A procedure for the design and evaluation of decentralised and model-based predictive multivariable controllers for a pellet cooling process

Abstract

The cooling zone of an induration furnace is a highly interactive multivariable process with strong nonlinearities and dissimilar dynamics. Linear controllers, implemented on a first-principles process model, are unable to properly control the unit in a wide operating range. This paper proposes a design procedure which considers relevant process characteristics, such as nonlinearity, interaction, directionality, and dynamics, for the synthesis of decentralised extended PIDs and model-based predictive controllers (MPCs). Linear controllers with variable transformations are used since the process model shows that a Hammerstein model can approximate the process nonlinear behaviour. The decentralised PIDs are tuned using efficient rules that take into account the process interaction. The performance of both control strategies is evaluated for set-point tracking, disturbance rejection, and robustness to modelling errors. Similar results are obtained for the gas temperature control, which is the most important process variable. Slightly better results are obtained with the MPC for the gas pressure, the fastest dynamic variable.

Introduction

PID controllers are found in most process industries. According to Åström and Hägglund (1995), more than 95% of the control loops are of PID type and most controllers only use the proportional and integral actions. The popularity of these controllers comes from their simplicity of implementation, since they are available in distributed control systems and programmable logic controllers, their flexibility, and their easy acceptance by operators (Gagnon, 1999). According to Skogestad and Morari (1987), they have fewer tuning parameters, are easier to understand, and are more easily made failure tolerant than decoupling controllers. In practice, decentralised control structures are preferred for ease of start-up, bumpless automatic/manual transfer, and fault tolerance in the event of actuator or sensor failures (Lakshminarayanan, Shah, & Nandakumar, 1997).

However, efficient tuning of decentralised PID controllers for multivariable processes is relatively complex. An input–output pairing selection must be done to design the controller diagonal matrix while considering the process interaction. For highly interactive processes, the performance obtained is often mediocre because of a wrong selection of the input–output pairing and poor controller tuning.

An alternative approach is to directly synthesise a multivariable controller, such as a model-based predictive controller (MPC), based on the minimisation of some objective function. The objective of MPC is to select a set of future control moves (control horizon) in order to minimise a function based on a desired output trajectory over a prediction horizon. MPC considers the process interaction and explicitly handled constraints. However, MPC are difficult to implement in most commercial control systems and require specialised software.

Centralised optimal (MPC) and decentralised PID control structures have advantages and disadvantages. For industrial multivariable processes, the choice of the appropriate control structure depends on the process characteristics, the economic value of improved control, and the available computing and process control resources. The successful industrial implementation of either a centralised or decentralised controller on a nonlinear multivariable process requires the following design steps. A first-principles dynamic model of the process is useful in order to characterise its nonlinearity and, when necessary, to study the different alternatives to linearise the process. Using the dynamic model, the process directionality should be studied and the scaling required applied. When algebraic control laws are used, the process interaction must be analysed for the pairing selection. Closed-loop performance specifications, compatible with the results of the directionality and interaction study, can then be selected. Subsequently, the control structures and controller settings can be determined. Finally, the various control structures are evaluated by taking into account the complexity of implementation, the robustness of the algorithm for parametric variations, and the performance for set-point changes and disturbance rejection.

The objective of this study is not simply to compare alternative control strategies, but also to illustrate a step-by-step design procedure for decentralised and centralised industrial controllers for a cooling process of iron oxide pellets used in pyrometallurgical installations. At the moment, the objective is not to implement the controllers on the real plant, but simply to assess the design procedure and the controller performance, using a simulator that describes the process by a set of algebraic and partial differential equations.

This paper first presents the process as well as its dynamic simulator. The process characteristics (nonlinearity, directionality, and interaction) are evaluated. Scaling and linearisation are then used before MPC and decentralised controllers are incorporated. Finally, for similar assigned performances of the controlled process, the control strategies are compared and evaluated for both set-point tracking, disturbance rejection, and robustness to modelling errors.