How to use PID Solver 360

From a process model to a tuned, verified controller in five steps. This guide walks through every part of the solver — the calculator, simulator, auto tuner, optimiser and identification tools — and shows you how to read the results.

Launch the solver Read the theory

The control loop you are building

Quick start in 5 steps

Enter a process model

In the left panel choose a transfer function (first-order, FOPDT, second-order or integrating) and type its gain K, time constant τ and dead time L. New to it? Load a ready-made example instead.

Load the temperature example

Pick a controller structure

Select P, PI, PD or PID. Start with PI for most process loops; add derivative (PID) only when the plant has significant lag. Switch between Kp/Ki/Kd and Kp/Ti/Td at any time — the solver converts automatically.

Open the calculator

Auto-tune the gains

Open the Auto-tune tab to get Kp, Ki, Kd from every classical rule — Ziegler–Nichols, Cohen–Coon, IMC/Lambda, SIMC, AMIGO and Tyreus–Luyben. Click “Apply & simulate” on the one you want.

Open Auto-tune

Simulate the closed loop

Press Simulate to run the loop with RK4 integration. Watch the animated playback, then read rise time, overshoot, settling time, steady-state error and the IAE/ISE/ITAE integrals in the Results panel.

Open the simulator

Check robustness & optimise

Review the gain and phase margins and the Bode/Nyquist plots, then let the optimiser refine Kp, Ki, Kd for your objective (minimise overshoot, settling time or IAE/ISE/ITAE). Export a PDF/CSV report when you are happy.

Open the optimiser

The five solver tabs

The centre of the solver has five tabs. Each does one job — click any card to open the solver on that tab.

A · Calculator

Evaluate one PID step symbolically and numerically: enter PV, previous error and the running integral to see the P, I and D terms and the (saturated) output, then advance a sample.

Open

B · Simulator

Run the full closed loop against the plant. Compare P/PI/PD/PID side by side, layer on a load disturbance, sensor noise or a setpoint ramp, and scrub the animated response.

Open

C · Auto tune

Compute gains from six classical rules, each with its assumptions and exact formulas. Set the IMC λ to trade speed against robustness, then apply and simulate in one click.

Open

D · Optimise

A Nelder–Mead search finds Kp, Ki, Kd that minimise your chosen objective and shows a before/after comparison of the gains and the key metrics.

Open

E · Identify

Have real data? Paste a bump-test CSV (time, input, output) to fit a FOPDT model, or use relay auto-tune to measure the ultimate gain and period — then push the result into the tuner.

Open

Reading the results

Performance metrics

Rise time, peak time, overshoot %, settling time (±2 %), steady-state error, peak error and the IAE/ISE/ITAE integrals — with a plain-language interpretation.

Stability & robustness

Gain margin, phase margin and the gain/phase-crossover frequencies, plus a Robust/Adequate/Marginal rating. Aim for 30–60° phase margin and > 6 dB gain margin.

Bode & Nyquist

The open-loop frequency response updates live with your gains and plant — no simulation needed — so you can see the margins graphically.

Export

Download the run as CSV data, a JSON configuration, PNG charts or a print-ready PDF report; or copy a shareable link that reopens the solver with your exact setup.

Worked example: tune a temperature loop

Follow these clicks end to end to tune the electric-oven example.

1Click “Load the temperature example” (or pick it from the examples menu) — the solver fills in a realistic electric-oven FOPDT model, units of °C and sensible actuator limits.
2Open the Auto-tune tab and click “Apply & simulate” on SIMC / Skogestad — a robust process-industry default.
3Watch the animated response draw in, then read the Results panel: aim for low overshoot and a settling time well inside the run.
4Look at the Robustness card — a phase margin of 30–60° and gain margin above 6 dB means a healthy loop.
5Not happy? Open Optimise, choose “Minimise ITAE”, and run it — then compare the before/after gains.
6Export a PDF report, or hit Share to copy a link that reopens this exact configuration.

Try this example now

Tips for good results

Keep the sample time small: Ts ≤ τ/10 and well below the dead time. The solver warns when it is too coarse.
Turn on anti-windup whenever the output saturates, and filter the derivative (N ≈ 8–20).
Prefer derivative-on-measurement and setpoint weighting (b < 1) to avoid derivative kick.
Classical rules like Ziegler–Nichols are aggressive; SIMC, AMIGO and Tyreus–Luyben are gentler.
Always confirm the frequency-domain margins as well as the time-domain step response.

Want the underlying theory? The documentation explains every term, tuning rule and metric in depth.