Journal ArticleDOI
Observers for multivariable systems
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TLDR
In this article, it was shown that the design of an observer for a system with M outputs can be reduced to the design for m separate observers for single-output subsystems.Abstract:
Often in control design it is necessary to construct estimates of state variables which are not available by direct measurement. If a system is linear, its state vector can be approximately reconstructed by building an observer which is itself a linear system driven by the available outputs and inputs of the original system. The state vector of an n th order system with m independent outputs can be reconstructed with an observer of order n-m . In this paper it is shown that the design of an observer for a system with M outputs can be reduced to the design of m separate observers for single-output subsystems. This result is a consequence of a special canonical form developed in the paper for multiple-output systems. In the special case of reconstruction of a single linear functional of the unknown state vector, it is shown that a great reduction in observer complexity is often possible. Finally, the application of observers to control design is investigated. It is shown that an observer's estimate of the system state vector can be used in place of the actual state vector in linear or nonlinear feedback designs without loss of stability.read more
Citations
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Journal ArticleDOI
An introduction to observers
TL;DR: In this paper, the identity observer, a reduced-order observer, linear functional observers, stability properties, and dual observers are discussed, along with the special topics of identity observer and reduced order observer.
Journal ArticleDOI
Optimisation of the anaerobic digestion of agricultural resources.
TL;DR: Current optimisation techniques associated with anaerobic digestion are reviewed and possible areas where improvements could be made are suggested, including the basic design considerations of a single or multi-stage reactor configuration, the type, power and duration of the mixing regime and the retention of active microbial biomass within the reactor.
Journal ArticleDOI
On the determination of the optimal constant output feedback gains for linear multivariable systems
William S. Levine,Michael Athans +1 more
TL;DR: In this article, the optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed and an algorithm for computing FAST is presented.
Journal ArticleDOI
On pole assignment in multi-input controllable linear systems
TL;DR: In this paper, it was shown that controllability of an open-loop system is equivalent to the possibility of assigning an arbitrary set of poles to the transfer matrix of the closed loop system, formed by means of suitable linear feedback of the state.
References
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Journal ArticleDOI
New Results in Linear Filtering and Prediction Theory
R. E. Kalman,R. S. Bucy +1 more
TL;DR: The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
Journal ArticleDOI
Mathematical description of linear dynamical systems
TL;DR: In this paper, it is shown that the input/output relations determine only one part of a system, that which is completely observable and completely controllable, and methods are given for calculating irreducible realization of a given impulse-response matrix.
Journal ArticleDOI
Observing the State of a Linear System
TL;DR: In this article, it was shown that the state vector of a linear system can be reconstructed from observations of the system inputs and outputs, and that the observer which reconstructs this state vector is itself a linear systems whose complexity decreases as the number of output quantities available increases.
Journal ArticleDOI
Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems
R. E. Kalman,J. E. Bertram +1 more
Journal ArticleDOI
Linear filtering for time-varying systems using measurements containing colored noise
Arthur E. Bryson,D. Johansen +1 more
TL;DR: In this paper, it is shown that if correlation times are not short, or if some measurements are free of noise, the optimal filter is a modification of the Kalman-Bucy filter which, in general, contains differentiators as well as integrators.