Modelling And Control Of Hot-Air System Under Conditions Of Uncertainty

The contribution deals with modelling and control of temperature in laboratory model of hot-air system under conditions of parametric uncertainty. In the first instance, the first and second order parametrically uncertain mathematical models of the plant are constructed, and then they are utilized for design of various controllers with conventional structure. The control synthesis exploits general solutions of Diophantine equations in the ring of proper and stable rational functions. Robust stability of final closed control loops is tested using the value set concept and zero exclusion condition. INTRODUCTION The uncertainty represents serious problem in many real control applications. One of convenient approaches to uncertain modelling and description supposes no variations in the structure but only in parameters of the controlled system. In such case, one speaks about parametric uncertainty. In spite of the uncertain conditions, the often requirement consists in application of a cheap controller with simple PI or PID structure and fixed coefficients which would ensure stability and desired control behaviour for all expected values of the uncertain parameters. A potential solution of this task consists in the usage of continuous-time controllers designed through general solutions of Diophantine equations in the ring of proper and stable rational functions (RPS), Youla-Kucera parameterization and divisibility conditions. The principal idea of this approach is adopted from (Vidyasagar 1985; Kucera 1993) while the control design itself is proposed and analysed e.g. in (Prokop and Corriou 1997; Prokop et al. 2002; Matusů et al. 2008). This method brings a single tuning parameter 0 m > which can be used for influencing the control response. Later on, closed-loop robust stability can be verified for example with the assistance of the value set concept and zero exclusion condition (Barmish 1994; Bhattacharyya et al. 1995). This paper aims to present a simple way of constructing a model with parametric uncertainty and also an algebraic approach to continous-time robust control design. The proposed techniques are applied during control of bulb temperature in laboratory model of hotair tunnel. In a set of experiments, the controlled system is approximated by first or second order transfer functions with parametric uncertainty, the controllers are designed, the robust stability is verified, and the final control responses are tested and evaluated. HOT-AIR PLANT DESCRIPTION The controlled plant has been represented by laboratory model of hot-air tunnel constructed in VSB – TU of Ostrava (Smutný et al. 2002). Generally, this object can be seen as multi-input multi-output (MIMO) system, however, the experiments have been done on a selected single-input single-output (SISO) loop. The model is composed of the bulb, primary and secondary ventilator and an array of sensors covered by tunnel. The bulb is powered by controllable source of voltage and serves as the source of light and heat energy while the purpose of ventilators is to ensure the flow of air inside the tunnel. All components are connected to the electronic circuits which adjust signals into the voltage levels suitable for CTRL 51 unit. Finally, this control unit is connected with the PC via serial link RS232. The diagram of the plant and the whole control system is shown in fig. 1. PC Electronic circuits Power supply CTRL 51 Unit Ventilator Photoresistor Light bulb Thermistors Thermoanemometer