Observer-based State Feedback Controller Research Articles

Saturation-induced limit cycles in observer-based state feedback control

Existence of saturation-induced limit cycles is studied for observer-based state feedback control systems. Two different observer based controller implementations are considered, one using the computed control signal for state estimation and the other using the control signal actually applied to the plant. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed loop stability are provided for both implementations. The condition for limit cycles is found to involve the yet unsolved problem of spectral radius characterization of the product of two matrix exponentials.

Two-Degree-of-Freedom IMC Paramertization of Multivariable Systems

This paper presents the systematic design method of two-degree-of-freedom parametrization of multivariable systems. It is shown that the four elements are required. The first one is to yield the inner-outer factorization, where the outer is low-pass filter to adjust the output response to the reference. The second is to stabilize the unstable plant and to adjust the response to the disturbance. The third is for internal stability and the last one is to yield the steady state characteristics. The design methods of them are presented. The total controllers are realized as observer-based state feedback controller.

A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems

A hybrid indirect and direct adaptive fuzzy output tracking control schemes are developed for a class of nonlinear multiple-input-multiple-output (MIMO) systems. This hybrid control system consists of observer and other different control components. Using the state observer, it does not require the system states to be available for measurement. Assisted by observer-based state feedback control component, the adaptive fuzzy system plays a dominant role to maintain the closed-loop stability. Being the auxiliary compensation, H/sup /spl infin// control and sliding mode control are designed to suppress the influence of external disturbance and remove fuzzy approximation error, respectively. Thus, the system performance can be greatly improved. The simulation results demonstrate that the proposed hybrid fuzzy control system can guarantee the system stability and also maintain a good tracking performance.

Gain-scheduled control of an electrostatic levitator

A simple gain-scheduling approach to the position control of electrostatically levitated materials is presented. An electrostatic levitator is currently being constructed at the German Aerospace Center (DLR). It can be used for containerless processing of metals and nonconducting materials. Time-varying sample charges and the fact that the plant is open-loop unstable make this a difficult and challenging control problem. The nonlinear parameter-dependent system is approximated by two local linear models. Based on these models, two local linear controllers are designed. LMI-based pole region assignment is used to reduce the design procedure to the tuning of three parameters with intuitive meaning. The sample charge is estimated with a discrete-time extended Kalman filter and used as scheduling parameter. Experimental results demonstrate that gain-scheduled control achieves a significantly better performance than fixed-gain, observer-based state feedback control.

Observer-based strict positive real (SPR) feedback control system design

This paper presents theory for stability analysis and design for a class of observer-based feedback control systems. Relaxation of the controllability and observability conditions imposed in the Yakubovich–Kalman–Popov (YKP) lemma can be made for a class of nonlinear systems described by a linear time-invariant system (LTI) with a feedback-connected cone-bounded nonlinear element. It is shown how a circle-criterion approach can be used to design an observer-based state feedback control which yields a closed-loop system with specified robustness characteristics. The approach is relevant for design with preservation of stability when a cone-bounded nonlinearity is introduced in the feedback loop. Important applications are to be found in nonlinear control with high robustness requirements.

Observer-Based Strict Positive Real (SPR) Feedback Control System Design

This paper presents theory for stability analysis and design for a class of observer-based feedback control systems. Relaxation of the controllability and observability conditions imposed in the Yakubovich-Kalman-Popov (YKP) lemma can be made for a class of nonlinear systems described by a linear time-invariant system (LTI) with a feedback-connected cone-bounded nonlinear element. It is shown how a circle-criterion approach can be used to design an observer-based state feedback control which yields a closed-loop system with specified robustness characteristics. The approach is relevant for design with preservation of stability when a cone-bounded nonlinearity is introduced in the feedback loop. Important applications are to be found in robotics (force control) and nonlinear control in hybrid control.

Fast Output Sampling Regulators with Integral Action

Fast output sampling controllers have been proposed as an alternative to observer-based state feedback control, and have been demonstrated to be useful for robust controller design. Here it is shown how integral action can be incorporated into the design. An LMI-based design procedure that has been proposed recently to trade fast decay of estimation errors against low noise-sensitivity, can be used at the same time to eliminate the estimation error resulting from an additional integrator loop. The proposed design method is illustrated by a practical application: a multivariable regulator for a turbogenerator is designed and experimental results are shown.

Fault tolerant control concepts applied to anesthesia

The first application of automatic control to a physiological variable during general anesthesia was reported in 1949. Since then a lot of research has been devoted to this topic. Still, today there is no commercial anesthesia system available with the patient in a feedback loop. One reason for this is that research has mainly been focused on controller design. Important aspects of clinical practice such as the treatment of measurement artifacts and faults have only marginally been addressed. In this thesis exactly such problems which are usually tacitly neglected but which are of great relevance are addressed. We are referring to these aspects as supervisory functions. Before addressing these supervisor functions some foundations are established. This involves in the first place a hard- and software research platform that allows to implement and test control algorithms as well as the supervisory functions in the operating theater. It is our view that fault handling must start with the design of a system. Special attention is therefore paid to the selection of the platform components and the software design. The software structure is built with special emphasis on extendibility. A second foundational building block is a mathematical model which describes the dynamic relationship between vaporizer concentrations and surgical stimulations on the input side and the inspiratory and endtidal Isoflurane concentration as well as mean arterial pressure (MAP) on the output side. A thorough review of the physiological background is followed by a step by step development of the model equations. Modeling is finalized with the identification of the system parameters and validation experiments. Since the design of control algorithms is not the main focus, controllers are taken form a thesis by Marco Derighetti. They are refined for broader applicability where necessary. The result of extensive clinical validations of an observer based state feedback (OBSF) controller for the endtidal Isoflurane concentration and an OBSF with endtidal overrides for MAP are presented. In view of the limited ability of this MAP controller to compensate heavy disturbances a control scheme based on disturbance anticipation is suggested. For the supervisor functions first a structure is suggested which allows to allocate all functions postulated in literature. A selection of these is developed in more detail. First, an elegant strategy to handle measurement artifacts in the framework of OBSF controller is proposed. It is based on a nonlinear modification of the output injection gain. The stability of this algorithm is proved and recordings of several successfully suppressed artifacts are shown. A large part of the thesis is then dedicated to fault tolerant control (FTC). Following a sequential design procedure developed by Prof. M. Blanke a strategy for handling the most critical faults in the system is obtained. In this context the concept of recoverability for linear time invariant (LTI) systems is developed. This concept is utilized to analyze to what degree the functionality of a faulty system may be recovered in case of a fault. Finally, a man machine interface (MMI) is designed. Aspects of MMI are important in this context since a well designed MMI increases operational safety. The main contribution of this thesis is to show that mathematical process models are a useful tool in dealing with faults also in a biomedical environment.

Fault Tolerant Control Concepts Applied to Anesthesia

The first application of automatic control to a physiological variable during general anesthesia was reported in 1949. Since then a lot of research has been devoted to this topic. Still, today there is no commercial anesthesia system available with the patient in a feedback loop. One reason for this is that research has mainly been focused on controller design. Important aspects of clinical practice such as the treatment of measurement artifacts and faults have only marginally been addressed. In this thesis exactly such problems which are usually tacitly neglected but which are of great relevance are addressed. We are referring to these aspects as supervisory functions. Before addressing these supervisor functions some foundations are established. This involves in the first place a hard- and software research platform that allows to implement and test control algorithms as well as the supervisory functions in the operating theater. It is our view that fault handling must start with the design of a system. Special attention is therefore paid to the selection of the platform components and the software design. The software structure is built with special emphasis on extendibility. A second foundational building block is a mathematical model which describes the dynamic relationship between vaporizer concentrations and surgical stimulations on the input side and the inspiratory and endtidal Isoflurane concentration as well as mean arterial pressure (MAP) on the output side. A thorough review of the physiological background is followed by a step by step development of the model equations. Modeling is finalized with the identification of the system parameters and validation experiments. Since the design of control algorithms is not the main focus, controllers are taken form a thesis by Marco Derighetti. They are refined for broader applicability where necessary. The result of extensive clinical validations of an observer based state feedback (OBSF) controller for the endtidal Isoflurane concentration and an OBSF with endtidal overrides for MAP are presented. In view of the limited ability of this MAP controller to compensate heavy disturbances a control scheme based on disturbance anticipation is suggested. For the supervisor functions first a structure is suggested which allows to allocate all functions postulated in literature. A selection of these is developed in more detail. First, an elegant strategy to handle measurement artifacts in the framework of OBSF controller is proposed. It is based on a nonlinear modification of the output injection gain. The stability of this algorithm is proved and recordings of several successfully suppressed artifacts are shown. A large part of the thesis is then dedicated to fault tolerant control (FTC). Following a sequential design procedure developed by Prof. M. Blanke a strategy for handling the most critical faults in the system is obtained. In this context the concept of recoverability for linear time invariant (LTI) systems is developed. This concept is utilized to analyze to what degree the functionality of a faulty system may be recovered in case of a fault. Finally, a man machine interface (MMI) is designed. Aspects of MMI are important in this context since a well designed MMI increases operational safety. The main contribution of this thesis is to show that mathematical process models are a useful tool in dealing with faults also in a biomedical environment.

Explicit Parametric Solution to Observer-Based Control of Self-Sensing Magnetic Bearings

This paper is concerned with the control of a position-sensorless, voltage-controlled active magnetic bearing system using a full-order observer-based state feedback controller. Using the eigenstructure assignment technique, explicit parametric formulae in direct closed forms are proposed for the state feedback gain K and the observer gain L, as well as the eigenvectors of the state feedback control system and the observer system. These formulae are in terms of the system physical parameters and the controller and observer poles. Applications of these formulae in some robustness issues are discussed.

Observer-based approach for controlling chaotic systems

This paper presents a nonlinear state observer for a class of nonlinear systems which have an output dependent nonlinearity. By the observer design scheme proposed herein, an observer-based linear state feedback control approach is then derived to stabilize this class of systems. Analysis results indicate that both error dynamics and the subsequent closed-loop system can be made exponentially stable. The control strategy is also applied to two well-known chaotic systems: R\"ossler chaos and Lorenz chaos. Numerical simulations demonstrate the effectiveness of the proposed scheme.

An observer-based state feedback control of parametrically excited systems

In the study of adaptive parameter identification, the parameter error dynamics resulting from the gradient algorithm represents a very special class of parametrically excited system, whose stability condition has been studied thoroughly. By utilizing this stability condition, one can develop a new active control design for a parametrically excited system which exhibits sustained but bounded oscillations due to the time-varying system matrix. The resultant observer-based state feedback control guarantees exponential decay of the state oscillation given that the system is both uniformly controllable and uniformly observable. The advantage of the proposed design is that it requires neither information of time derivatives of the parametric excitations, nor predicting future information of the parametric excitations.

Äquivalenz zwischen Ausgangsund beobachtergestützter Zustandsrückführung - Eine allgemeine Form des Separationsprinzips

This paper demonstrates that an output stabilizing controller can be equivalently presented by an observer-based state feedback controller. This result can be considered as a general form of the separation principle.

An integrated control/diagnostic system for a hard disk drive

This paper describes the implementation of an integrated control/diagnostic system for an advanced hard disk drive (HDD) servo system. An observer-based state feedback control design with the pole placement technique has been successfully applied to achieve a bandwidth of 688 Hz, which is quite satisfactory at a 4.5 kHz sampling frequency. Experimental results indicate, however, that the performance of this high precision, high-order control system deteriorates seriously when faults occur. Therefore, a fault identification filter (FIDF) was adopted for fault detection of sensor and actuator failures and accommodation of the actuator failure. In cases where either sensor or actuator fault occurs, experimental results indicate that to maintain high precision and control performance for the HDD system, DSP implementation of the high-order integrated control/diagnostic system is necessary.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design of reduced-order observers with precise loop transfer recovery

This paper concerns the design of reduced-order observers for systems in which the number of measurements is more than the number of controls. We develop an algorithm that applies to regular systems that have no transmission zeros. The algorithm uses eigenstructure assignment whereas other approaches use Kalman filter methods. The advantages of this approach are the following: 1) precise loop transfer recovery rather than approximate loop transfer recovery, 2) finite observer gain rather than asymptotic observer gain, and 3) modest computational tools and operations counts. Case studies are presented illustrating these features. T HE problem of designing an observer that can achieve loop transfer recovery (LTR) has received continuous at- tention since Doyle1 presented an example with a Kalman-fil- ter-based observer (linear quadratic Gaussian (LQG)) design lacking robustness even though the full-state feedback (linear quadratic regulator (LQR)) controller had impressive robust- ness properties, namely gain margins of - 6 dB to + oo dB and phase margins of ±60 deg.2 To alleviate this problem, Doyle and Stein3 developed a robustness recovery procedure in which fictitious process noise is added to the input in the design model. The LQR robustness properties are preserved with the loop open at the input since the loop transfer function is re- covered asymptotically as the intensity of the fictitious pro- cess noise is increased. Stein and Athans4 call this procedure LQG/LTR. There have been further developments and appli- cations of LQG/LTR by a number of workers. Madiwale and Williams5 extended the theory to reduced-order observer- based LQG designs for nonsquare, minimum phase, and left invertible plants. Calise and Prasad6 developed an approach for designing a fixed-order compensator and obtained an ap- proximate LTR for nonsquare, minimum phase systems. It is similar to the full-order compensator design of ordinary LQG/ LTR. Fu7 developed the necessary and sufficient condition for exact LTR employing a general feedback structure for model matching control that includes the observer-based state feedback control as a special case. He formulated the prob- lem of model matching by assigning certain stable matrices such that the desired loop transfer function became equal to the associated loop transfer function of the closed-loop input- output transfer function. He claimed that exact LTR is achiev- able under the conditions for strong stabilization of systems. Tsui8'9 introduced a theoretical analysis of an entirely new approach to the problem of loop transfer recovery. His ap- proach was to minimize the observer gain to the system input by observer pole selection. Furthermore, he claimed that this new approach aimed directly at achieving the necessary and sufficient condition of LTR. The purpose of this paper is to present a computational algorithm for the solution of the constrained matrix Sylves- ter equation that arises in Tsui's approach for designing ro- bust reduced-order Luenberger observers.10 Precise LTR is achieved with finite observer gain for regular nonsquare plants with no transmission zeros, for which the number of sensors is greater than the number of controls. Other approaches have been unable to attain these results. The method developed here provides freedom to select eigenvalues and eigenvectors for the observer.

Robust Control Design for Linear Systems with Structured Uncertainty

Abstract This paper presents a linear robust control design algorithm for linear deterministic uncertain systems whose parameters vary within given bounded sets. The algorithm explicitly incorporates the structure of the uncertainty into the design procedure and utilizes the elemental perturbation bounds developed recently. A linear state feed-back controller is designed by parameter optimization techniques to maximize (in a given sense) the elemental perturbation bounds for robust stabilization. The design algorithm is then extended to the case of observer (Luenberger) based state feedback controllers and the relative trade offs are discussed.

Robust tracking for a class of uncertain linear systems

Tracking of a specified nominal output within an arbitrary error bound in the presence of uncertainties is formulated in terms of topological neighbourhoods in the function space Lκ∞ [0, ∞). It is shown that an observer-based state-feedback controller can be constructed to effect the desired robust tracking for a class of multi-input-multi-output linear systems containing uncertain parameters. The controller and the observer gains for this structure are chosen on the basis of a quantitative pole placement. This pole placement is based on an inequality arrived at by separating the uncertain effects of the true system from a nominal set of equations containing no uncertainties. The applicability of the proposed scheme is illustrated by synthesizing a controller for a second-order system.