Nominal Plant Research Articles

Design of suboptimal robust controllers under unknown weights of perturbations

In the classical formulations of the problems of design of the robust optimal controllers, the equations of the nominal plant and the weights of the permissible perturbations are assumed to be known. In the present paper, consideration was given to a nonclassical formulation of the design problem where the weights of perturbations are assumed to be unknown and subject to estimation from the measurement data. The multivariable discrete-time controlled plant was described by a given transfer matrix with perturbations in the irreducible factors and a bounded external perturbation. The problem of determination with a predefined accuracy of the perturbation weights that are best coordinated with the measurements and of their corresponding suboptimal controller was solved.

Active control vibration isolation using dynamic manifold

A robust controller for multi-degree-of-freedom active vibration isolation accounts for plant uncertainties and payload disturbances using frequency-shaped sliding control. Modal decomposition is used to rewrite a multi-degree of freedom vibration control problem as a combination of individual modal control problems in modal coordinates. Modal parameters for decomposition and modelling can be extracted from theoretical or experimental modal analysis. The target frequency-domain performance of isolation, for example a skyhook model, is recast as a frequency-shaped sliding surface. Boundary layer approximation is examined. The ideal skyhook effect can be robustly achieved. The frequency-shaped manifold is also extended to adaptive vibration isolation without model reference, which has been verified by experiments, and demonstrated to be very effective for vibration isolation. Nonlinear target dynamics of the same order as the nominal plant can also be attained. Control can be achieved without measuring the excitation, such as ground motion. Further, performance during the transient stage can be guaranteed. Also, control can be achieved even without knowing the values of entries for mass, stiffness and damping matrices. The methods of controller design can be used to design control for plants subject to disturbances other than only vibration. The plant can be mechanical, electrical, thermal, or any that can be described by system equations that are mathematically of the same character as are those that describe mechanical dynamic systems. The target dynamics need not be skyhook dynamics, but can be any dynamics desired, even non-linear.

ANALYSIS AND SYNTHESIS OF DISTURBANCE OBSERVER AS A TOOL FOR NONLINEAR ROBUST CONTROL

Linear disturbance observer (DOB) approach has been successfully employed as a tool for robust control and disturbance rejection in the industry. While it is widely used, little has been done to develop the underlying theory. Motivated by this, we have analyzed the linear DOB in the state-space framework, and have derived a necessary and sufficient condition for robust stability. The lessons from it then lead to a new DOB structure for nonlinear systems in this paper. The proposed nonlinear DOB is a semi-global output-feedback inner-loop controller, which works in harmony with a (pre-designed) nominal outer-loop controller of any type. In particular, we prove that the proposed nonlinear DOB recovers not only the steady-state performance but also the transient performance of the nominal plant under plant uncertainties and input disturbances.

Design of Low Order Robust Controllers for a VSC HVDC Power Plant Terminal

This paper describes the design of controllers for a Voltage Source Converter High Voltage Direct Current (VSC HVDC) power terminal, a MIMOpl ant that must operate over a wide range and that experiences disturbances due to Pulse Width Modulation (PWM) switching. The controllers are designed using two approaches: the Glover–McFarlane loop shaping procedure (LSDP), and a novel implementation of a multiple operating point version of the LSDP using the ellipsoidal set approach, in which low order controllers are obtained using an iterative sequence of LMI programs and a convexifying potential function formulation. The LSDP provides controllers that give robust performance in the neighborhood of the nominal plant but poorer behavior at distant operating points. The novel approach is demonstrated to be practical on a rigorous plant model including the switching behavior. Both full and low order controllers are designed whose overall behavior is better than that of the standard LSDP.

Variable-Gain Controllers for Nonlinear Systems Using the T–S Fuzzy Model

This correspondence proposes two novel control schemes with variable state-feedback gain to stabilize a Takagi-Sugeno (T-S) fuzzy system. The T-S fuzzy model is expressed as a linear plant with nonlinear disturbance terms in both schemes. In controller I, the T-S fuzzy model is expressed as a linear plant around a nominal plant arbitrarily selected from the set of linear subsystems that the T-S fuzzy model consists of. The variable gain then becomes a function of a gain parameter that is computed to neutralize the effect of disturbance term, which is, in essence, the deviation of the actual system dynamics from the nominal plant as the system traverses a specific trajectory. This controller is shown to stabilize the T-S fuzzy model. In controller II, individual linear subsystems are locally stabilized. Fuzzy blending of individual control actions is shown to make the T-S fuzzy system Lyapunov stable. Although applicability of both control schemes depends on the norm bound of unmatched state disturbance, this constraint is relaxed further in controller II. The efficacy of controllers I and II has been tested on two nonlinear systems.

Enhanced disturbance suppression in sampled-data systems and its application to high density data storage servos

Precise servo control systems require strong disturbance rejection capabilities for accurate positioning in the nanometer scale world today. In this paper, we propose an add-on DDO (disturbance decoupling observer) and DDOS (DO with extraneous sensor) for stronger disturbance suppression. Our proposed control methodology uses a nominal plant model and its inverse to reject input and output disturbances simultaneously in sampled-data systems. The plant inverse controller is approximated by tuning a single parameter ɛ. Experimental results on a PZT actuated servo system with air flow of mean speed of 50 m/s corresponding to 15,000 rpm in today’s high end hard disk drives show an improvement of 69.2% of 3σ PES (position error signal) during track-following.

A comparison of multirate robust track-following control synthesis techniques for dual-stage and multisensing servo systems in hard disk drives

This paper presents the system modeling, design, and analysis of multirate robust track-following controllers for a dual-stage servo system with a microelectromechanical systems (MEMS) microactuator (MA) and an instrumented suspension. A generalized model is constructed which includes a nominal plant, disturbances, uncertainties, and multirate sensing and control. Two major categories of controller design methodologies are considered. The first includes synthesis methodologies that are based on single-input single-output (SISO) design techniques, and includes the sensitivity decoupling (SD) and the PQ methods. In this case, a high sampling-rate inner loop damping control is first implemented using the auxiliary sensor signals. Subsequently, a low-rate outer loop controller is designed for the damped plant using either the SD or PQ design methods. The second category of design methodologies includes those based on multirate, multi-input multi-output (MIMO) design techniques, including mixed H/sub 2//H/sub /spl infin//, mixed H/sub 2///spl mu/, and robust H/sub 2/ synthesis. In this case, a set of controllers, which is periodically time-varying due to multirateness, is designed by explicitly considering plant uncertainty and hence robust stability. Comparisons are made between all the design techniques in terms of nominal H/sub 2/ performance, robust stability, and robust performance between these controllers, when the feedback controller is closed around the full order, perturbed plant. The advantages and disadvantages of each of these methods are discussed, as well as guidelines for their practical implementation.

Improved quantitative feedback theory technique and application to three-axis hydraulic simulator

In order to meet tracking performance index of three-axis hydraulic simulator, based on classical quantitative feedback theory (QFT), an improved QFT technique is used to synthesize controller of low gain and bandwidth. By choosing a special nominal plant, the improved method assigns relative magnitude and phase tracking error between system uncertainty and nominal control plant. Relative tracking error induced by system uncertainty is transformed into sensitivity problem and relative tracking error induced by nominal plant forms into a region on Nichols chart. The two constraints further form into a combined bound which is fit for magnitude and phase loop shaping. Because of leaving out pre-filter of classical QFT controller structure, tracking performance is enhanced greatly. Furthermore, a cascaded two-loop control strategy is proposed to heighten control effect. The improved technique's efficacy is validated by simulation and experiment results.

Observer-based nonlinear control of a torque motor with perturbation estimation

This paper presents an observer-based nonlinear control method that was developed and implemented to provide accurate tracking control of a limited angle torque motor following a 50Hz reference waveform. The method is based on a robust nonlinear observer, which is used to estimate system states and perturbations and then employ input-output feedback linearization to compensate for the system nonlinearities and uncertainties. The estimation of system states and perturbations allows input-output linearization of the nonlinear system without an accurate mathematical model of nominal plant. The simulation results show that the observer-based nonlinear control method is superior in comparison with the conventional model-based state feedback linearizing controller.

05/02514 A robust damping controller for SMES using loop-shaping technique

A robust damping controller for a power system installed with super-conducting magnetic energy storage (SMES) has been designed using a simple graphical loopshaping technique. The graphical method starts by selection of a nominal plant function satisfying the robust stability and performance criterion. The variations in operating conditions from the nominal values are modeled as multiplicative structured uncertainty. The generator-SMES system has been represented with a detailed dynamic model for the control design. The robust design, with generator speed variation as the controller input, was tested for a range of operating points considering various disturbances. It is observed that the fixed parameter robust controller provides very good damping for a wide range of operating conditions. COPY; 2005 Elsevier Ltd. All rights reserved.

Projeto de controladores robustos com especificações temporais

O projeto de compensadores robustos com especificações no domínio do tempo visando ao acompanhamento do sinal de referência e a rejeição de distúrbios é discutido neste artigo do ponto de vista freqüencial. As condições de projeto são obtidas em função de modelos de referência, os quais contêm as especificações temporais associadas. Mostra-se que quanto maior for a distância entre o modelo nominal da planta e o modelo de referência a ser seguido, mais restritivas serão as condições de projeto. Os problemas podem ser formulados como casos de model matching e o procedimento proposto pode reduzir o conservadorismo normalmente associado com esse tipo de projeto. Admite-se que a planta esteja sujeita a incertezas não estruturadas e as condições de projeto são escritas na forma usual de restrições sobre o diagrama de Bode. Desta forma, ferramentas de projeto como H<FONT FACE=Symbol>¥</FONT> e LQG/LTR podem ser aplicadas. Para ilustrar o uso da metodologia proposta, considera-se como exemplo um tanque de misturas multivariável.

Multirate Adaptive Robust Control for Discrete-Time Non-Minimum Phase Systems and Application to Linear Motors

It is well known that a plant becomes non-minimum phase in discrete-time domain when the relative degree of the original continuous-time plant is greater than 2 even if the plant is minimum-phase in continuous-time domain. Thus, it was difficult to apply the conventional adaptive controllers directly to these systems. In this paper, multirate adaptive robust control (MARC) is proposed for these systems. This scheme is developed by the good combination of perfect tracking control (PTC) with multirate feedforward control which has been proposed by the first author and discontinuous projection based adaptive robust control (ARC) which has been proposed by the second author. Although the original PTC can assure perfect tracking only for nominal plant, the proposed MARC can guarantee: 1) perfect tracking for plant with parametric uncertainty and 2) overall stability even if there exist modeling error and disturbance. The proposed scheme is applied to the high-speed position control of a linear motor, and the advantages are demonstrated through experiments.

Dimensionless robust control with application to vehicles

The selection of a nominal plant model and an uncertainty representation is a central design choice for a robust controller design. In this brief, we examine the choice of both a plant model and an uncertainty representation from a dimensionless viewpoint. We develop a dimensionless representation of a linear bicycle model for vehicle dynamics that is suitable for a generalized vehicle analysis. Within such a dimensionless framework, the average of vehicle parameters becomes well defined thereby giving a nominal vehicle. Additionally, it becomes easy to develop perturbations of the vehicle model about the nominal one that reasonably encompass all production vehicles. These uncertainty bounds are then used to generate a robust controller suitable for any vehicle. Tighter uncertainty bounds result from the dimensionless analysis versus a dimensioned one and therefore provide less conservative controllers. For the purposes of demonstration, the focus of this brief is a lateral-positioning control task. The resulting control design approach is demonstrated on a scaled experimental vehicle as well as through simulations.

New analytical design of the Smith predictor controller for high-order systems

In this paper, a new analytical Smith predictor (SP) controller design method is proposed for industrial and chemical high-order systems. Firstly, by using the integral-squared-error (ISE) performance specification, the ideally optimal SP controller is analytically derived according to the nominal high-order plant model, which inevitably results in the high-order controller. Then the analytical controller reduction formulae based on the mathematical Maclaurin and Padé expansions are proposed to duplicate it in the form of a low-order controller such as the proportional-integral-derivative (PID). Hence, the difficulty of controller implementation in practice is significantly relieved without pitiful system performance degradation in comparison with many existing methods. At the same time, the control system robust stability is analysed. Accordingly, the on-line tuning rule of the single adjustable parameter of the proposed controller is provided to cope with the actual system uncertainties. Finally, several illustrative simulation examples are included to demonstrate the effectiveness of the proposed method.

Asymptotic hyperstability under unstructured and structured modeling deviations from the linear behavior

This paper deals with the asymptotic hyperstability of nominally asymptotic hyperstable linear systems in the presence of unstructured modeling errors. It is assumed that the nominal plant is linear, time-invariant and of strictly positive real transfer function with the feedback loop satisfying a Popov's type input–output time integral inequality for all time and the combination resulting in an asymptotically hyperstable closed-loop system. The current plant is assumed to be subjected, in general, unstructured deviations from its nominal behavior but then asymptotic hyperstability results are also obtained for particular structured modeling errors like time-varying linear dynamics, bilinear or delay-dependent dynamics. The key technique used for obtaining the results is to guarantee that a measure of the input/output energy of the forward current dynamics is positive and uniformly bounded for all time for certain amounts of modeling errors provided that the nominal one exhibits the same property.

A robust damping controller for SMES using loop-shaping technique

A robust damping controller for a power system installed with super-conducting magnetic energy storage (SMES) has been designed using a simple graphical loop-shaping technique. The graphical method starts by selection of a nominal plant function satisfying the robust stability and performance criterion. The variations in operating conditions from the nominal values are modeled as multiplicative structured uncertainty. The generator-SMES system has been represented with a detailed dynamic model for the control design. The robust design, with generator speed variation as the controller input, was tested for a range of operating points considering various disturbances. It is observed that the fixed parameter robust controller provides very good damping for a wide range of operating conditions.

Solar chimney power plants for high latitudes

A solar chimney system for power production at high latitudes has been designed and its performance has been evaluated. A mathematical model and a code on MATLAB platform have been developed based on monthly average meteorological data and thermodynamic cycle. The thermal performance of a 5 MW nominal power production plant at three locations in Canada, namely Ottawa, Winnipeg and Edmonton, is studied. The sloped collector field is built at suitable mountain hills, which also functions as a chimney. Then a short vertical chimney is added to install the vertical axis air turbine. The results showed that solar chimney power plants at high latitudes may have satisfactory thermal performance and produce as much as 85% of the same plants in southern locations with horizontal collector field. The overall thermal performance of these plants is a little less than 0.5%.

Graph Topologies, Gap Metrics, and Robust Stability for Nonlinear Systems

Graph topologies for nonlinear operators which admit coprime factorizations are defined w.r.t. a gain function notion of stability in a general normed signal space setting. Several metrics are also defined and their relationship to the graph topologies are examined. In particular, relationships between nonlinear generalizations of the gap and graph metrics, Georgiou-type formulae, and the graph topologies are established. Closed loop robustness results are given w.r.t. the graph topology, where the role of a coercivity condition on the nominal plant is emphasized.

THE PARAMETRIZATION OF ALL ROBUST STABILIZING REPETITIVE CONTROLLERS

In this paper, we investigate the parameterization of all robust stabilizing repetitive controllers for single-input/single-output continuous time non-minimum phase systems. The repetitive control system is a type of servo mechanism designed for a periodic reference input. When repetitive control design methods are applied to real systems, the influence of uncertainties in the plant must be considered. In some cases, the uncertainties in the plant make the repetitive control system unstable, even though the controller was designed to stabilize the nominal plant. The stability problem with uncertainty is known as the robust stability problem. Several papers to design robust stabilizing repetitive control systems have been published. However the parametrization of all robust stabilizing repetitive controllers has not been considered. In this paper, we propose the parametrization of all robust stabilizing repetitive controllers for non-minimum phase systems. Finally, a numerical example is illustrated to show the effectiveness of the proposed parametrization.

On validating closed-loop behaviour from noisy frequency-response measurements

It is shown how noisy closed-loop frequency-response measurements can be used to obtain pointwise in frequency bounds on the possible difference between the actual closed-loop system and the closed-loop comprising a nominal model of the plant and the stabilising controller. To this end, Vinnicombe's gap metric framework for robustness analysis plays a central role. Indeed, an optimisation problem and corresponding algorithm are proposed for estimating the chordal distance between the frequency responses of the nominal plant model and a plant that is consistent with the closed-loop data and a priori information, when projected onto the Riemann sphere.