I have a PID loop controlling a system successfuly. The question is, are the P, I and D values unique, or would other values also control the loop? [Ignoring slight changes to the original value]
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Depends on how unique your controlled systems are. How much production variance and possible site variance do you have? – winny Oct 21 '22 at 13:03
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Control theory and PID parameters aside, you could have things like for example a hardware/software filter which is filtering input before handing it to the PID algorithm. Then depending on how you tune the filter, it will of course affect the control loop. Consider a simple RC low pass filter in hardware for example. The R and C values will naturally have an impact on everything. As will the overall resolution/accuracy of passives, system clock, PWM, ADC and so on. – Lundin Oct 21 '22 at 13:27
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There is no uniquely correct solution to a PID controller.
The three gain values, kp, ki and kd determine the actual behavioural characteristics of the closed loop system.
Varying those gain values will alter rise-time, overshoot etc of the closed loop system.
By varying the 3 gain values you are varying the positions of the closed loop poles on the s-plane upon which system behaviour depends.
Approximating a higher order system by a second order system, the positions of the poles on the s-plane determine the values of the natural resonant frequency (wn) and the damping ratio (zeta) upon which 2nd order system behaviour depends.
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If you have perfect information on the plant and a fixed definition of "optimally" then the numbers should be unique. But there are infinite possible definitions of optimal tuning.
For example, if you can tolerate 5% overshoot the tuning constants will be different to those if you cannot tolerate more than 1% overshoot.
Examples include, Ziegler–Nichols rule (Ziegler & Nichols, 1942), symmetric optimum rule (Kessler, 1958; Voda & Landau, 1995), Ziegler–Nichols’ complementary rule (Mantz & Tacconi, 1989), some-overshoot rule (Seborg, Edgar, & Mellichamp, 1989), no-overshoot rule (Seborg et al., 1989), refined Ziegler–Nichols rule (Hang, Astrom, & Ho, 1991), integral of squared time weighted error rule (Zhuang & Atherton, 1993), and integral of absolute error rule (Pessen, 1994).
Spehro Pefhany
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