Vassilis Sakizlis

Recent advances in optimization-based simultaneous process and control design

Abstract In this work, we first discuss recent advances towards the integration of process design, process control and process operability from the open literature and then we focus on techniques towards this endeavor that were developed within our group at Imperial College. While most of the approaches employ controllability measures to achieve this goal, our developments can be classified as a simultaneous process and control design methodology. Based on novel mixed integer dynamic optimization algorithms, our strategy features high fidelity process dynamic models, conventional PI control schemes, explicit consideration of structural process and control design aspects (such as number of trays, pairing of manipulated and controlled variables) through the introduction of 0–1 variables, and explicit consideration of time-varying disturbances and time-invariant uncertainties. The application of this strategy to a typical distillation system is discussed. In the second part of this chapter we present an extension of the process and control design framework that incorporates advanced model-based predictive controllers. Parametric programming is used for the controller derivation giving rise to a closed-form controller structure and removing the need for solving an optimization problem on-line. The resulting parametric controller is readily incorporated in the design optimization framework bringing about significant economic and operability benefits. The key features and advantages of this approach are highlighted via a simple binary distillation example.

Design of robust model-based controllers via parametric programming

In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller is derived off-line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasible operation in the presence of bounded input uncertainties by (i) explicitly incorporating in the controller design stage a set of feasibility constraints and (ii) minimizing the nominal performance, or the expectation of the performance over the uncertainty space. An extension of the method to problems involving target point tracking in the presence of persistent disturbances is also discussed. The general concept is illustrated with two examples.

New algorithms for mixed-integer dynamic optimization

Abstract Mixed-integer dynamic optimization (MIDO) problems arise in chemical engineering whenever discrete and continuous decisions are to be made for a system described by a transient model. Areas of application include integrated design and control, synthesis of reactor networks, reduction of kinetic mechanisms and optimization of hybrid systems. This article presents new formulations and algorithms for solving MIDO problems. The algorithms are based on decomposition into primal, dynamic optimization and master, mixed-integer linear programming sub-problems. They do not depend on the use of a particular primal dynamic optimization method and they do not require the solution of an intermediate adjoint problem for constructing the master problem, even when the integer variables appear explicitly in the differential–algebraic equation system. The practical potential of the algorithms is demonstrated with two distillation design and control optimization examples.

The Explicit Control Law for Hybrid Systems via Parametric Programming

In this paper an algorithm is presented for the derivation of the explicit optimal control policy for linear dynamical systems that also involve (i) logical decisions and (ii) constraints on process inputs and outputs. The control actions are usually computed by solving at regular time intervals an on-line optimization problem based on a set of measurements that specify the current process state. The approach presented in this paper derives the optimal control law off-line as a function of the state of the process, thus mating the repetitive solution of on-line optimization prob lems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.

Robust model-based tracking control using parametric programming

In this work, a method is presented for obtaining the explicit robust model-based tracking control law for constrained dynamic systems. The proposed control scheme guarantees optimal and feasible operation under the presence of unknown bounded input uncertainties by introducing in the controller design stage a set of feasibility constraints and employing an estimation scheme for ensuring robust offset free output tracking. The controller features a simple structure that is derived off-line via parametric programming prior to any process implementation.

The explicit control law for hybrid systems via parametric programming

An algorithm is presented for the derivation of the explicit optimal control policy for linear dynamical systems that also involve (i) logical decisions and (ii) constraints on process inputs and outputs. The control actions are usually computed by solving at regular time intervals an on-line optimization problem based on a set of measurements that specify the current process state. The approach presented in the paper derives the optimal control law off-line as a function of the state of the process, thus eliminating the repetitive solution of on-line optimization problems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.

Output feedback Parametric Controllers for an Active Valve Train Actuation System

The first commercial camless car engines featuring continuously variable valve timing are expected to be available by 2010 to meet the strict legislation on NOx and COx emissions. A key factor for the development of this technology is the design of controllers that can maintain accurate signal tracking in the presence of variations in engine parameters and running conditions. Towards this direction, we present a control design methodology and a new control implementation of an advanced optimizing parametric controller (Parco) for a research active valve train system at Lotus Engineering. The controller is based on a mathematical model for the active valve train and is derived off-line using novel parametric programming techniques. The simple explicit form of the controller enables its implementation on the currently available commercial microprocessor with sampling times of 0.1 ms. Simulation and experimental results demonstrated the superiority of the parametric controller in comparison with a conventional proportional derivative (PD) control scheme

PARAMETRIC MODEL PREDICTIVE CONTROL OF AIR SEPARATION

Abstract This paper describes the application of Parametric Model Predictive Control to small processing units, in particular small Air Separation plants. Multiparametric optimization techniques are used to rigorously solve the MPC problem in two steps: an offline solution which generates a parametric mapping of the optimal control adjustments, and an online solution which reduces to a simple lookup operation. Because of the speed and simplicity of this lookup operation we are able to implement MPC in low-end computing devices such as PLCs, reaping the benefits of model-based control by implementing it at low cost in small plants where otherwise it would not be justified by the cost/benefit ratio.

A parametric optimisation approach for robust MPC

Abstract In this paper an algorithm is presented for deriving the explicit robust model based optimal control law. The system is represented by linear, discrete-time, time-invariant model with constraints on control and state variables and a quadratic objective function. Using the fundamentals of flexibility analysis the algorithm proposed in this paper derives the robust optimal control law off-line as a function of the state of the process, thus eliminating the repetitive solution of on-line optimisation problems. Hence, the on-line implementation is reduced to a sequence of simple function evaluations. The key advantageous features of the algorithm are demonstrated via an illustrative example.

Robust parametric predictive control design for polytopically uncertain systems

In this paper we present an algorithm for the design of robust model based predictive controller for polytopically uncertain systems via parametric programming. A min-max approach is adopted to design robust parametric predictive controllers, which guarantees feasible plant operation for maximum violation of polytopic uncertainty in system matrices and bounded input disturbances. The resulting piece wise affine optimal control law is a function of states and can be implemented online as a sequence of simple function evaluations. An example is presented to illustrate the details of the proposed robust parametric predictive controller design.