# (186f) State Estimation-Based Economic Model Predictive Control of Nonlinear Systems

- Conference: AIChE Annual Meeting
- Year: 2012
- Proceeding: 2012 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Tuesday, October 30, 2012 - 10:15am-10:35am

Traditionally, optimal operation and control policies for chemical

process systems are addressed via a two layer

approach in which the upper layer carries steady-state process

optimization to obtain economically optimal

process operating points (steady-states) while the lower layer utilizes

appropriate feedback control systems to steer the process state to an

economically optimal steady-state.

Model predictive control (MPC) is widely used in the lower layer to obtain

optimal manipulated input values by minimizing a (typically) quadratic

cost function which usually penalizes the deviation of the system state

and manipulated inputs from their economically-optimal steady-state values subject to

input and state constraints [1]; however, this

two-layer approach usually limits process operation around a steady-state.

Economic model predictive control (EMPC) framework deals with a

reformulation of the conventional MPC quadratic cost function in which an

economic (not necessarily quadratic) cost function is used directly as the

cost in MPC, and thus, it may, in general, lead to time-varying process

operation policies (instead of steady-state operation), which directly optimize process economics.

In a previous work [2], we presented a

two-mode Lyapunov-based economic MPC (LEMPC) design for nonlinear systems which is also capable of handling asynchronous and delayed measurements and extended

it in the context of distributed MPC [3]. Currently, all economic MPC schemes have been developed under the assumption of state

feedback.

State estimation in certain classes

of nonlinear systems can be carried out within the framework of high-gain

observers, however,

at this stage these estimation techniques have not been used in

conjunction with economic MPC schemes. Motivated by this, in this work, we focus on a class of nonlinear

systems and design an estimator-based EMPC system.

Working with the class of full-state feedback linearizable nonlinear systems, we use

a high-gain observer to estimate the nonlinear system state using output

measurements and a Lyapunov-based approach to

design an EMPC system that uses the observer state estimates. We prove,

using singular perturbation arguments, that the closed-loop system is

practically stable provided the observer gain is sufficiently large. We

use a chemical process example to demonstrate the ability of the

state-estimation based

EMPC to achieve process time-varying operation that leads to a superior

cost performance metric compared to steady-state operation. In the

example,

the high-gain observer is used to obtain estimates of the reactant

concentration from temperature measurements; a meaningful case in process control practice.

[1] P. D. Christofides, J. Liu, and D. Munoz de la Pena. "Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications", Advances in Induatrial Control Series. Springer-Verlag, London, England, 2011.

[2] M. Heidarinejad, J. Liu, and P. D. Christofides. "Economic model predictive control of nonlinear process systems using Lyapunov techniques" ,AIChE Journal, 58:855–870, 2012.

[3] X. Chen, M. Heidarinejad, J. Liu and P. D. Christofides, "Distributed Economic MPC: Application to a Nonlinear Chemical Process Network'', Journal of Process Control, 22, 689-699, 2012.

See more of this Session: Advances In Process Control

See more of this Group/Topical: Computing and Systems Technology Division

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