Estimated State Feedback Research Articles

Fuzzy model-based control of complex plants

In the field of fuzzy modeling, the Takagi-Sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants. The paper addresses two control design problems associated with state-space realizations of such fuzzy models. First, we treat the stability robustness of fuzzy model-based controllers against modeling uncertainty. Second, we develop observer-based control schemes and further investigate the behavior of estimated-state feedback. In both cases, we provide sufficient conditions that guarantee stability of the closed loop. The results are demonstrated on the fuzzy model of a gas furnace process.

Tracking Control of a Parallel Robot with Estimated State Feedback

Abstract The tracking control problem of a parallel robot including the electrical actuator dynamics is addressed in this paper. The proposed control law in armatures' input voltages is ivestigated with the consideration of some inaccessible states such that velocities but under the assumption of an exact model knowledge. The formulated model is in standard form that allows the application of singular perturbations techniques. Computer simulations are performed on the electrically-driven six degrees-of-freedom (dot) parallel robot. The results show the efficiency of the two time-scale decomposition and the performance of the proposed controller-observer with a good trajectory tracking.

Designing stabilising controllers and observers for uncertain linear systems with time-varying delay

A procedure to design the memoryless state-estimation feedback controller for uncertain dynamic systems with time-varying delay is presented. The uncertainties are time varying and are bounded. The design procedure involves solving two linear matrix inequalities. If there exist two positive definite matrices which satisfy these two linear matrix inequalities, then the asymptotic stabilisability of the closed-loop system is guaranteed. Furthermore, the state observer and control law can be constructed from these solutions. An example is given to illustrate the results.

A Riccati Equation Approach to the Design of Memoryless Stabilizing Controllers and Observers for Uncertain Linear Systems with Time-Varying Delay

In this paper, a procedure for designing the memoryless state estimation feedback controller for uncertain dynamic systems with time-varying delay is presented. The uncertainties are time varying and are bounded. The design procedure involves solving two Riccati equations. If the positive-definite solutions of Riccati equations also satisfy a matrix inequality then the asymptotic stability of the closed-loop system is guaranteed. Furthermore, the state observer and control law can be constructed from these solutions.

Robust stabilization of large-scale time-delay systems with estimated state feedback

This paper proposes a class of observers and uses the estimated state feedback to stabilize a perturbed large-scale time-delay system in which the state is unmeasurable. An inequality representing the relationship among the perturbation bounds, interconnection magnitudes, and gains of observers and controllers is derived to ensure that the system is stabilized and the state is estimated. Moreover, this inequality does not need the solution of a Lyapunov equation or Riccati equation and is independent of time delays.

On the structure of a two-degree-of-freedom H ∞ loop shaping controller

Explicit state-space formulae are presented for a two degree-of-freedom (2-DOF) controller that stabilizes an augmented plant with respect to unstructured additive coprime factor perturbations whilst simultaneously providing robust model following. The 2-DOF problem was known to inherit certain features of the McFarlane-Glover loop shaping design method, from which it is derived. In this paper, the precise structure of one admissible controller is derived. That structure is shown to comprise a state-estimator, an on-line step-response model, and an augmented state estimate feedback law. The formulae derived herein are applied to a classical nonlinear stabilization problem.

Stabilization of Composite Nonlinear Systems by an Estimated State Feedback

In this paper we investigate the stabilizability problem in an observer design for a class of composite nonlinear systems. In particular, we consider the cascade of a globally asymptotically stable nonlinear system with an imput-output stabilizable bilinear system. If the bilinear subsystem is stabilizable by an estimated state feedback, and under a growth condition on the nonlinear subsystem, the partially bilinear system is stabilisable by an estimated state feedback.

Stabilization of Partially Linear Stochastic Systems via Estimated State Feedback Law

In this paper, we investigate the stabilizability problem (in the sense of exponential stability in mean square) for composite partially linear stochastic systems by means of an observer design. We prove, under general assumptions, that there exists a linear feedback law depending on an estimation given by an observer which exponentially stabilizes in mean square the system at its equilibrium.

Computation of generalized H 2 optimal controllers

The generalized H 2 optimal control problem for a linear time-invariant system is one in which the conventional H 2 norm is replaced by an operator norm. The closed-loop system is described in terms of a mapping between the space of time-domain input disturbances in L 2 and the space of time-domain regulated outputs in L ∞. A minimum of this norm is then sought over all stabilizing controllers. It is shown that optimal controllers for such problems have the structure of a Kalman filter with estimated state feedback, where the feedback gains are obtained from the solution to a weighted LQR problem. A computational algorithm is presented to determine the weights in this LQR problem, and examples are given which demonstrate various problems which may arise in obtaining the optimal weights. In particular, it is shown that the generalized H 2 problem may involve the solution to a singular LQR problem.

Entwurf strukturbeschränkter zeitdiskreter Zustandsregler mittels balancierter Realisierungen

In this paper methods are proposed to determine state controllers with structural limitations. All these method are based on balanced realizations of the plant or the closed loop. The approximation of the behaviour of a compensator which is designed without considering structural limitations is strived for. Regarded limitations are the number of measured variables to determine an output feedback and the order to determine a dynamic compensator consisting of state estimator and state feedback

On the observer-based structure of covariance controllers

The problem of finding the set of all stabilizing full-order controllers is equivalent to a problem of finding all matrices which can be assigned to the closed-loop system as a state covariance. The necessary and sufficient conditions for a given matrix to be assignable as a covariance are given, and all controllers (of plant order) which assign a specific covariance are parametrized explicitly. The structure of covariance controllers is shown for the first time to be observer-based (state estimator plus estimated-state feedback). The ‘central’ state estimator of the covariance controller is shown to be the Kalman filter. Unlike the traditional estimator-based controller, the separation principle does not hold, but one can design a controller by assigning the estimation error covariance and the plant state covariance simultaneously.

Robust control of robots via linear estimated state feedback

In this note we propose a robust tracking controller for robots that requires only position measurements. The controller consists of two parts: a linear observer part that generates an estimated error state from the error on the joint position and a linear feedback part that utilizes this estimated state. It is shown that this computationally efficient controller yields semi-global uniform ultimate boundedness of the tracking error. An interesting feature of the controller is that it straightforwardly extends results on robust control of robots by linear state feedback to linear estimated-state feedback.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Trajectory tracking in robot manipulators via nonlinear estimated state feedback

High-precision measurements of joint displacements are available on robot manipulators. In contrast, velocity measurements obtained through tachometers are, in many cases, contaminated by noise. It is therefore economically and technically interesting to investigate the possibility of controlling robot dynamics by only using angular position measurements. Two alternative approaches for trajectory tracking control via nonlinear estimated state feedback are presented. The first scheme is based on smooth functions, whereas the second uses switching gains. The stability of the closed-loop system is investigated. Both approaches yield exponentially stable closed-loop systems. The local attraction areas are characterized in terms of controller and observer gains, initial state values, and robot model parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sensitivity and Roundoff Noise Optimization of a State-Estimate Feedback Controller

Expressions are derived for the sensitivity and the roundoff noise gain of the closed loop transfer function of a system when the state estimate feedback controller is implemented with a finite word length and when the computations are performed in finite precision, The set of state space models minimizing either the sensitivity or the roundoff noise gain is computed.

Adaptive Control within the Class of Stabilizing Controllers for a Time Varying Nominal Plant

In this paper, we consider enhancing the performance of a stabilizing causal controller Ko (possibly time varying) for a causal nominal plant G (possibly time varying), with controller augmentations including an adaptive stable subsystem Q. The objective is to search on-line in the class of stabilizing causal controllers for the nominal plant, characterized in terms of Q and state space descriptions of G, Ko. For the case of time-invariant plants, most of the algorithms and theory of the paper specialize to known results. One formulation of the coprime factorizations using state- space description of time-varying systems, and associated characterization of the class of all stabilizing causal controllers used in our work, specializes to known results when the stabilizing controller has a full order state estimate feedback state space description.So as to view the results in terms of familiar schemes, specialization to the well-studied self-tuning regulator and parallel model reference adaptive controller are presented. The latter provides an illustration of the application of the results to two-degree-of-freedom design.

All stabilizing controllers as frequency-shaped state estimate feedback

It is shown that the class of all strictly proper stabilizing controllers for proper linear plants can be structured as state estimate feedback with frequency shaping in the state estimates and/or in the state estimate feedback law. The selection of where the frequency shaping takes place is at the designer's discretion. The parameterization of the controller class can be in terms of an arbitrary proper stable transfer function, with the closed-loop system transfer functions affine in the transfer function. With constant output feedback permitted in addition to the state estimate feedback, the class of all proper stabilizing controllers can be generated in a like manner. >

Optimal finite precision implementation of a state-estimate feedback controller

Expressions are derived for the sensitivity and the roundoff noise gain of the closed-loop transfer function of a system when the state estimate feedback controller is implemented with a finite word length and when the computations are performed in finite precision. This allows one to compare the sensitivity and noise gain over all equivalent state-variable implementations of the observer plus controller. The set of state-space models minimizing either the sensitivity or the roundoff noise gain is computed. Simulations compare the performance of the optimal implementations with respect to companion forms and a particular delta model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Doubly coprime factorizations, reduced-order observers, and dynamic state estimate feedback

Doubly coprime factorizations of the transfer function of a lumped linear time-invariant system are a starting point for many of the results in the factorization approach to multivariabie control system analysis and synthesis. In work by Nett et al. (1984), explicit state-space realizations of these factorizations are derived using results from state estimation/state feedback theory. Here new doubly coprime factorizations are developed based on minimal-order observers. Following on from this, various extensions are noted, and it is proved that the class of all proper stabilizing controllers for a given plant can be generated by dynamic feedback of the reduced-order state estimate.

On a class of stabilizing partially decentralized controllers

Classes of stabilizing decentralized controllers for linear systems with plant state estimate feedback at each control station are studied. For the case when information flow between control stations is permitted with transmission delay, a class of stabilizing controllers is conveniently characterized in terms of an arbitrary proper stable transfer function. With zero delays, and thus centralized control, the class defined is the entire class of stabilizing linear controllers. The results suggest how information flow between control stations, perhaps with delay, can be implemented so that performance/robustness can be optimized and yet so that if transmission loss occurs, stability is maintained.

Adaptive control within the class of stabilizing controllers for a time-varying nominal plant†

In this paper, we consider enhancing the performance of a stabilizing causal controller K0 (possibly time-varying) for a causal nominal plant G (possibly time-varying), with controller augmentations including an adaptive stable subsystem Q. The objective is to search on-line in the class of stabilizing causal controllers for the nominal plant, characterized in terms of Q and state space descriptions of G, K 0. For the case of time-invariant plants, most of the algorithms and theory of the paper specialize to known results. One formulation of the coprime factorizations using state-space description of time-varying systems, and associated characterization of the class of all stabilizing causal controllers used in our work, specializes to known results when the stabilizing controller has a full order state estimate feedback state space description. So as to view the results in terms of familiar schemes, specialization to the well-studied self-tuning regulator and parallel model reference adaptive controller ...