Jesus Alvarez

Nonlinear decoupling control of free-radical polymerization continuous stirred tank reactors

Abstract 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 unstable 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.

Nonlinear bounded control for a class of continuous agitated tank reactors

Abstract Chemical reactors planned under efficiency and tight product quality considerations usually lead to a process where sensitivity and nonlinearity are essentials. This poses a nonlinear control problem where the control input exhibits propensity to meet its bounds. Control saturation induces an additional nonlinearity whose effect on stability must be understood when designing a control scheme. In practice, the bounded control problem design is circumvented by first designing a stable control for the no saturation case, and then by tuning its gains so that control bounds are no met, and successful implementation demands extensive tuning and testing. In fact, such designs may have unnecessary conservative dynamic performance. In this work, we address the bounded nonlinear control problem for a class of two-state chemical reactors where heat removal rate is the manipulated variable. Based on physical restrictions, reactor open-loop dynamics and nonlinear control via complete and partial linearization, we devise a global nonlinear geometric framework to establish solvability of the problem and to characterize its closed-loop dynamics. A specific reactor example and numerical simulations are used to illustrate and corroborate results.

Global nonlinear control of a continuous stirred tank reactor

Abstract A chemical reactor, modelled by two nonlinear ordinary differential equations with a manipulable input, is controlled by means of a nonlinear control law. A differential geometric approach enables the characterization, in a global sense, of the structural solvability of the nonlinear control problems. The structural characterization consists in establishing a well-defined region of the state space where global controllability, stability and transformability to a linear equivalent can be assured. The nonlinear controller arises after expressing a linear feedback, for an equivalent system, in original coordinates. The tuning of the controller is done by pole placement in the equivalent system. The nonlinear controller allows for process regulation of stable stationary points and stabilization of unstable ones. Proportional and proportional-integral designs for the equivalent system are considered. By numerical simulations, the performance of the controller is favorably compared and contrasted with the performance of conventional controllers.

Planar linear systems with single saturated feedback

Abstract We study planar linear systems with a linear or non-linear feedback global stabilizer subjected to saturation. The number of open-loop unstable eigenvalues characterizes the set of the equilibrium points and the shape of the asymptotic stability region (ASR). Some topological bifurcations on the shape of the ASR are described.

On the effect of the estimation structure in the functioning of a nonlinear copolymer reactor estimator

Abstract In this work, the effect of the estimation structure on the performance and robustness characteristics of a geometric nonlinear estimator is studied for free-radical continuous solution copolymerization reactors where conversion, composition, average molecular weight, solid mass fraction, and production rate are inferred from temperature, density, refractive index, volume, and flowrate measurements. The case study is based on the geometric characterization of the robust detectability property, yielding a set of admissible estimator structures that represent a degree of freedom in the estimator design. The choice of structure determines the estimator reconstruction rate and error propagation mechanism. Measures of estimability (i.e., robust detectability) are introduced to discriminate structures. The estimator functioning results confirm the ones drawn from the structural assessment stage, and yield that the best estimator behavior is attained with a structure different from the nominal detectability structure that underlies the nonlinear fixed-structure EKF and Luenberger techniques employed in previous polymer reactor estimation studies.

Nonlinear state estimation with robust convergence

Abstract The problem of designing a dynamic measurement processor for the on-line estimation of the state of a multi-input multi-output nonlinear plant is addressed. The plant can be either observable or detectable, encompassing a broad range of cases in process systems engineering. On the basis of the structure of a suitable property of robust nonlinear estimability, an estimator is built and its convergence studied, yielding sufficient conditions for robust convergence, a systematic construction, and a tractable gain tuning procedure. The estimability property has a verifiable test, and the execution of the tuning procedure, as well as the interpretation of its convergence features can be achieved within a conventional control framework for linear single-input controllers or single-output filters. The estimation of a continuous polymer reactor is considered as an application example.

Poly(vinyl alcohol) as a stabilizer in the suspension polymerization of styrene: The effect of the molecular weight

The interfacial tension of the water- (PVA)/styrene system was measured as a function of the poly(vinyl alcohol) (PVA) concentration and temperature. Average size and particle-size distribution were obtained for a suspension of styrene in water using PVA as a stabilizer. We discuss the interfacial tension through the Zykonski equation to establish the behavior of the adsorption isotherms in unstirred systems and discuss the apparently contradictory results of the stirred experiment. We propose a simple configuration model that is congruent with both results. q 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67: 71-77, 1998

Robust estimation of continuous nonlinear plants with discrete measurements

Abstract In this work the problem of designing a state estimator for completely or partially observable continuous nonlinear plants with discrete measurements is addressed. The combination of a geometric approach with a stability analysis yields an estimator design methodology with a nonlinear detectability condition susceptible of testing, a systematic estimator construction, a robust convergence criterion coupled with a simple tuning scheme, as well as a rationale to explain the interplay between sampling time, estimator gains, and estimator functioning. Comparing with the continuous measurement case where the convergence is attained by tuning the gain above a low limit, in the discrete measurement case the loss of information due to the measurement sampling increases the size of the lower gain limit, and imposes sampling time and high gain limits. The proposed methodology is applied to address the estimation problem of a class of solution homopolymerization reactors, and is tested with a methyl-methacrylate polymerization run taken from a previous extended Kalman filter implementation study with experimental data.

Semiglobal stabilization of multi-input linear systems with saturated linear state feedback

Abstract For multi-input linear systems with eigenvalues in the closed left-half comlex plane, we address the problem of stabilization by a linear state feedback subject to saturation. Using an eigenvalue-generalized eigenvector assignment technique, we prove that such systems can be semiglobally stabilized with a saturated linear state feedback. Based on this result, we propose an algorithm to calculate an e-parametrized family of state feedback gain matrices that semiglobally stabilize the system. Two examples are used to illustrate the results.

SEMIGLOBAL NONLINEAR CONTROL BASED ON COMPLETE INPUT-OUTPUT LINEARIZATION AND ITS APPLICATION TO THE START-UP OF A CONTINUOUS POLYMERIZATION REACTOR

Abstract We address the control problem of output tracking with disturbance rejection and preclusion of internal dynamics for multi-input multi-output nonlinear plants subjected to known disturbances. The closed-loop output error dynamics is required to be linear and noninteractive. Necessary and sufficient conditions for semiglobal solvability of the nonlinear control problem are given, yielding a construction of the related feedforward—feedback controller and identifying the basic information required on the measured and the assigned signals. The start-up of an open-loop unstable continuous free-radical homopolymerization reactor is considered as an application example. The solvability of the reactor control problem is characterized in terms of conditions that have direct meaning. Results are corroborated with numerical simulations.