The main goal of this contribution is to show simulation results for two types of External Linear Models (ELM) used in the adaptive control as a linear representation of the originally nonlinear system. The nonlinearity is dispathed with the use of recursive identification which recomputes parameters of ELM in each step according to actual state of the system. The controller design employes polynomial approach with pole-placement method and spectral factorization and all these techniques together satisfies basic control requirements. The verification was done on the mathematical model of Continuous Stirred Tank Reactor (CSTR) as a typical member of the nonlinear equipment widely used in chemical industry. INTRODUCTION The adaptive control (Astrom and Wittenmark 1989) is not new control technique but his advantages could be found in the big theoretical background and usability to cooperate with other control approaches such as a robust control, a predictive control etc. Several methods used in adaptive control are introduced for example in (Bobal et al. 2005). The polynomial approach (Kucera 1993) in the control synthesis can be used for systems with negative properties from the control point of view such as nonlinear systems, nonminimum phase systems or systems with time delays. Moreover, the pole-placed method with spectral factorization satisfies basic control requirements such as disturbance attenuation, stability and reference signal tracking. Although the polynomial synthesis is considered for the continuous-time ELM, the recursive identification with exponential forgetting (Rao and Unbehauen 2005) runs in discrete time which is better from computation and programming point of view. This disagreement could be overcome with the use so called Delta (δ-) models (Middleton and Goodwin 2004) that belong the discrete-time models but parameters approaches to the continuous ones for the small sampling period (Stericker and Sinha 1993). The nonlinear plant in the verification part is represented by Continuous Stirred Tank Reactor with van der Vusse reaction inside and cooling in the jacket (Chen et al. 1995). The mathematical model of this reactor is described by the set of four nonlinear Ordinary Differential Equations (ODEs) which can be easily solved with standard methods for numerical solving. All simulation studies were done on mathematical simulation software Matlab, version 6.5.1.
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