E I 1 E Results of the open-loop frequency response of an industrial automation system using...

   

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E I 1 E Results of the open-loop frequency response of an industrial automation system using PID control are given in Table 1. Assume unity feedback. @ (rad/s) G₂ (jo) (dB) ZG₂ (jo) (°) 0.05 20 - 95 0.1 3.5 - 115 Table 1 0.2 -3.7 - 136 0.3 -8.8 -154 0.5 - 16.7 -180 (a) Plot the results of Table 1 on a Nichols chart. Use your plot to determine the bandwidth (b) of the closed loop system and apply it using one of the equations given overleaf to estimate the 0-95% rise time, T.(0-95%), for a step input to the closed-loop system. (b) In order to reduce the system response time, the gain parameter is increased by 2 (+6 dB). Show how this increase in gain changes the Nichols chart for the system, and use it to determine the new 0-95% rise time for a step input to the closed-loop system. (c) Using the Nichols chart of part (b), calculate (i) the percentage step response overshoot and (ii) the ±5% settling time for a step input to the closed-loop system. E I 1 E Results of the open-loop frequency response of an industrial automation system using PID control are given in Table 1. Assume unity feedback. @ (rad/s) G₂ (jo) (dB) ZG₂ (jo) (°) 0.05 20 - 95 0.1 3.5 - 115 Table 1 0.2 -3.7 - 136 0.3 -8.8 -154 0.5 - 16.7 -180 (a) Plot the results of Table 1 on a Nichols chart. Use your plot to determine the bandwidth (b) of the closed loop system and apply it using one of the equations given overleaf to estimate the 0-95% rise time, T.(0-95%), for a step input to the closed-loop system. (b) In order to reduce the system response time, the gain parameter is increased by 2 (+6 dB). Show how this increase in gain changes the Nichols chart for the system, and use it to determine the new 0-95% rise time for a step input to the closed-loop system. (c) Using the Nichols chart of part (b), calculate (i) the percentage step response overshoot and (ii) the ±5% settling time for a step input to the closed-loop system.