State Variable Feedback Research Articles

Sliding Mode Position Control of a DC Motor

The sliding mode control is applied to the position control of a DC drive. The variable structure is realized by the commutation of the command device according to a state variables feedback strategy. The definition of an equivalent command variable allows to determine the existence conditions and the domain of the sliding mode in the state space. The parameter design of the controller is computed by a poles assignment method. The practical application to a position control of a DC drive shows that it is also possible to limit the internal variables (current and speed).

Performance of Feedforward Current Regulators for Field-Oriented Induction Machine Controllers

To achieve instantaneous control of induction motor torque using field-orientation techniques, it is necessary that the phase currents be controlled to maintain precise instantaneous relationships. Failure to do so results in a noticeable degradation in torque response. Most of the currently used approaches to achieve this control employ classical control strategies which are only correct for steady-state conditions. A modern control theory approach which circumvents these limitations is developed. The approach uses a state-variable feedback control model of the field-oriented induction machine. This state-variable controller is shown to be intrinsically more robust than PI regulators. Experimental verification of the performance of this state-variable control strategy in achieving current-loop performance and torque control at high operating speeds is included.

Use of modal functions for continuous-time system identification and state observer design

Abstract This paper defines and discusses modal state functions and their use both for the realization of state observers and for the identification of continuous-time dynamic systems. It is shown that modal state functions have a continuous-time auto-regressive-moving-average structure. The conditions for existence of modal state functions are given in theorem form. Applications to observer design, state variable feedback controllers, and parametric and non-parametric system identification are given.

A generalization of Rosenbrock's theorem

This note presents the simple generalization of Rosenbroek's theorem, concerning the limits of linear state variable feedback in modifying the dynamics of constant linear multivariable systems.

状態変数フィードバックにより配置可能なグラミアンの必要十分条件とそのクラス

状態変数フィードバックにより配置可能なグラミアンの必要十分条件とそのクラス

Conditions for the delay-independent stabilization and the decay rate assignability of linear systems

Abstract In a previous paper (Amemiya 1983) two sufficient conditions were introduced for the delay-independent stabilization of linear systems by means of state-variable feedback including no delays. In this paper the concept of delay-independently upper or lower bound of decaying rate assignability (DIUDA or DILDA) are introduced and it is proved that the two conditions previously obtained are necessary and sufficient condition for DIUDA and necessary condition for DILDA of linear systems by means of state-variable feedback including no delays. The conditions obtained are also applicable to systems including time-varying delays.

Two Contrasting Versions of the Optimal Active Vehicle Suspension

It is generally agreed that vehicle suspensions should isolate the body from roadway unevenness inputs but it is less clear on which other functions are most important. Some studies focus on keeping the wheel-road contact force excursions as small as possible for safety reasons and others focus on limiting the main suspension deflection for good rigid body motion control. In this paper, two performance indices are used which lead to optimal state variable feedback laws for the suspension force. Body isolation is traded off in one case against contact force variation and in the other against suspension deflection. The use of symmetric root locus sketches shows the types of system that result in both cases. It is shown that optimal active suspensions designed according to different criteria are not necessarily comparable and it may not be fair to compare an optimal suspension with a conventional one, unless all aspects of suspension performance are considered simultaneously.

On parametric state feedback design

An explicit parametric expression for the controller gain matrix in linear state-variable feedback is derived. It involves both the case where the set of closed-loop eigenvalues does not include any open-loop eigenvalue, and the case where the two eigenvalue sets have elements in common. Some advantages of this new explicit parameterization of the controller gain matrix are illustrated by two numerical examples.

Linear-quadratic Gaussian with loop-transfer recovery methodology for the F-100 engine

The design of a multivariable feedback control system for the F-100 turbofan jet engine is a challenging task for control engineers. This paper employs a linearized model of the F-100 engine to demonstrate the use of the newly developed linear-quadratic Gaussian with loop-transfer recovery design methodology that adopts an in- tegrated frequency and time-domain approach to multivariable feedback control synthesis so as to meet stability robustness, command following, and disturbance rejection specifications. ODERN turbofan jet engines represent an important multiple-input/multiple-output (MIMO) control ap- plication area since the dynamic coordination of fuel flow and several engine geometry variables can lead to improved performance and efficiency, while maintaining safe fan and compression stall margins. Indeed, the MIMO feedback con- trol of turbofan and turboshaft engine has received a great deal of attention in the past few years.18 The F-100 turbofan engine was used as a main design exam- ple for which different MIMO control methodologies were employed. The so-called linear-quadratic-regulator (LQR) ap- proach9'10 was the basis of engineering designs and evaluations14 that required the feedback of several F-100 state variables. In the past five years significant advances have been made in integrating time-domain optimization-based approaches (such as LQR and linear-quadratic Gaussian (LQG)) with fre- quency domain approaches. Such an integrated frequency- domain and state-space approach to MIMO control systems design was pioneered by Stein and his colleagues1114 and has culminated to the so-called linear-quadratic Gaussian with loop-transfer recovery (LQG/LTR) methodology for MIMO feedback control synthesis. The primary objective of this paper is to illustrate the LQG/LTR design methodology using a four-input/fou r- output linear model of the F-100 engine. Specifically, we stress how MIMO command following and disturbance rejection performance specifications, as well as stability robustness specifications are naturally posed in the frequency domain us- ing the singular values of suitably defined loop-transfer matrices. Then, we demonstrate how the LQG/LTR design procedure is used to meet the posed specifications. Further-

The active control of structural vibration by an active mass damper (Modal control of active mass damper)

This paper presents a study of the active control of structural vibration by an active mass damper system, which consists of a combination of a force generator, a sensor and a servomechanism. The systematic procedure for the synthesis of an active mass damper system is based on the use of modal control theory. The effectiveness of an active mass damper system is demonstrated by the results of a numerical analysis of the undamped vibration of a single degree of freedom system, and it is shown that the eigenvalues of the system can be assigned any arbitrary values by linear feedback of state variables.

Computer-aided Design of Multivariable Stochastic Control Systems with A-Priori Prescribed Dynamical Properties

This paper presents a comouter-aided procedure for designing multi variable controllers which simultaneously achieve a variety of desired design goals in stochastic, unity feedback, linear multivariable systems. The multivariable control system simultaneously ensures: 1)decoupling closed-loop design using linear estimation state variable feedback in combination with feedforward compensator, 2)complete and arbitrary closed-loop pole placement which implies desirea transient performance as Well as closed-loop stability, 3) steady-state output rejection of nondecreasing deterministic part of stochastic disturbances with non-zero mean values, and 4) optimal steady-state estimation of plant's state vector using Kalnan filter. In the design procedure the polynomial matrix approach in s-domain is used. The overall multivariable stochastic control problem is divided into two equivalent problems: stochastic state kalman filtering ana deterministic control of the state estimation and output feedback. The consiaerations are illustrated by a numerical example for simplified version of the ship possitionnig control system.

A Program Structure Based on Exception Handling for Variable Structure Control Systems

Modern control systems such as state variable feedback control systems with observers or adaptive control systems are introduced in industry at a very slow rate. A major reason for this is that engineers must be convinced first that the algorithms of modern control theory are at least as powerful and reliable as the long proven three-term controller. A block-structured exception handling mechanism embedded in the real time operating system MODEB V2 coded in Modula-2 is proposed as a base for a general program structure adapting itself to variable environmental conditions. A variable structure control system consisting of a three-term controller, a state variable feed-back controller, and an adaptive controller as well as the outline of the system imple-mentation are given to illustrate the proposed program structure.

The Use of Active Controls to Augment Rotor/Fuselage Stability

The use of active blade pitch control to increase helicopter rotor/body damping is studied. Control is introduced through a conventional nonrotating swashplate. State variable feedback of rotor and body states is used. Feedback parameters include cyclic rotor flap and lead-lag states, and body pitch and roll rotations. The use of position, rate, and acceleration feedback is studied for the various state variables. In particular, the influence of the closed loop feedback gain and phase on system stability is investigated. For the rotor/body configuration analyzed, rotor cyclic inplane motion and body roll-rate and roll-acceleration feedback can considerably augment system damping levels and eliminate ground resonance instabilities. Scheduling of the feedback state, phase, and gain with rotor rotation speed can be used to maximize the damping augmentation. This increase in lead-lag damping can be accomplished without altering any of the system modal frequencies. Investigating various rotor design parameters (effective hinge offset, blade precone, blade flap stiffness) indicates that active control for augmenting rotor/body damping will be particularly powerful for hingeless and bearingless rotor hubs.

A Versatile Digital Controller Algorithm Incorporating a State Observer and State Feedback

A digital controller algorithm is developed which forces a single-input single-output plant, defined by its transfer function, to respond according to a specified model transfer function. The algorithm is implemented by two difference equations and incorporates a state variable observer and state variable feedback control. The procedure used is sometimes referred to as a model reference feedback control system.

Decoupling techniques applied to the design of a controller for an unregulated synchronous machine

Decoupling techniques using state variable feedback are proposed for the design of a controller for a 2-input 2-output linear time-invariant multivariable model of an unregulated synchronous machine supplying power to an infinite grid, to accomplish single-input single-output decoupling and pole assignment, and thus enhance the dynamic (stability) characteristics of the resulting closed-loop system.

Comments on ‘ A precompensator design to achieve the decoupling condition in the frequency domain ’

The necessary and sufficient condition for decoupling through linear state variable feedback (l.s.v.f.) alone presented by Moness and Lantos (1984) is incorrect. This condition is equivalent to the sufficient condition proposed by Vardulakis (1981).

A design method of discrete output feedback control system based on improved optimal regulator theory

A design method of an output feedback control system is proposed on the basis of an improved optimal regulator technique and application of the method to an electrical drive system is presented. The control system structure of the output feedback control system is clarified by comparing it with that of the full state variable feedback control system synthesized by the improved optimal regulator technique. Difference action as well as proportional and integral actions are included in the controller of the output feedback control system, on the other hand, only proportional action and integral action are introduced in the controller of the full state feedback control system. Low static sensitivity for variations of the parameters of the controlled object is attained, and the compensating action for the input delay times due to the processing time required to execute the employed control algorithm with the microprocessor are also taken into account.

A gyro drift and dynamics state estimator for satellite attitude control systems utilizing a star mappert†

A recursive estimator is presented which, when given attitude measurements from a star mapper and rate integrating gyro, together with control signals, provides filtered estimates of gyro drift, disturbing angular acceleration, body angular velocity and attitude. Attention is restricted at present to satellites with substantially rigid body dynamics and negligible inter-axis coupling. A single axis attitude control system is considered, this being sufficient for demonstration of the principles. The estimator is based on the Kalman filter with the following developments ; (a) A low level fictitious covariance matrix element is introduced to facilitate estimation of the disturbing angular acceleration, and (b) the gain matrix is modified to enable the real-time model iterations and gyro sampling to be carried out at a much higher rate than the star mapper sampling. Furthermore, the part of the gain matrix relevant to the star mapper output is adapted to enable the correction to the model to be applied continuously, thereby avoiding stepping of the state estimate following new star mapper measurements. A form of the estimator is presented in which it is unnecessary to know the time to the next star mapper reading. Digital simulation results are given for a complete control system in which two control loops are completed by state-variable feedback, comprising a linear gyro-drift control law and a non-linear gas jet control law.

Decoupling and distrubance rejection control of a binary distillation column with pressure variation.

The perturbed linear system equations for a binary distillation column with pressure variation are derived. The application of modern control theory to this model shows that there exists a pair of constant precompensator and state variable feedback which completely decouples the system and rejects the effect of the feed composition disturbance. Based on the subspace concept, we found that five state variables have to be measured and three poles can be arbitrarily assigned. If we use the dynamic precompensator, seven poles can be assigned while eight measurement variables are required. A simulation study was carried out to show the power of the approach.

MICROPROCESSOR OPTIMAL CONTROL OF DUAL CONVERTER-FED DC DRIVES

Abstract A new method is described which allows us to determine. a control law, suitable for microprocessor implementation, using optimal control techniques, for a dual converter-fed DC motor. drive. This method allows us to obtain a closed loop control scheme, based on the state variables feedback, though the source- voltage supply cause a considerable ripple on the armature current The parameters of the. controlled obtained have the same values both in continuous and discontinuous conduction. The simulation experiments presented for a 3-hp motor. show that both the steady state and dynamic behaviour of the closed loop control system is wholly satisfactory.