Recursive Identification Methods

Since the dynamics of real systems are either time varying or nonlinear in nature, the self-tuning controller design is appropriate where a recursive identification algorithm is utilized to monitor or track the process behaviour. The systems identification algorithms are utilized to estimate the parameters representing the dynamics of the underlying process in linear, nonlinear or both forms, depending upon the required analysis. Therefore, the controller parameters can be tuned on line by reference to the periodically updated plant model. Ideally, the controller synthesis should optimize plant performance taking the uncertainty in the model into account as well as the performance criterion. However, for simplicity, the plant model is usually considered accurate during control synthesis yielding the certainty equivalence self-tuner. Self-tuning control combines the design of feedback controllers based on plant system models with the on-line estimation of the model parameters or the controller parameters using input and output data measurements. The robustness or alertness of self-tuning is totally dependent upon the robustness of the system identification algorithm and its ability to detect and track rapid changes in system performance. The identification techniques find its way into aerospace applications through identifying the flight parameters, adaptive control or adaptive signal and image processing. For example, it could be used to identify the attitude of an aircraft or a missile, engine parameters like engine load variations, fluctuations in fuel supply, and aerodynamic effects from the airstream that change considerably,... etc. The subject of system identification has extremely diverse approaches depending upon the purpose of identifier and the underlying process to be identified. The choice between them depends on factors among among them are: model complexity, noise-to-signal ratio, convergence rate, and computational expenses. The most popular and easiest method for system identification is the least squares (LS) approach. Therefore, this paper presents some of these algorithms in a simplified way leading to the equations that must be solved through the specified algorithm, without going deeply into the derivation of each algorithm. Then, one of them is numerically implemented/evaluated for some examples. In addition, it highlights the identifiability which is a joint property of an identification experiment and a model and establishes the environment for adequate parameters estimates from the injected signal point of view yielding what is called the persistency of excitation. The results showed good convergence, fast response and good tracking utilizing some of the mechanisms or techniques that improve the numerical robustness of any identification algorithm