In digital PID, long sample time adds phase delay, and derivative action can amplify noise. Saturation, anti-windup, and quantization matter in implementation. Continuous-to-discrete conversion uses the Tustin (bilinear) map $s=\frac{2}{T_s}\frac{z-1}{z+1}$.
How to read it
The step response shows delay and staircase behavior as Ts increases.
The sampled view shows control output updating in steps.
The gain breakdown shows derivative sensitivity to sample time.
Learn Digital PID Discretization by dialogue
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When reading Digital PID Discretization, where should I look first? Moving Proportional gain Kp changes both the plots and the result cards.
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Start with Discrete integral coefficient, but do not treat the number as the whole answer. Use Discrete PID step response to confirm the assumed state, then read Sampled update view for the distribution or trend. The step response shows delay and staircase behavior as Ts increases.
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I can see why Proportional gain Kp changes Discrete integral coefficient. How should I judge the influence of Integral time Ti?
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Move Integral time Ti in small steps and watch Discrete derivative coefficient. That reveals which term is controlling the result. In digital PID, long sample time adds phase delay, and derivative action can amplify noise. Saturation, anti-windup, and quantization matter in implementation. A single operating point is not enough; sweep the realistic scatter range.
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What is PID coefficient breakdown for? It feels like the ordinary curve already tells the story.
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PID coefficient breakdown is for finding boundaries where the condition becomes risky or margin collapses quickly. The sampled view shows control output updating in steps. In Choosing sample time for PLC or MCU PID, the important question is often what happens after a small change, not only the nominal value.
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So if Discrete integral coefficient is within the target, can I accept the condition?
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Treat this as a first-pass review. It helps with Checking continuous-to-discrete controller implementation and Balancing derivative noise against response speed, but final decisions still need standards, measured data, detailed analysis, and vendor limits. The gain breakdown shows derivative sensitivity to sample time.
Balancing derivative noise against response speed.
FAQ
Start with Discrete integral coefficient and Discrete derivative coefficient. Then use Discrete PID step response to confirm the assumed state and Sampled update view to read distribution or bias. The step response shows delay and staircase behavior as Ts increases
Move Proportional gain Kp alone, then move Integral time Ti by a comparable amount and compare the change in Discrete integral coefficient. PID coefficient breakdown shows combinations where margin or performance changes quickly.
Use it for Choosing sample time for PLC or MCU PID. Instead of trusting a single point, widen the input range and check whether Discrete integral coefficient keeps enough margin before moving to detailed analysis.
In digital PID, long sample time adds phase delay, and derivative action can amplify noise. Saturation, anti-windup, and quantization matter in implementation. Final decisions still require standards, measured data, detailed analysis, and vendor limits.
How to Use
Enter continuous PID gains: proportional gain (Kp in 1/V), integral time constant (Ti in seconds), and derivative time constant (Td in seconds). For a temperature controller, typical values are Kp=0.5, Ti=120s, Td=5s.
Set the sampling time (Ts) in milliseconds—common industrial values are 10ms for servo loops, 100ms for process control, or 1000ms for slow thermal systems.
Click Simulate to compute discrete coefficients, identify sampling delay phase lag, and calculate derivative filter noise amplification at the Nyquist frequency.
Worked Example
A flow control valve with Kp=2.0 (output %/L/min error), Ti=45s, Td=8s, and Ts=50ms (20Hz sampling). The simulator returns: discrete integral coefficient ki=Kp·Ts/Ti=0.00222, discrete derivative coefficient kd=Kp·Td/Ts=320, and a derivative noise gain of about 27.7 (with the default filter coefficient 12), which is why a low-pass filter on the derivative term is required.
Practical Notes
Derivative noise gain above 100 indicates poor sensor signal conditioning; add an analog low-pass filter (cutoff=1/(2π×Td)) upstream or increase Ts to 100ms minimum.
Sampling delay of more than 20% of loop period destabilizes fast loops; verify PLC/microcontroller interrupt latency and communication lag in your control platform.
For pneumatic actuators (Ts≥500ms), use derivative filtering factor N=8–12 to prevent chattering; for brushless servos (Ts=5ms), N=3–5 suffices.