Sairam Valluri

Shortest-prediction-horizon non-linear model-predictive control

Abstract This article concerns non-linear control of single-input-single-output processes with input constraints and deadtimes. The problem of input-output linearization in continuous time is formulated as a model-predictive control problem, for processes with full-state measurements and for processes with incomplete state measurements and deadtimes. This model-predictive control formulation allows one (i) to establish the connections between model-predictive and input-output linearizing control methods; and (ii) to solve directly the problems of constraint handling and windup in input-output linearizing control. The derived model-predictive control laws have the shortest possible prediction horizon and explicit analytical form, and thus their implementation does not require on-line optimization. Necessary conditions for stability of the closed-loop system under the constrained dynamic control laws are given. The connections between (a) the developed control laws and (b) the model state feedback control and the modified internal model control are established. The application and performance of the derived controllers are demonstrated by numerical simulations of chemical and biochemical reactor examples.

Nonlinear control of input-constrained systems

Abstract This paper presents an optimization-based method for deriving model-based controllers that are applicable to input-constrained, multi-input multi-output, nonlinear processes described by a discrete-time mathematical model. By this method, nonlinear model-based control laws that inherently include optimal directionality and windup compensators are derived. The control laws can minimize the mismatch between constrained and unconstrained process responses, are input–output linearizing in the absence of input constraints, and allow one to adjust the rate of decay of the mismatch between constrained and unconstrained process responses when the constraints are no longer active. The connections between (a) the derived control laws and (b) model state feedback control and modified internal model control are established. The application and performance of the derived control laws are demonstrated by three examples.

Input constraint handling and windup compensation in nonlinear control

This paper presents new, high-performance, nonlinear control laws for single-input single-output nonlinear processes with input constraints. Whether input constraints are present or not, each of these dynamic control laws minimizes the mismatch between the closed-loop output response and the nominal linear output response that the same control law induces when there are no constraints. The connections between the developed control laws and the modified internal model control are established. The superior performance of the derived control laws is demonstrated by an example of chemical reactor.

A non-linear controller design method for processes with saturating actuators

An optimization approach is proposed to derive non-linear model-based control laws for non-linear processes with actuator saturation non-linearities. The derived control laws induce a linear closed-loop process output response in the absence of input constraints (are input-output linearizing), are able to minimize the mismatch between the constrained and the linear unconstrained process output responses, and inherently include optimal directionality and windup compensators. Connections between the derived control laws and (a) already available, input-output linearizing, non-linear, control methods, (b) modified internal model control, and (c) model state feedback control, are established. The application and performance of the derived control laws are shown by examples.

Model predictive control of systems with actuator amplitude and rate saturation

We develop a continuous-time model predictive control design procedure for single-input single-output linear systems with actuator amplitude and rate saturation. This design methodology formulates the actuator amplitude and rate saturation problem as an equivalent amplitude saturation problem with system dynamics augmented by rate dynamics. It is shown that the MPC laws have closed-form analytical solution in the limit that the prediction horizon is small. The stability analysis is performed using a Lyapunov function framework which results in a subset of domain of attraction for guaranteed closed-loop stability in the event of actuator amplitude and rate saturation. A numerical example is presented for illustrating the proposed control design methodology.

Calculation of optimal feasible controller output in multivariable processes with input constraints

Presents an optimal directionality compensator for multivariable processes with actuator saturation nonlinearities. Given an unconstrained controller output and the characteristic (decoupling) matrix of the process under consideration, the compensator calculates an optimal constrained (feasible) plant input that once applied to the process, the resulting process response is as close as possible to the response of the same process to the controller output. The compensator can be used for both linear and nonlinear processes, irrespective of the type of controller being used. When the characteristic matrix is diagonal, the optimal directionality compensator is identical to a series of limiters (clippers). The performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation approaches, by numerical simulation of a linear example under decentralized PID control and a nonlinear bioreactor under input-output linearizing control.

Geometric control of input saturated systems with guaranteed closed-loop performance and stability

We study the issue of stability of input constrained closed-loop systems with a class of differential geometric controllers. Specifically, a Lyapunov function-based method is presented for determining the closed-loop stability under geometric control laws for single-input single-output systems. This method provides a subset of the domain of attraction for guaranteed stability of the closed-loop system. Furthermore, it offers flexibility in adjusting the closed-loop performance while ensuring closed-loop stability in the presence of input saturation. Hence, by using this framework the designer can a posteriori verify overall stability of the closed-loop system for a desired closed-loop performance.

Stability analysis for linear/nonlinear model predictive control of constrained processes

We present a stability analysis method for input constrained SISO linear/nonlinear systems with model predictive controllers. Specifically, this method is based on a Lyapunov function framework and provides a subset of the domain of attraction for the closed-loop stability under the shortest-prediction-horizon model predictive control laws. By using this framework a designer can a posteriori verify the overall stability of closed-loop system for a desired performance in the event of actuator saturation. The effectiveness of the method is demonstrated by considering linear and nonlinear examples.

Multivariable nonlinear controller synthesis in discrete-time

Abstract For a nonlinear process with a generically singular characteristic matrix, input–output linearization is usually not achievable with a static state feedback, and one has to use a dynamic state feedback. A systematic and general approach to input–output linearizing feedback control of nonlinear processes with a egenerically singular or nonsingular characteristic matrix is presented. Mixed error- and state-feedback, error-feedback, and mixed error- and output-feedback control laws are derived. The derived feedback control laws reject step disturbances asymptotically and induce linear, input–output, closed-loop behavior to the process under consideration. The theoretical connections between the derived control laws and (a) model predictive control and (b) several already-available linear deadtime compensation methods are established. The application and performance of the derived control laws are illustrated and compared with those of model predictive control, by numerical simulation of a chemical reactor.