Control algorithm, variable sample-time

The variable sample time control algorithm was tested experimentally and the results compared with computer simulations. Tests were made with and without modeling error (parameter shift) for set point and load changes. 

Variable Sample Time Algorithm for Microcomputer Control of a Heat Exchanger... 

Set Point Changes, Constant Sample Time. When the constant twenty seconds was added to the variable residence time, the resulting variable sample times were in the 22-26 second range. Since this variable sample time is similar to a long constant sample time, the performance of the control algorithm was tested with various constant sample times. The constant sample times... 

Results for an intermediate constant sample time of 10 seconds are shown in Figure 5. The control in this case and also for the 15 second sample time case, not shown, is improved compared with the constant 25 and 5 second sample times. This suggests that an optimal constant sample time exists for application of the variable sample time algorithm. The optimum constant sample time appears to be on the order of 2 to 3 thermocouple time constants plus the average fluid residence time. 

In a digital computer-control system, the feedback controller has a pulse transfer function. What we need is an equation or algorithm that can be programmed into the digital computer. At the sampling time for a given loop, the computer looks at the current process output x, compares it to a setpoint, and calculates a current value of the error. This error, plus some old values of the error and old values of the controller output or manipulated variable that have been stored in computer memory, are then used to calculate a new value of the controller output m,. 

The purpose of the present study is to present a simply derived and implemented DDC algorithm for the flow-forced heat exchanger which does not require storage of previous values of the manipulated variable or error. The algorithm requires that Steady-state exist at the sampling instants which means that the sample time is variable. However, the algorithm is shown to control for the constant sample time case. 

The nonlinear simulation was used to illustrate the closed-loop response of the controlled variable X2 following a 30 percent increase in feed composition. The results are shown in Figure 21.4b with the feedback-only dual and PID algorithms. Control is immensely improved with the feedforward action. The slight deviation in X2 with feedforward control is due to inaccuracies in the linear model and the long sampling time relative to the process dead time. The... 

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