Quiz on Proportional Integral (PI) Control
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1. Increasing the integral time constant `\tau_I` has what effect on a Proportional Integral (PI) controller?
$$u(t) = u_{bias} + K_c \, e(t) + \frac{K_c}{\tau_I}\int_0^t e(t)dt$$
- Incorrect. A larger value in the denominator makes the overall value of the integral term smaller
- Incorrect. A larger value in the denominator makes the overall value of the integral term smaller, leading to a slower response
- Correct. A larger value in the denominator makes the overall value of the integral term smaller, leading to a slower response to set point error.
2. Given `K_p`=2, `\theta_p`=2.0, and `\tau_p`=200.0, find `K_c` for a PI controller using ITAE regulatory control tuning for a PI controller.
- Correct. $$K_c = \frac{0.859}{K_p}\left(\frac{\theta_p}{\tau_p}\right)^{-0.977} \quad \tau_I = \frac{\tau_p}{0.674}\left(\frac{\theta_p}{\tau_p}\right)^{0.680}\quad\mathrm{Disturbance\;rejection}$$
- Incorrect. Regulatory control is disturbance rejection, the equation is found under ITAE tuning correlations
- Incorrect. Regulatory control is disturbance rejection, the equation is found under ITAE tuning correlations
- Incorrect. Regulatory control is disturbance rejection, the equation is found under ITAE tuning correlations
3. A nuclear plant provides a steady amount of electricity that is either stored or sold to the grid depending on current demand. A proposed control system is using a PI controller to adjust power level for load following and is currently losing money due to a slow reaction time. What adjustment could be made to the controller parameters could best address the problem?
- Correct. This is a good way to tune a controller that is too slow. You may need a regulatory commission approval for changes.
- Incorrect. The question asks for adjustments to the controller parameters, where dead-time is a parameter that describes the system response.
- Incorrect. This would slow the response.
- Incorrect. This would slow the response.
4. What is the purpose of anti-reset windup for the integral error ie[i]?
op[i] = op_lo
ie[i] = ie[i] - e[i] * delta_t # anti-reset windup
This code section is from the example PID control code.
- Incorrect. Anti-reset windup pauses the change in the integral ie[i] when the controller output is saturated.
- Incorrect. Anti-reset windup pauses the change in the integral ie[i] when the controller output is saturated.
- Incorrect. Anti-reset windup does not reset the integral term but pauses the change in the integral ie[i] when the controller output is saturated.
- Correct. Anti-reset windup is needed to avoid a large integral term if the controller output saturates at a lower or upper limit and the process variable (PV) is unable to meet the set point (SP) for an extended period of time. This persistent offset would lead to a large or small integral term that would cause the controller output to continue at the saturation limit even if the controller set point were to be brought back to an attainable level.
