Michael J. Kurtz

Input-output linearizing control of constrained nonlinear processes

Abstract An input-output linearization strategy for constrained nonlinear processes is proposed. The system may have constraints on both the manipulated input and the controlled output. The nonlinear control system is comprised of: (i) an input-output linearizing controller that compensates for processes nonlinearities; (ii) a constraint mapping algorithm that transforms the original input constraints into constraints on the manipulated input of the feedback linearized system; (iii) a linear model predictive controller that regulates the resulting constrained linear system; and (iv) a disturbance model that ensures offset-free setpoint tracking. As a result of these features, the approach combines the computational simplicity of input output linearization and the constraint handling capability of model predictive control. Simulation results for a continuous stirred tank reactor demonstrate the superior performance of the proposed strategy as compared to conventional input-output linearizing control and model predictive control techniques.

Selection of model parameters for off-line parameter estimation

Mechanistic dynamic models often contain unknown parameters whose values are difficult to determine even with highly specialized laboratory experiments. A practical approach is to estimate such parameters from available process data. Typically only a subset of the parameters can be estimated due to restrictions imposed by the model structure, lack of measurements, and limited data. We present a simple parameter selection method which accounts for the first two factors independent of the data available for parameter estimation. The magnitude of each parameter effect on the measured variables is quantified by applying principal-component analysis to the steady-state parameter-output sensitivity matrix. The uniqueness of each parameter effect is determined by computing the minimum distance between the sensitivity vector of the particular parameter and the vector spaces spanned by sensitivity vectors of the parameters already selected for estimation. A recursive algorithm that provides a tradeoff between the magnitude and linear independence of parameter effects yields a ranking of the parameters according to their inherent ease of estimation. The parameter-selection procedure is applied to the problem of kinetic parameter estimation for an industrial model of a polymerization reactor. For this specific example, the proposed method yields superior estimation results than those obtained with a parameter-selection technique based on the Fisher information matrix (FIM).

State and disturbance estimation for nonlinear systems affine in the unmeasured variables

Abstract The problem of estimating unmeasured state and disturbance variables for nonlinear process control applications is considered. We assume that the process model is affine with respect to the unmeasured disturbances and any unmeasured state variables. The disturbances are considered as additional state variables, and a nonlinear observer is designed for the augmented state-space system. The observability of the augmented system is analyzed, and a constructive procedure for calculating the nonlinear observer gains is proposed. Full-order and reduced-order observers are constructed for both the full-state and partial-state feedback cases. Stability results for the nonlinear observer are presented. An output feedback controller is obtained by combining the nonlinear observer with an input–output linearizing controller. The proposed estimation strategy is compared to linear estimation techniques using a fluidized bed reactor model.

Feedback linearizing control of discrete-time nonlinear systems with input constraints

A feedback linearizing control strategy for discrete-time nonlinear systems subject to input constraints is proposed. The control system comprises: (i) a feedback linearizing controller; (ii) a constraint mapping algorithm that transforms the actual input constraints into constraints on the feedback linearized system; and (iii) a linear model predictive controller that regulates the resulting constrained linear system. Closed-loop stability analysis is a challenging problem because the transformed constraints are state dependent. Sufficient conditions for asymptotic stability are presented for fully and partially feedback linearizable systems. As part of the analysis, a new stability result for unconstrained discrete-time nonlinear systems which parallels a well-known continuous-time result is derived.

Constrained output feedback control of a multivariable polymerization reactor

A multivariable, nonlinear control strategy which accounts for unmeasured state variables and input constraints is developed for the free-radical polymerization of methyl methacrylate. Monomer concentration and reactor temperature are controlled using a technique which combines input-output decoupling and linear model predictive control. Input constraints are handled explicitly by applying linear model predictive control to the feedback linearized system. Unmeasured initiator and solvent concentrations are accounted for by treating the live polymer concentration as an unknown parameter which is estimated online. The performance of the control strategy is evaluated through closed-loop simulations.

Feedback Linearizing Controller Design for Chemical Processes: Challenges and Recent Advances

Abstract Many chemical processes are difficult to control due to their inherent nonlinear characteristics. Feedback linearization is a promising approach for controlling such highly nonlinear processes. In this paper, we discuss a few problems which are encountered when feedback linearization is applied to chemical processes and provide an overview of our attempts to address these problems. More specifically, we focus on several issues not adequately addressed by existing feedback linearization theory including: (i) unmeasured state variables; (ii) unmeasured disturbances; (iii) time delays; and (iv) process constaints. The concepts are illustrated using a simple chemical reactor model which exhibits many of the nonlinear characteristics observed in industrial processes.

Nonlinear control of competitive mixed-culture bioreactors via specific cell adhesion

A nonlinear control strategy for continuous biological reactors with competitive mixed-cultures is proposed. The desired operating point, which corresponds to coexistence of the two cell populations, is unstable because the cellular growth rates differ. We utilize specific cell adhesion to separate and selectively recycle the slower growing population in order to stabilize the desired coexistence steady state. The recycle loop is operated periodically so that the adhesion column can be regenerated after each sample is processed. The nonlinear control law is derived by applying input-output linearization to an approximate dynamic model that assumes continuous separation of the cell populations. A nonlinear closed-loop observer is used to generate one-time-delay-ahead predictions of the measured cell concentrations and the unmeasured substrate concentration. The efficacy of the proposed control strategy is evaluated via simulation.

Stability analysis of a feedback linearizing control strategy for constrained nonlinear systems

A feedback linearizing control strategy for discrete-time nonlinear systems subject to input constraints is analyzed. The control system comprises (i) a feedback linearizing controller; (ii) a constraint mapping algorithm that transforms the actual input constraints into constraints on the feedback linearized system; and (iii) a model predictive controller which regulates the resulting constrained linear system. Stability analysis is a challenging problem because the transformed constraints are state dependent. Sufficient conditions for asymptotic stability are presented for fully and partially feedback linearizable systems. As part of the analysis, a new stability result for unconstrained discrete-time nonlinear systems which parallels a well known continuous-time result is derived.