Rodolfo Suárez

Global stabilization of nonlinear cascade systems

Abstract We present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems. These are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section. For polynomial systems, in particular, the stabilizing feedback is given explicitly.

Linear systems with bounded inputs: global stabilization with eigenvalue placement

This work presents a technique for obtaining a bounded continuous feedback control function which stabilizes a linear system in a certain region. If the open-loop system has no eigenvalues with positive real part, the region of attraction of the resulting closed-loop system is all ℝn, i.e., the feedback control is a global stabilizer; otherwise, the region contains an invariant (‘cylindric-like’) set where the controller does not saturate. The proposed control is a linear-like feedback control with state-dependent gains. The gains become implicitly defined in terms of a nonlinear scalar equation. The control function coincides in an ellipsoidal neighbourhood of the origin with a linear feedback law which is a solution of a linear quadratic regulator problem. This design allows eigenvalue placement in a specified region.

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.

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.

Global stabilization of a certain class of nonlinear systems

Abstract Systems are considered which can be reduced to a regular form and possess an invariant manifold such that the restriction of the system to the manifold is globally asymptotically stable (GAS). We construct a feedback which renders the manifold globally attracting. It was proved that in this situation boundedness of all orbits is necessary and sufficient for the control system to be GAS. A Lyapunov type condition for the latter property adapted to the situation in question is given. Results of Andreini, Bacciotti, and Stefani are shown to be a special case of our result.

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.

Global stabilization of discrete‐time linear systems with bounded inputs

In this paper we present a technique to stabilize discrete-time linear systems with bounded inputs. Based on optimal control techniques, we construct a continuous bounded state feedback which leads to global asymptotic stabilization for the case where the open-loop system has all its eigenvalues with modulus less than or equal to one. If the open-loop system has eigenvalues with modulus greater than one, a region of attraction of the origin is obtained. The resulting state feedback can be seen as a pointwise linear feedback with state-dependent gains, which are defined in terms of a non-linear algebraic equation.

Sufficient algebraic conditions for stability of cones of polynomials

In this paper a sufficient condition for a cone of polynomials to be Hurwitz is established. Such condition is a matrix inequality, which gives a simple algebraic test for the stability of rays of polynomials. As an application to stable open-loop systems, a cone of gains c such that the function u=−kcTx is a stabilizing control feedback for all k>0 is shown to exist.