Multivariable Control

Only a limited number of multivariable control studies is available and only one of them has been tested experimentally. A state space model must be the basis for a multivariable control design:

Figure 7 Measured (A) open and (B) closed loop responses of the counter signal, the median crystal size and the product magna density due to a disturbance in the product flow at a and c for the open loop experiment and at a and b for the closed loop experiment (Eek, 1995).

x is the vector of state variables. The crystallizer model must therefore be transformed into a state space representation. This can be achieved by the moment transformation, which is however only valid for a mixed suspension mixed product removal (MSMPR) type of crystallizer with simple crystallization kinetics. Application of the method of lines also yields a state space representation of the model.

An important topic in the design of a multivariable controller is the choice of the input-output pairs. On the basis of a relative gain array analysis with experiments done on a 1 m3 KCl crystallizer, a control structure with the fines, the product and the feed flow rate as process inputs, and the mean crystal size, the weight percentage of solids and the supersaturation as process outputs has been proposed.

On the basis of a controllability analysis the median crystal size has been rejected as an output variable because of the long delays. The control structure shown in Figure 8 was proposed as an alternative. This control structure was experimentally analysed on the 1000 L evaporative DTB crystallizer using a model predictive controller in combination with a state estimator. The controller was based on a linearized first principle model using the method of lines to transform the model into a state space representation. The controller showed good performance with respect to stabilization, disturbance rejection and setpoint tracking, which was slightly better than that of a multiloop PI controller. This improvement is related to the interaction, which is taken into account in a multivariable model predictive control (MPC) controller, and the better constraint handling of this controller.

Solar Panel Basics

Solar Panel Basics

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