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controller behavior is by the choice of the prediction horizon. This horizon corresponds to the number of controller updates specified for the controller to achieve set point. A short prediction horizon results in large transient actuator movements, as these are required to achieve closed loop time constants that are faster than the open loop time constant of the process. Percent of Scale 70 60 50 40 30 20 10 0 1 70 139 208 277 346 415 484 553 622 691 Sample Number 760 829 898 967 1036 1105 1174 1243 1312 1381 1450 Figure 1.7: Closed Loop Control of Self Regulating Process Process Set Point Actuator The effect of reducing the prediction horizon is shown in Fig. 1.7. The first pair of setpoint changes is performed with a prediction horizon of 60 samples, the second pair with a prediction horizon of 40 samples, and the last pair with a prediction horizon of 30 samples. Due to the significant dead time in the process, the prediction horizon cannot be lowered much further because this will require that the controller make very large transient actuator movements with a long delay before feedback is obtained from the process. This also places unreasonable accuracy requirements on a small area of the process model in the region just beyond the dead time. At the limit, the prediction horizon cannot be lower than the process dead time as it becomes physically impossible to achieve setpoint. For integrating processes, the closed-loop control performance is adjusted in a different manner. By default, BrainWave will attempt to achieve setpoint as quickly as possible, limited only by the allowable range of actuator travel. For these processes, the available performance adjustments are oriented toward reducing the control performance from this theoretical ideal. By imposing output limits on the allowable actuator travel, the setpoint change performance can be slowed. Further reductions to the setpoint change performance can be achieved by introducing an internal low pass filter on the setpoint, in the spirit of a two degrees of freedom controller. 24
Percent of Scale 100 90 80 70 60 50 40 30 20 10 0 1 66 131 196 261 326 391 456 521 586 651 Sample Number 716 781 846 911 976 1041 1106 1171 1236 1301 1366 Figure 1.8: Closed Loop Control of Integrating Process Process Set Point Actuator Fig. 1.8 shows an integrating process under closed-loop control with Brain- Wave. The first pair of setpoint changes shows the control performance when the actuator is unrestricted. Note that the complete transient actuator movement is being accomplished well before the process even begins to respond and the full range of actuator travel is being used to achieve setpoint as rapidly as possible. The second pair of setpoint changes shows the controller performance when a high limit of 75 % is imposed on the actuator, resulting in a longer elapsed time to achieve set point. The third pair of setpoint changes shows the controller performance when a low pass filter has been applied internally to the setpoint. 1.7 Industrial application examples These examples illustrate a few of the practical problems that industry experiences with the control of processes that exhibit time delay and potentially integrating characteristic using conventional PID controllers. The model-based predictive controller described is providing a practical alternative to PID control. This enables industry to better deal with the common problem of time delay in process control. 1.7.1 Applications to batch reactors Batch production processes are playing an essential role in the chemical and food industry. Many pharmaceutical or biochemical substances and a large number of polymers are produced in such reactors. For a variety of reasons, each batch run is different. 25
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Page 3 and 4: 1.2 The Laguerre Modelling Method M
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Page 11 and 12: variable uf requires an additional
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Page 23: an identification of the feedforwar
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Page 29 and 30: E.O. Feed Rate (LBS/HR) 7000 6000 5
Page 31 and 32: this equilibrium point, the reactor
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