Jesús Alvarez - Academia.edu (original) (raw)

Papers by Jesús Alvarez

Chemical Engineering Science, 1990

The combination of autoacceleration and poor heat removal in exothermic continuous polymerization... more The combination of autoacceleration and poor heat removal in exothermic continuous polymerizations move reactor design towards operation at high state sensitivity with reduced stability margins or unstabie operation. A nonlinear temperature control does not guarantee stable operation. Stable control and improved dynamics can be attained when conversion and temperature set-points are regulated by manipulating initiator feedrate and heat removal rate. The use of measured input disturbances (feed conversion and temperature) provides disturbance rejection capabilities. This poses a control design for a multivariable, nonlinear, interactive process with measured input disturbances. It is found that there exists a nonlinear controller which assures a closed-loop operation about a unique attractor with a well-defined domain of stability which accommodates well the region of feasible operation. The methodology is constructive and provides a nonlinear multivariable feedforward-feedback control scheme that cancels both the nonlinearity and the interaction, permitting single-loop tuning with conventional linear techniques. Numerical simulations corroborate the findings and illustrate the performance of the control technique. 'Author to whom correspondence should he addressed. *Departamento de Matemhticas. Jzsirs ALVAREZ et al. relationships for m?nomer-polymer mixtures in mass or in solution. Henderson (1987) used those results combined with standard correlations for heat transfer in jacket cooled vessels (Kern, 1950, Oldshue, 1983a, b) to obtain expressions for heat transfer coefficients that depend on conversion and temperature. The nonlinear static and dynamic behavior of free-radical polymerization CSTRs has been studied with simulations (Jaisinghani and Ray, 1977; Brooks, 1981) and with laboratory experiments (Spitz et al., 1976; Arai and Saito, 1976; Brooks, 1985). In spite of not including conversion and temperature dependence of the heat transfer coefficient, important nonlinear features can be found in those works. Henderson (1987) and Henderson and Cornejo (1987) considered viscosity effects on the heat transfer coefficient to obtain Van Heerden multiplicity diagrams. The later two works show how unstable operation is obtained for reactor designs of practical interest. Issues such as sensitivity, dynamics and control were addressed in a descriptive fashion. It can be said that there exist elements to characterize the essential nonlinear dynamics of the free-radical polymerization in CSTRs. Recently, research in nonlinear control systems, with differential geometric methods (Herman and Krener, 1977; Hunt et al., 1983b; Tsidori, 1985; Vidyasagar, 1986), has produced interesting results which generalize, for a class of nonlinear systems, concepts and tools from linear control theory. One of those results is the generalization of the state feedback design, for controllable linear systems, based on transformations to controllability canonical forms (Hunt and Su, 1981; Su, 1982; Hunt et al., 1983a, b). These techniques have been applied to control chemical reactors. Using local theory, Hoo and Kantor (1985, 1986) controlled one-input two-state reactors (one of them biological), and Alvarez and Gonzalez (1986) controlled a one-input three-state reactor which included jacket dynamics. Alvarez et al. (1989) established global solvability of the control problem for a one-input two-state reactor. Calvet and Arkun (1988b) extended Su's (1982) results to a class of nonlinear systems with time-invariant input disturbances and one control input. As a result, the control scheme for a one-input two-state reactor (Calvet and Arkun, 1988a) included a feedforward path. Hitherto, nonlinear reactor control design has been done for one-input reactors with simple kinetic schemes and constant heat transfer coefficients. When complete state exact linearization cannot be accomplished, input-output linearization (Tsidori el al., 1981; Tsidori, 1985, Byrnes and Isidori, 1988) can be used. This technique has been applied to single-input (Kravaris and Chung, 1987) and two-input reactors (Gamas, 1988). Kravaris et al. (1989) used these techniques to track a single reference trajectory with one control input for a batch copolymerization reactor. In this work, the control problem of a free-radical polymerization, taking place in a cooled CSTR, is addressed. The isothermal version of our reactor exhibits multiplicity with unstable operation point. As a of the Latinamerican Automatic Control Congress,

Chemical Engineering Science, 1990

The combination of autoacceleration and poor heat removal in exothermic continuous polymerization... more The combination of autoacceleration and poor heat removal in exothermic continuous polymerizations move reactor design towards operation at high state sensitivity with reduced stability margins or unstabie operation. A nonlinear temperature control does not guarantee stable operation. Stable control and improved dynamics can be attained when conversion and temperature set-points are regulated by manipulating initiator feedrate and heat removal rate. The use of measured input disturbances (feed conversion and temperature) provides disturbance rejection capabilities. This poses a control design for a multivariable, nonlinear, interactive process with measured input disturbances. It is found that there exists a nonlinear controller which assures a closed-loop operation about a unique attractor with a well-defined domain of stability which accommodates well the region of feasible operation. The methodology is constructive and provides a nonlinear multivariable feedforward-feedback control scheme that cancels both the nonlinearity and the interaction, permitting single-loop tuning with conventional linear techniques. Numerical simulations corroborate the findings and illustrate the performance of the control technique. 'Author to whom correspondence should he addressed. *Departamento de Matemhticas. Jzsirs ALVAREZ et al. relationships for m?nomer-polymer mixtures in mass or in solution. Henderson (1987) used those results combined with standard correlations for heat transfer in jacket cooled vessels (Kern, 1950, Oldshue, 1983a, b) to obtain expressions for heat transfer coefficients that depend on conversion and temperature. The nonlinear static and dynamic behavior of free-radical polymerization CSTRs has been studied with simulations (Jaisinghani and Ray, 1977; Brooks, 1981) and with laboratory experiments (Spitz et al., 1976; Arai and Saito, 1976; Brooks, 1985). In spite of not including conversion and temperature dependence of the heat transfer coefficient, important nonlinear features can be found in those works. Henderson (1987) and Henderson and Cornejo (1987) considered viscosity effects on the heat transfer coefficient to obtain Van Heerden multiplicity diagrams. The later two works show how unstable operation is obtained for reactor designs of practical interest. Issues such as sensitivity, dynamics and control were addressed in a descriptive fashion. It can be said that there exist elements to characterize the essential nonlinear dynamics of the free-radical polymerization in CSTRs. Recently, research in nonlinear control systems, with differential geometric methods (Herman and Krener, 1977; Hunt et al., 1983b; Tsidori, 1985; Vidyasagar, 1986), has produced interesting results which generalize, for a class of nonlinear systems, concepts and tools from linear control theory. One of those results is the generalization of the state feedback design, for controllable linear systems, based on transformations to controllability canonical forms (Hunt and Su, 1981; Su, 1982; Hunt et al., 1983a, b). These techniques have been applied to control chemical reactors. Using local theory, Hoo and Kantor (1985, 1986) controlled one-input two-state reactors (one of them biological), and Alvarez and Gonzalez (1986) controlled a one-input three-state reactor which included jacket dynamics. Alvarez et al. (1989) established global solvability of the control problem for a one-input two-state reactor. Calvet and Arkun (1988b) extended Su's (1982) results to a class of nonlinear systems with time-invariant input disturbances and one control input. As a result, the control scheme for a one-input two-state reactor (Calvet and Arkun, 1988a) included a feedforward path. Hitherto, nonlinear reactor control design has been done for one-input reactors with simple kinetic schemes and constant heat transfer coefficients. When complete state exact linearization cannot be accomplished, input-output linearization (Tsidori el al., 1981; Tsidori, 1985, Byrnes and Isidori, 1988) can be used. This technique has been applied to single-input (Kravaris and Chung, 1987) and two-input reactors (Gamas, 1988). Kravaris et al. (1989) used these techniques to track a single reference trajectory with one control input for a batch copolymerization reactor. In this work, the control problem of a free-radical polymerization, taking place in a cooled CSTR, is addressed. The isothermal version of our reactor exhibits multiplicity with unstable operation point. As a of the Latinamerican Automatic Control Congress,