Reduced-order State Observer Research Articles

State observer design and stabilization control for a class of nonlinear systems†

In this article, the design problems of full-order state observer, reduced-order state observer and dynamic output feedback stabilization control are investigated for a class of systems with nonlinear uncertainty. Inspired by Ha and Trinh (Automatica, 40, pp. 1779–1785, 2004), the nonlinear uncertainty is assumed to be a combination of a known Lipschitz nonlinear part and an unknown state-dependent part, on which there is no restriction, such as Lipschitz condition or monotonicity etc., imposed. The existence conditions and design methods of full-order and reduced-order state observers are obtained by means of linear matrix inequalities. Moreover, a dynamic output feedback control is constructively given to exponentially stabilize the closed-loop system. †This work was completed during the author's postdoctrol period in Academy of Mathematics and Systems Science, Chinese Academy of Science.

Delayed Observers for Linear Systems With Unknown Inputs

We present a method for constructing reduced-order state observers for linear systems with unknown inputs. Our approach provides a characterization of observers with delay, which eases the established necessary conditions for existence of unknown input observers with zero-delay. We develop a parameterization of the observer gain that decouples the unknown inputs from the estimation error, and we use the remaining freedom to ensure stability of the error dynamics. Our procedure is quite general in that it encompasses the design of full-order observers via appropriate choices of design matrices

Torsional Vibration Control of the Main Drive System of a Rolling Mill Based on an Extended State Observer and Linear Quadratic Control

In the main drive system of a rolling mill, shaft torsional vibration is often generated when a motor and a roll are connected with a flexible shaft. State feedback control can effectively suppress the torsional vibration of the main drive system of a rolling mill. Because of the difficulty of measuring the load speed and the shaft torque, and moreover the sensitivity of the Luenberger observer to the model uncertainties and the noise include in the detected signal, in this paper, we propose an extended state observer (ESO), a new observer, to estimate the unknown states and the load torque disturbance. We propose an ESO and linear quadratic (LQ) based speed controller with an integrator and load torque feedforward compensation for torsional vibration suppression in a two-mass main drive system of a rolling mill. The simulation results show the controller effectively improves the performances of command following, torsional vibration suppression, and robustness to parameter variation. This is the first time that the ESO has been utilized in torsional vibration control of the main drive system of a rolling mill, and its validity and superiority is verified in comparison with the conventional proportional integral (PI) controller and the state feedback controller based on a reduced-order state observer.

Robust mixed-norm position and vibration control of flexible link mechanisms

This paper introduces a general and practical procedure for the design of high-performance and robust control schemes for the position and vibration control of flexible link mechanisms. The procedure is developed based on a mixed H 2/ H ∞ optimization which allows trading explicitly between nominal performance and robust stability. The controller synthesis, which is iterative, is performed making use of a state–space linear model and initially assuming that the complete state of the system is available. In this phase, only the uncertainty arising from neglecting the unmodeled nonlinear dynamics is considered in order to prevent overly conservative designs. Even if a prototype of the studied mechanism is not available, a truthful definition of the uncertainty model bounds in the frequency domain can obtained by comparing the spectral responses yielded by an accurate nonlinear model, and by the linear one employed in the control design. Appropriate models are briefly described in the paper. Then, the additional uncertainty arising from discarding the spillover dynamics is taken into account by evaluating the effect on the controller robustness of the introduction of a reduced-order state observer. Simulation results prove the effectiveness of the control design method applied to a four-bar linkage with all the links flexible.

Improved Performance of Motor-Drive Systems by SAW Shaft Torque Feedback

The paper describes the application of a non-contact, high bandwidth, low cost, SAW-based torque measuring system for improving the dynamic performance of industrial process motor-drive systems. Background to the SAW technology and its motor integration is discussed and a resonance ratio control (RRC) technique for the coordinated motion control of multi-inertia mechanical systems, based on the measurement of shaft torque via a SAW-based torque sensor is proposed. Furthermore, a new controller structure, RRC plus disturbance feedback is proposed, which enables the controller to be designed to independently satisfy tracking and regulation performance. A tuning method for the RRC structure is given based on the ITAE index, normalized as a function of the mechanical parameters enabling a direct performance comparison between a basic proportional and integral (PI) controller. The use of a reduced-order state observer is presented to provide a dynamic estimate of the load-side disturbance torque for a multi-inertia mechanical system, with an appraisal of the composite closed-loop dynamics. The control structures are experimentally validated and demonstrate significant improvement in dynamic tracking performance, whilst additionally rejecting periodic load side disturbances, a feature previously unrealisable except by other, high-gain control schemes that impose small stability margins.

On parameterization design for linear observers

In this paper, the design of observers is further investigated via the parameterization technique. Two new observer parameterizations are addressed related to nonminimal reduced-order state observers. The known results in the references available can be obtained as particular results from the present parameterizations. For plants with input disturbances, parameterizations of estimation error dynamics are derived, providing useful tools for the design of robust optimal observers. An illustrative example is given for describing the parameterization procedure.

The Class of All Reduced-order State Observers

The class of all state observers for linear systems is characterized. A free parameter in observers is restricted within the ring of strictly proper stable rational functions. The order of observers is lower than the known ones by the number of output. When input disturbances exist in the plant, the resultant parameterization of estimation error dynamics is also given, which provides a tool to solve reduced-order robust estimation problem.

Shaft Sensorless Vector Controlled PMSM Servo Drive using Reduced Order Speed Observer

The application of vector control techniques in variable speed ac drives demands accurate position and velocity feed back information for the current and speed control loops. A novel method for shaft sensor elimination of the high performance PMSM servo drives is presented in this paper. A reduced order state observer is proposed to be used as a software transducer, which reconstructs the speed and position of the sinusoidal backemf PMSM from the stator current and voltage measurements. The observer is developed from the d-q model of the machine. The state estimation technique used to achieve global stability of the speed observer is discussed along with the design considerations. Since this method totally eliminates the gain scheduling, which is the major difficulty in implementing any conventional observer based scheme, the implementation of the proposed scheme is very simple and easy. The performance of the observer depends on the accuracy of the parameters in the motor model. To take into account these parameter uncertainties along with the load torque variations, a local disturbance torque observer is used. Simulation results using realistic measurement disturbances and drive parameter uncertainties are also presented to investigate the stability and accuracy of the proposed observer. The simulation results show that the proposed scheme gives good results even at near zero speeds.

Design of linear functional observers for linear systems with unknown inputs

This paper presents a reduced-order linear functional state observer for linear systems with unknown inputs. A simple observer construction procedure is provided. A numerical example is given to illustrate the properties of the observer. The example deals with a linear system comprising of 20 states, 2 inputs, 10 outputs and 5 unknown inputs for which a fourth-order observer is designed to estimate two linear functions of the states.

Self Control System of Superconducting Maglev Synchronized with the Phase of Electromotive Force

In the Yamanashi Maglev Test Line, the location of the train is detected with the inductive radio system within the deviation of 3 degrees. The inductive radio system is very reliable and accurate. However using the inductive radio system, we have to lay the cross inductive cable along the guideway and set up the detecting system of train's location in each power conversion station. Therefore the construction costs of the system is expensive. On the other hand, from the safety point of view, we have to examine the other method of detecting train's location, in case of inductive radio system down.In this paper, we propose a new train's location detecting system using the phase of Electromotive Force (EMF). In this system, the inductive radio system is not required. In the LSM drive control system, the phase locked loop (PLL) uses the phase of EMF that is estimated by EMF observer. The reduced-order state observer estimates the phase of EMF according to output voltages and currents of Inverter. We report the configuration and the basic characteristics of the EMF observer in the Yamanashi Maglev Test Line.

Distributed state observer scheme for large-scale interconnected systems

This paper presents a new reduced-order distributed state observer for large-scale interconnected systems. The proposed observer composes of two parts: a local dynamic part and a static part. The dynamic part is systematically constructed using only local information. Its order is equal to the number of unstable and/or poorly damped eigenvalues of the global system only. The static part is systematically constructed based on the knowledge of the control input to each subsystem. It is shown that local states for each subsystem can be estimated with arbitrarily chosen dynamics. A simple and systematic design method is presented. A numerical example is given to illustrate both the properties of the new observer and its design method.

A reduced-order state observer for large-scale discrete-time systems

This paper presents a novel reduced-order state observer for large-scale discrete-time systems. The dynamics of the reduced-order observer are derived based only on a set of unstable and/or poorly damped eigenvalues of the system. It is shown that arbitrarily chosen dynamics can be assigned to the observer. A simple and systematic design method is presented. A numerical example is given to illustrate the properties of the new observer and its design method.

Robust issues in exact model matching

In an ideal environment, an exact model matching (EMM) system is internally stable and the plant output follows perfectly the reference model output. In a real environment, however, there are many kinds of harmful perturbation, which cause not only tracking error but even instability for some kinds of perturbation. There are two free polynomials q ( s ) and gamma( s ), the former being the characteristic polynomial of the reduced order state observer, and the latter being an interactor of scalar version. The function of controller depends on the choice of these polynomials. Robust EMM design is defined as the proper choice of these polynomials so as to strengthen the robustness against perturbation as much as possible. It is shown that the controller function does not depend on these polynomials independently but on the product q ( s )gamma( s ). Robust EMM design is examined for each perturbation of nonzero initial conditions, input disturbance, unmodeled dynamics and incorrect implementation of controller.

Balancing and Attitude Control of Double and Triple Inverted Pendulums

The design of robust computer control systems for balancing and attitude control of double and triple inverted pendulums is considered in this paper. For the double inverted pendulum, a DC motor mounted at the upper hinge is used to balance and control attitude of the upper link. For the triple inverted pendulum a DC motor mounted at the middle hinge is used to control the middle link, whereas proportional position control applied to a motor at the upper hinge is utilised to maintain the upper link in alignment with the middle link. In both cases the lower hinge is left free to rotate. The controller designs are based on linearised discrete-time models of the inverted pendulums. Each controller utilises state feedback implemented via reduced-order state observers. The relative stability properties of the control systems are evaluated using Nyquist plots of suitably defined functions. The controllers are designed using Matlab and implemented in a PC using C language. Experimental results showed satisfactory performance.

High performance current regulator for a field-oriented controlled induction motor drive

In this paper, a novel strategy of current regulation of a field-orientation induction motor drive using the GTO inverter is proposed, which is based on a multivariable state feedback control with an integrator. The controller is designed by pole placement technique of multivariable system regulation theory. In addition, feedforward control is included in the control laws to improve transient responses. For the linear state feedback control, the rotor flux is separated as a disturbance and is estimated with a reduced-order state observer. A good steady-state performance is obtained by means of an integral compensation and symmetrical space voltage vector PWM, and fast transient response is also feasible since the required voltage is directly calculated from the feedforward control. Also, it is demonstrated that an instantaneous current control without the calculation time delay can be implemented. The excellence of the proposed current regulation scheme is verified by experiments for the GTO inverter-fed induction motor drive system controlled by a DSP-TMS320C30.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Parametric eigenvalue-eigenvector assignment in reduced-order observer design

The design of reduced-order state observers for linear multivariable systems is considered. The procedure used is based on the assignment of prespecified sets of eigenvalues and associated eigenvectors to the observer model, whereby the state estimation error is effectively governed. It is shown, in particular, that the restrictions on the assignable eigenvectors are removed when the number of system outputs equals or exceeds half the number of state variables. Moreover, with the outputs in excess of half the state variables, some design parameters remain unaffected by the assignment of both sets of eigenvalues and eigenvectors. A certain part of these additional parameters can be adjusted to alleviate the impact of misalignment between the system and the observer initial states. The remaining part contributes to the identification of the observer matrices—other than the dynamical coefficient matrix. The one-to-one correspondence between the observability of the system and the eigenvalue assignability of ...

EIGENSTRUCTURE ASSIGNMENT FOR REDUCED ORDER OBSERVER DESIGN

A reduced order state observer design procedure for multivariable linear time-invariant systems is developed. The procedure is based on the eigenstructure assignment approach. A compact form for the obsever gain matrix is derived according to any arbitrary prespecified set of eigenvalues and eigenvectors. A set of free (design) parameter vectors is required upon which the eigenvector assignability is determined. In case of having observer dynamics of order equal to or less than the number of system outputs. complete assignability can be achieved. Having such a reduced order observer in a feedback loop. the choice of the free parameters in order to reduce the impact of the initial mismatch between the system states and the corresponding estimates is derived. The approach developed is applied to minimize the effect of external gust on the lateral axis of L-1011. aircraft at cruise flight condition .

INDUCTION MOTOR FLUX RECONSTRUCTION VIA NEW REDUCED-ORDER STATE OBSERVER

ABSTRACT In this paper a new type of the reduced-order time-varying state observer for voltage- and current-fed induction motor is presented. The observer error decreasing rate is arbitrarily formed by a suitable choice of the observer eigenvalues, which does not depend on the rotor speed. Stability of the observer is proved. Dynamical properties of such observers in various operating conditions of the drive system are analysed. Results are numerically verified by simulation.

Application of Decoupling and State Space Control in Processing Machines with Continuous Moving Webs

Optimizing the control of multi-motor drives in processing machines with continuous moving webs, normally the influence of the web forces is neglected. Poor dynamic behaviour is observed in the case of unfavourable dimensions of the plant. By solving a Riccati matrix equation a decentral reduced-order state observer is found which reconstructs the web forces. An adaptation to practical demands yields a simplified first-order observer circuit which is able to decouple the drives from the web forces. Its parameters are independent from the speed of the plant. The circuit is robust against large variations of the parameters of the system. Theoretical and experimental investigations have shown that the dynamic performance of a cascade controlled large-scale system can be improved considerably. Besides the use of decoupling with observers, the optimal constant output feedback has been applied to the speed control of a multi-motor drive. The results points out a better control compared to the traditional cascade control. Especially a decrease of about factor 10 of the speed deviation is possible when a step function of the force occured.

Synthesis of linear systems with desired equivalent form

A method for feedback synthesis of linear control systems with desired linearly equivalent form of the closed loop system matrix is proposed. The method is based on the serial canonical form of linear multivariable systems which is an alternative to the Luenberger canonical form. A stable computational algorithm for finding the serial canonical form using orthogonal similarity transformations is described. The algorithm for synthesis involves a simple recurrent procedure and gives the possibility to achieve any attainable equivalent form of the closed loop system. The results obtained are extended to the synthesis of reduced order state observers.