Model Predictive Control

Model predictive control has been successfully extended to non-linear processes. The advantages of non-linear predictive control include explicit handling of process time- delays, constraints, the ability to handle non-minimum phase systems and incorporating knowledge of future set point changes (Sistu et al., 1993).

Model predictive control (MPC) is defined as a control scheme in which the controller repeatedly determines (optimises) a manipulated variable profile. An open-loop performance is optimised on a time interval extending from the current time to the

horizon technique is introduced as a natural, computationally feasible feedback law. The method has proven to have desirable stability properties for non-linear systems. Also, the generality of the performance objective, as opposed to standard integral square error between measurement and set point, provides the opportunity to design MPC controllers for higher level functions such as energy or waste minimisation (Eaton & Rawlings, 1992).

As a consequence of its structure (Figure 4-4), a MPC is a feedforward controller for known process changes and a feedback controller for unknown process changes. Thus, MPC can reject measured disturbances more rapidly than conventional controllers, by anticipating their impact on the process. Set point changes are achieved efficiently through their ability to predict an optimal sequence of manipulated variable outputs. The feedback element of a MPC compensates for the effects of unmeasured disturbances on the process outputs and deviations between model outputs and those measured (process/model mismatch) (Brengel & Seider, 1989).

The prediction horizon allows the MPC controller to take control action at the current time in response to forecast error even though the error at the current time is zero. Also the predictive controller may be given information about future constraints and future inputs such as planned set point changes or forecasts of loads or disturbances. Eaton & Rawlings (1992) showed that it is precisely this property of the MPC controller that is beneficial for controlling (scheduling) non-minimum phase plants. Implementing MPC with a neural network approach, involves utilising a neural network model to provide predictions of the future plant response over the specified horizon. The predictions supplied by the neural network model are passed to a numerical optimisation routine, which attempts to minimise a specified performance criterion in calculating a suitable control signal. The control signal may be chosen so as to minimise a quadratic performance criterion -

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subject to the constraints of the dynamic model. The constants N1 and N2 define the horizons over which the tracking error and control increments are considered. The values of λ are the control weights. The remaining parameters are illustrated in Figure 4-4 (Hunt et al., 1992).

Another alternative, is to train a further neural network to mimic the action of the optimisation routine. The controller network is consequently trained to produce the same control output for a given plant input (Hunt et al., 1992).

Model predictive control's multi-step strategy has proven performance in controlling processes in unstable operating regimes. However, the MPC approach remains sensitive to modelling errors in these unstable regions. A disadvantage of the MPC approach is the computationally intensive execution of the optimisation algorithm, especially where linearisation of non-linear system is not applicable. Also, the solution of the optimisation problem - therefore the controller behaviour - depends on a number of tuning parameters. These tuning parameters include the weighting coefficients in the objective function, the convergence criterion, the scaling of the variables and the magnitude of the velocity bounds (Psichogios & Ungar, 1991). The costs and effort required to implement an advanced control algorithm, such as MPC, include (1) the development of models to describe the process dynamics, (2) the dedication of processing power, and the (3) tuning of more parameters relative to analogue controllers. An MPC implementation is normally only justified for processes that cannot be adequately controlled by using less complex algorithms. These processes typically include the production of chemicals in high purities, chemical reactors with multiple steady state and periodic attractors, extraction processes with narrow two- and three- phase regions (e.g. supercritical extraction), distillation towers with temperature and concentration fronts sensitively coupled to the reflux ratio (azeotropic distillation towers), and processes required to operate in the region of many design and operating constraints (Brengel & Seider, 1989).

Process u d yp Σ - + e_i r M C Model Reference ym u' e_i yr Non-linear optimiser

Model predictive control is the industry standard for advanced process control. The complexity of practical problems solved in MPC frameworks far outstrips those attempted with direct inverse control frameworks. Temeng et al. (1995) implemented a non-linear MPC strategy for an industrial packed bed reactor for converting SO2 to

SO3. The reaction is exothermic and requires interstage cooling after each catalyst

pass. The process is characterised by significant process interaction, long time delays, slow dynamics and frequent disturbances. The process is normally operated in the open loop by human operators. Furthermore, the product composition constraints (i.e., environmental considerations) and minimum reaction temperatures pose hard operating constraints. The process has five process variables and five manipulated variables. Dynamic response tests in the open loop generated the training and validation data for MIMO neural network modelling of the process. The control task involved regulatory control of the three pass temperatures, manipulating the cooling water valves that supply the heat exchangers directly. The NMPC strategy was implemented and good disturbance rejection and set point tracking was evident. Temeng et al. (1995) concluded that owing to the significant process interaction, better regulator control was achieved than was possible with decentralised multi-loop controllers (Temeng et al., 1995). Clearly, the interactive, non-linear and MIMO nature of this control problem is far more challenging than those solved with direct inverse control in section 4.1.1.

A different approach to non-linear control entails developing control strategies using evolutionary algorithms, more akin to model reference control (Figure 4-3) than direct inverse control or MPC.

4.2 SINGLE CHROMOSOME AND CO-EVOLUTIONARY CONTROL