Linear State Variable Feedback Research Articles

Design, testing and implementation of a linear state variable feedback controller for providing tracking/regulation of a large platform of a Maglev vehicle

The basic parameters of an electromagnetic levitation systems are resistance of the coil, inductance of the coil, air-gap between magnet and the object, coil current, mass of the object, controller parameters and so on. The levitation systems are highly unstable and strongly non-linear. In real-life applications, these parameters are supposed to vary. A proportional–integral controller for the inner current control loop and a lead compensator for the position control loop have been designed and tested. The performance study under various parametric effects has been investigated broadly. Finally, both the stability for the proposed levitation system has been achieved with a better operating zone using linear state variable feedback controllers. The system dynamic performances have been recorded for variations of physical system parameters. The sensitivity/robustness of the set-up has been studied. This study will give an insight for designing any corrective measures and an overall idea to develop a levitation system.

LQG Control Performance With Low-Bitrate Periodic Coding

Several specific low-bitrate coding strategies are examined through their effect on LQ control performance. By limiting the subject to these methods, we are able to identify principles underlying coding for control; a subject of significant recent interest but few tangible, i.e. implementable, results. In particular, we consider coding the quantized output signal deploying period-two codes of differing delay-versus-accuracy tradeoff. The quantification of coding performance is via the LQ control cost over a long but finite horizon up to a specified average \textit{escape time}. Infinite-horizon stabilization is replaced by a mean-time-before-failure property, which is a new viewpoint but allows contact with uncoded controllers. The feedback control system comprises the coder-decoder in the path between the output and the state estimator, which is followed by linear state-variable feedback, as is optimal in the memoryless case. The static quantizer is treated as the functional composition of an infinitely-long linear staircase function and a saturation. This permits the analysis to subdivide into estimator computations, seemingly independent of the control performance criterion, and

LMI-based robust tracking of a class of MIMO nonlinear systems

Reference tracking problem for MIMO Lipschitz nonlinear systems is examined here. Presently a vast literature exists on observer design of unforced systems containing Lipschitz nonlinearities. However, these existing results cannot be readily extended for controller design containing reference tracking ability. Here a Linear State Variable Feedback (LSVF) controller is designed for MIMO Lipschitz nonlinear systems with norm-bounded parametric uncertainties using the concept of input to state stability Lyapunov functions. The whole problem is cast into a framework of Linear Matrix Inequalities, to exploit its numerical capabilities. Analytical proofs are supplemented with simulation examples, which show certain advantages over existing results. Apart from state feedback, observer-based output feedback is also considered for controller design.

Robust Control of An Uncertain Nonlinear System With Unobservable Dynamics

This work examines controller design based on feedback linearisation of a nonlinear system in the presence of parametric uncertainty and unobservable dynamics. In this case various analytic constraints make it difficult to design a robust controller in the conventional manner (Isidori (1995)). Through a design example, linear state variable feedback controllers are computed via eigen structure assignment to illustrate the effectiveness of the proposed method. Also sufficient conditions are mentioned which guarantee the stability of the closed-loop system.

H2/H∞ Control of Singularly Perturbed Systems: The State Feedback Case

The design of a mixed H2=H1 linear state variable feedback (LSVF) suboptimal controller for a continuoustime singularly perturbed system using reduced order slow and fast subsystems is described. It is shown that the designed controller based on reduced order models and the corresponding performance index (PI) both are Oð� Þ close to those synthesized using the full order system. Each of the three algebraic matrix equations to be sequentially solved in our study, contains three matrix variables coupled in them. Two of these equations can be made independent of the matrix gain variable under mild restrictions.

Delay Independent Stabilization and ASC

On the quadratic stabilization of uncertain linear time varying systems by means of linear state variable feedback, Wei introduced the concept of antisymmetric stepwise configuration (ASC) and proved that having this configuration is a necessary and sufficient condition for uncertain linear systems to be quadratically stabilizable by means of a linear state variable feedback. However, because his condition is constructed on the basis of quadratic lyapunov functions, his method is not applicable if the state variables contains delays. In this report the conditions for the delay independent stabilization so far obtained on the basis of delay differential inequalities is further developed and it is proved that generally to have ASC is also a sufficient condition for the delay independent stabilizability of linear uncertain delayed systems by means of linear state variable feedback.

H2/H∞ Control of discrete singularly perturbed systems: the state feedback case

The design of a mixed H2/H∞ linear state variable feedback suboptimal controller for a discrete-time singularly perturbed system using reduced order slow and fast subsystems is described. It is shown that the designed controller based on reduced order models and the corresponding performance index both are O(ε) close to those synthesized using the full order system.

Extension of tethered satellites in the atmosphere

An important application of tethered satellites is atmospheric studies by extension of a subsatellite into the atmosphere through tether while the parent spacecraft flies at an altitude high enough so that the deleterious effects of the atmosphere on it are inconsequential. The key issue in the operation is the swift extension of the tether. Inordinate librations of the tether during extension are undesirable. Tension control, in conjunction with a thruster to control the out-of-pane motion, is a popular technique of control during extension. Many nonlinear feedback tension control laws based on Liapunov's direct method have been proposed. In this paper, an alternate technique, a linear state variable feedback control law is used. The control gains are determined from theorems in analytical mechanics. Simulation of the nonlinear equations using this controller affirms that the tether extends to the desired length in a reasonable amount of time.

Time delay compensation: the PIP philosophy

The design of control systems for processes with appreciable time delay is still an area of ongoing research. The continued popularity of the Smith predictor strategy, first introduced in 1957, may be symptomatic of the worries expressed by control practitioners of their lack of appreciation of more elegant but analytically complex solutions, especially those coming under the global banner of long-range predictive control. This paper presents a simple solution to the above dilemma. The PIP (proportional-integral-plus) algorithm arises from the application of linear state variable feedback using a non-minimal state space (NMSS) description of the process to be controlled. After briefly establishing the theoretical basis of the algorithm, its predictive nature is highlighted by a series of simulations using the MATLAB/SIMULINK environment. The paper concludes with the design of a PIP controller for an industrial flow loop using some prototype software.

Parallel algorithm for pole assignment of multi-input systems

A general parallel algorithm for pole placement via linear state variable feedback based on Sylvester's equation is proposed. The prescribed eigenvalues may be the same as the open-loop eigenvalues or disjoint from them and can be of any order of multiplicity. The algorithm uses block Hessenberg forms for numerically reliable computation. Results of robustness of closed-loop pole assignment are given along with complexity analysis.

Optimization and Control of an Industrial Scale Multivariable Nonlinear Microalgae Fermentation

Different optimization and control techniques of an industrial microalgae fermentation have been studied in this work. The optimization techniques were verified in real time application on the fermenter and in addition in a theoretical analysis on the dynamical model of the fermentation process, which was also the subject for the verification of the different control algorithms. The optimization goal was to maximize the cellular productivity by using several techniques such as Pontryagin’s Maximum Principle, Feedback Sub-Optimal Policy and the Direct Search Method. The latter one has shown to be the preferable technique by applying it to the dynamical model of the fermentation. Real time Feedback Sub-Optimal Policy showed very good resemblance with the theoretical results. The reference conditions obtained from the optimization algorithms are the set points for the multi- variable controller. Linear State Variable Feedback has shown totally unsatisfactory behavior. Two advanced control techniques, Globally Linearizing Control and multivariable adaptive control have shown to perform very satisfactorily.

Eigenstructure assignment in high-gain feedback systems

Using the two-time scale property of a high-gain feedback system, the set of closed-loop eigenvectors which can be assigned by linear state-variable feedback corresponding to a prescribed set of eigenvalues is characterised in this paper. Algorithms to compute the feedback matrix for assigning eigenvalues and eigenvectors are described. The above algorithmic procedure for eigenstructure assignment suggests an elegant way of selecting weighting matrices in linear-quadratic optimal control problems and of computing the optimal feedback matrix without solving the Riccati equation; it will also assign a given eigenstructure.

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.

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.

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.

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 precompensator design to achieve the decoupling condition in the frequency domain

This paper deals with the problem of designing a precompensator, by using the frequency domain approach, for linear systems having weak inherent coupling such that the composite system will be decouplable through linear state variable feedback (l.s.v.f.) alone. Three algorithms are presented for such a purpose. The first one makes use of a new theorem for dynamic decoupling through l.s.v.f. alone, while the other two make use of the interactor concept. The algorithms always yield stable precompensators. Moreover, the controllability and observability of the composite system are guaranteed.

Two-step decoupling algorithm for multivariable systems

In Wolovich's frequency domain theory and algorithm for the decoupling of multi-variable systems, the precompensator is first determined so that the decoupled system with suitable poles is obtained in the form of open-loop control. The open-loop control system is then transformed into input dynamics plus linear state variable feedback via a general compensation technique developed by himself. This method, however, has several defects : rather a large amount of computation is required in relation to a general compensation algorithm, zeros cannot be assigned arbitrarily, and unstable plant zeros often cause instability of the resulting decoupled system. The two-step decoupling algorithm proposed in this paper is intended to remove those undesirable features.

Biped side step in the frontal plane

A three-link planar model of a biped is studied in the frontal plane. When this model is subjected to certain on-off constraints, the forces of constraint are derived as functions of the system state and the input, and can be shown in a simple block diagram. Linear state-variable feedback is designed to stabilize and decouple the system for small motions about an equilibrium state. The motion of this biped is implemented as a sequence of state transitions between stable equilibrium states. Ramp state and input references are used to guide the biped system from one equilibrium state to the next. Single-support postural stabilization and side step and return motions were investigated by computer simulation in order to evaluate the effectiveness of this control strategy.