Feedback Linearizing Control of a Fluidized Bed Reactor z H. AOUFOUSSI, M. PERRIER*, J. CHAOUKI**, C. CHAVARIE and D. DOCHAIN‘ De‘partement de Ge‘nie Chimique, Ecole Polytechnique de Montre‘al, Campus de 1 ’Universite‘de Montrial, CP 6079, Succursale zyxwvut ‘3 zyxwv ”, Montrial, Que‘bec, Canada H3C 3A7 The design of an adaptive nonlinear controller for the control of a fluidized bed reactor is derived by using exact linearization techniques. Reset action and parameter adaptation are used to make more robust the precise compensation of nonlinear terms, which is called for in the linearization technique. zyxwv A nonlinear antiwindup mechanism is introduced to handle reset windup problem and to provide fast response without large overshoot. Simulation results show that the proposed adaptive controller guarantees good setpoint tracking. The developed estimation algorithm allows accurate estimation of the parameters for which the regressor component is not zero. La commande adaptative non lintaire d’un rtacteur catalytique zyxwvu ti lit fluidist est abordte en utilisant les techniques de lintarisation externe. L‘action inttgrale et I’adaptation paramttrique sont utilistes pour rendre plus robuste la com- pensation exacte des termes non lintaires qui est le fondement m&me des techniques en question. Nous avons propose un mtcanisme de dtsaturation de I’inttgration dans I’optique de pallier ti ces inconvenients et d’assurer une rtponse rapide sans de larges dtpassemenrs. Les rtsultats de simulation montrent que le contrbleur developpt assure une honne poursuite du signal de rtfirence. L’algorithme d’estimation developpt permet d’identifier avec prtcision les paramktres dont la composante correspondante du rtgresseur est non nul. Keywords: linearizing control, adaptive control, fluidized bed reactor. t is well known that the performance of chemical reactors I may be improved substantially by operation at an unstable stationary point (Bailey, 1977) or in an induced periodic tran- sient regime (Lee and Bailey, 1980; Watanabe et al., 1982). There is a clear incentive to design efficient controllers for this type of reactor operation. In particular, one may expect good control performances from control schemes which take into account the well known process nonlinearities. One potential solution is to consider linear adaptive control. Since it is essentially based on an only locally valid linearized representation of the process, it is very difficult to prove the stability and to emphasize the efficiency of linear adaptive control over a large range of operating conditions of the non- linear process. In particular, it may not perform well in servo control problems such as start-up/shut-down or optimal pro- file tracking of batch processes. These observations suggest that control strategies based on the nonlinear model of the process could be useful for the control of a reactor. Recently, nonlinear control based on differential geom- etry emerged as a tool to treat a large class of nonlinear systems (Bastin and Dochain, 1990; Kravaris and Kantor, 1990; Henson and Seborg, 1990; McLellan et al., 1990). The main idea is to look for nonlinear transformations on the state and/or the manipulated input, which, when applied to a given nonlinear system, will provide a closed-loop linear dynamical behaviour. Linearity of the closed loop system is sought in some sense, e.g. linearity of the closed-loop state equations (Brockett, 1978; Hunt et al., 1983), or linearity of the input-output equations (Isidori and Ruberti, 1984; Kravaris and Chung, 1987). Once, the nonlinear system is transformed into a linear system, one can then proceed with the design of the controller by using one of the available tech- niques for linear systems. The theory is now well developed for both the continuous time (Isidori, 1989) and the discrete time domains (Monaco et al., 1986). Dead time compen- sation based on Smith predictor method (Kravaris and Wright, 1989) and feedforward compensation of measured ‘Current aftiliation: Pulp and Paper Research Institute of Canada. 570 Bl$ St-Jean, Montreal, Quebec H9R 359. +Chercheur qualifit FNRS (Belgium). To whom correspondence should be addressed. disturbances (Daoutidis and Kravaris, 1989) were also recently developed. One potential drawback of linearizing control techniques is that they rely on exact cancellation of nonlinear terms in order to obtain a linear input-output behavior. Indeed, the cancellation is no longer exact when there are uncertainties in the model parameters and in the model structure or in presence of unmeasured disturbances. One way to overcome this problem is to introduce integral action in the control law. However, if the gain of the integrator is high, overshoot will occur. This is, at least, highly undesirable in some situations like exothermic reactor temperature control (Ray, 1981 ). In face of parametric uncertainty, parameter adaptive control appears to be a rather natural and interesting solution since one can hope to have an asymptotically exact cancellation of the nonlinear terms (Sastry and Isidori, 1987; Nam et al., 1988; Bastin and Dochain, 1988). Another attempt in this regard was made by Taylor et al. (1989), who considered the effect of parasitics dynamics on their adaptation scheme. Despite the apparently restrictive conditions (linearity in the parameters, for instance) of these adaptive schemes, appli- cations are reported in many fields such as bioreactors (Dochain and Bastin, 1984; Bastin and Dochain, 1990) and robot manipulators (Craig et al., 1987). In this paper we describe the design and the application of recently developed nonlinear feedback linearization tech- niques to the temperature control of a Fluidized Bed Reactor (FBR). Modifications are suggested to the basic control law to handle the problems associated with the introduction of integral action. We suggest to add a nonlinear antiwindup mechanism to guarantee satisfactory dynamic and static (zero offset) performances. The adaptive and non adaptive ver- sions of the proposed controller are also formulated. The paper is organized as follows. First, we give a brief review of the model reference linearizing control method together with the modifications to the basic algorithm to handle the reset windup problem. We then formulate the adaptive version of the nonlincar controller. The design of four nonlinear Model Reference Linearizing Controllers (withlwithout reset action and nonadaptive/adaptive con- trollers) are presented in the Feedback Linearizing Control Method and in Adaptive Model Reference Linearizing zy 356 THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, VOLUME 70, APRIL. 1992