This work presents and evaluates a new method, based upon tracer gas techniques, for determining interzonal airflows and effective volumes in a multizone enclosure. Presently used tracer gas techniques have a number of drawbacks including the need for multiple tracers when analyzing a multizone structure. Also, traditional techniques cannot be used to independently determine flows and effective volumes in the multizone case. The proposed method uses a single tracer gas to disturb the zones. A state-space formulation is used to model the multizone system. The concentration data are used in combination with a recursive least-squares identification algorithm to determine all of the interzonal airflows and effective volumes. A number of simulations are then used to evaluate the method. The simulations show that there are important considerations when selecting the type of input applied to each zone. They also indicate that the proper choice of sampling interval is critical for accurate identification. The recursive least-squares formulation is also readily adapted to the case where the system parameters are varying. A number of simulations show that this method can be used to track varying interzonal flows and effective volumes provided they are changing slowly with time. A three-zone experimental test facility was constructed to validate the simulation results as well as test the identification algorithms under more realistic conditions. The results indicate that the single gas tracer technique was able to estimate the interzonal airflows and effective volumes of the experimental facility to within 10%, in most cases. The tests also showed that for one-, two-, and

Characterizing the dynamics of a multizone enclosure by identifying unknown system parameters using tracer gas techniques and least squares identification algorithms

Recursive algorithms are presented for the on-line state and parameter estimation of a linear time-invariant discrete time system of large size. A variant of the observable canonical model with a one-way coupling form of the state model is chosen for developing a solution to the problem. Exploiting the canonical structure of the model, the proposed solution turns out to be computationally simpler than the existing solution, moreover a decentralized state and parameter estimation scheme can be developed in two steps. In the first step, the parameter of the system matrices are estimated by a recursive least-square algorithm or by a normalized stochastic approximation algorithm in a decoupled manner. These parameters are then employed for state estimation in step 2 using a centralized conventional Kalman filter or a decentralized adaptive Kalman filter, which in turn reduces instrumentation and telemetry costs. The results are illustrated by considering two different systems.

On-line state and parameter estimation of multivariable systems based on transformed model

This paper describes an efficient algorithm for parameter estimation and control of a multivariable discrete-time systems using input-output data. Parallel recursive least square algorithms based on special observable canonical innovation model are considered to estimate model parameters and subsequently parallel state estimation schemes are developed by partitioning the conventional Kalman-filter equation. Proposed observable canonical structure turns out to be more simpler than that of Desai and Mahalanabis [4] which in turn reduces the overall computational burden in the parameter estimation stage. Parameter estimates are then utilized to implement a simple controller that minimizes a single-stage performance index [4]. This scheme has some limitations and more specifically, the parameter estimates do not converge to true value for a weakly controllable system [1]. To avoid this difficulty, a numerically reliable and stable controller based on singular value decomposition (SVD) is considered. Simulatio...

On-line parameter identification and design of multivariable discrete- time regulator

This paper introduces an new approach for parameter estimation and two-level control of large-scale discrete systems using input-output data. Parallel recursive least square esti­ mation algorithms based on special observable canonical innovation model are considered and subsequently, parallel state estimation schemes are developed by partitioning the con­ ventional Kalman-filter equation. Two-level controller is implemented by using estimated parameters. Global output feedback controller is designed to reduce the effect of state in­ teraction between the subsystems and subsequently, a numerically reliable and stable local controller based on singular value decomposition (SVD) technique is considered to stabilize a'-d improve the performance of the composite system. Simulation studies for parameter estimation and control of discrete time systems are carried out by considering a numerical example of flight control problem.

http://www.kybernetika.cz/view_file.html?item=1522

On-line parameter estimation and two-level control of large-scale discrete time systems

The problem of combined parameter and state estimation was originally posed as a nonlinear filtering problem using the extended Kalman filter. This led to problems of divergence and excessive computation, especially for multivariable systems. A two-stage online parameter and state estimator for multivariable stochastic systems is proposed that avoids these difficulties. A special canonical form of the state-space equations that simplifies the parameter estimation problem is used. In the first stage the parameters of the system matrices and of the steady-state Kalman filter matrix are estimated by a normalized stochastic approximation algorithm assuming known states. These parameter estimates are then utilized for state estimation in the second stage using the linear Kalman filter. The two stages are then coupled in a bootstrap manner.

H. E. El-Sherief

Papers

State and parameter estimation of linear stochastic multivariable sampled data systems