in noisy environments, increasing the noise immunity of the control loop. This paper focuses on giving some criteria and practical hints to choose both the KF and LQ design parameters to achieve null steady-state tracking error, channel decoupling, and noise immunity. Furthermore, this paper analyzes the steady-state KF approximation that allows a significant decrement in the computational complexity of the algorithm at nearly no cost in accuracy. Simulation and experimental results prove the correct operation of the proposed LQG current control and the possible advantages of using KF to estimate the state vector.

Intermittent tapping control

Control using a sequence of ‘taps’, in contrast to the usual smooth control, is shown to fit within the established intermittent control framework. In particular, a specially designed generalised hold gives rise to tapping behaviour optimised according to the underlying linear-quadratic design. Both fixed-interval and event-driven tapping are included in this approach and some basic stability analysis is given. Illustrative examples are presented and the advantages of tapping in the context of electromechanical servo systems with friction are explored using a laboratory experiment.

Optimal control of UPFC for load flow control and voltage flicker elimination and current harmonics elimination

Recent advances in the power system handling capabilities of static switches have made the use of the voltage source inverter (VSI) feasible at both transmission and distribution levels. Most of the control schemes introduced were designed either for eliminating current harmonics or eliminating voltage flickers or for load flow control. They are mostly based on the PI controller. None of these control schemes were based on a systematic optimal control law that can control the converters to achieve all purposes at the same time, load flow control, voltage flicker elimination and also current harmonics elimination. This paper presents three novel control strategies: optimal control with tracking according to desired steady-state behaviour, optimal control with linear quadratic tracker design, and optimal control with tracking with PI controllers. The strategies were tested using a power system distribution model. The presented results show that all three control strategies improve the performance of the load flow and eliminate the current harmonics and voltage flicker. The controller design based on the desired steady-state behaviour is superior compared to other way of designs as the low value of the weighting matrix Q is satisfactory to obtain the desired tracking.

Progressive accommodation of parametric faults in linear quadratic control

In this paper, a strategy based on the linear quadratic design, which progressively accommodates the feedback control law, is proposed. It significantly reduces the loss of performance that results from the time delay needed by fault accommodation algorithms to provide a solution. An aircraft example is given to illustrate the efficiency of progressive accommodation.

Optimal control of multirate sampled-data feedback systems via a polynomial approach

The linear quadratic Gaussian design of multirate-sampled multivariable feedback systems using input-output models is described. The theoretical emphasis is placed upon the formulation of augmented representations in which each variable is specified at its associated sample instants throughout one cycle of the sequence of sampling operations. The structures of the polynomial matrices utilised illuminate the causality issues involved and facilitate the acquisition of the optimal control solution from coupled diophantine equations.

Design Method of ILQ Servo System with Tracking Robustness

A robustness problem of output trajectories is considered here in the design of servo systems. Our purpose is to design a robust servo system with tracking robustness in that its output trajectory remains in a neighborhood of the nominal trajectory when the dynamics of the system is perturbed. For this purpose we propose a control configuration of robust servo system with a conditional feedback. In this configuration the robust servo system is designed by the Inverse Linear Quadratic (ILQ) design method as proposed by the second author, and the conditional feedback is added to achieve tracking robustness of the output response. First, we state the configuration of this servo system, called Model Reference ILQ (MR-ILQ) servo system, and then provide a theoretical basis for parameter tuning. Second, we clarify the relation between these parameters and the closed loop performances such as robust stability and tracking robustness. Finally, we establish a new design method of ILQ servo system with tracking robustness. We also illustrate a numerical example to show the validity of our results.

Reliable control design using a two-stage linear quadratic reliable control

Two-step linear quadratic optimal control update equations and a sequential gain updating scheme are used to design a reliable guaranteed cost discrete-control system called two-stage linear quadratic reliable control (TSLQRC). Using this method reliable linear quadratic design results for continuous-time systems can be easily extended to discrete-time systems. The stability and performance gain margins of the TSLQRC are evaluated to show the connections between the continuous-time and the discrete-time designs.