tailieunhanh - Process Control Systems Episode 5

Tham khảo tài liệu 'process control systems episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Linear Controllers 1 113 F1G . Zero damping results when a R T j M 2 or b R Td At. The period of oscillation shown in Fig. is 4 At while that in Fig. is 6 At. Add to these the period of 2 At when dead time is zero and the formula for with integral control is readily derived To 2 At 4rd The contribution of the sampling element is evident in that the natural period of a dead-time process with integral control is 4rti without sampling. Sampling adds 2 At to the period. The phase shift introduced by the sampling element can then be related to the period of the loop ỘA -7T -180 To To The existence of any dead time whatever in the loop precludes critical damping with integral control. The value of reset time necessary for zero damping was for both Figs. and although their periods of oscillation differed. But as oscillation becomes more sinusoidal . as more sampling intervals make up a period for zero damping R approaches just as in a continuous loop. The sampled wave in Fig. is square while that of contains three steps such that R departs somewhat from T0 27r. For -amplitude damping R is to be doubled. The above estimates of reset time are based on unit process gain. They must be multiplied by the process steady-state gain in order to arrive at the required loop gain. Two-mode Control Two-mode control combines the speed of response of proportional action with the elimination of offset brought about by automatic reset. The proportional mode is just as valuable in a sampled dead-time loop as it was in one without sampling. In fact proportional action enables any loop whose dead time is less than the sampling interval to he critically damped. Figure shows how this is done. 114 I Selecting the Feedback Controller The proportional action produces an instantaneous change in output which is removed when the error returns to zero. Some overshoot does occur but it disappears before the next sample. Only one combination of proportional and reset .

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