Control engineering and dynamic systems
Analyse and design plant models, step responses, time-domain metrics and standard controllers with transparent calculations.
Identify the plant, assess its time response, choose a controller structure, then verify parameters in simulation or testing.
Calculators in this category
Transfer Function Poles and Zeros Calculator
Calculate poles, zeros, damping, natural frequency and stability of a transfer function G(s) from time constants, PT2 parameters or polynomial coefficients.
Open calculator →Bode Plot Calculator with Phase and Gain Margin
Calculate the open-loop Bode plot from plant and controller with crossover frequency, phase margin and gain margin – including dead time.
Open calculator →Nyquist Plot Calculator for Closed-Loop Stability
Calculate the Nyquist plot of G₀(jω) and check closed-loop stability with the general and simplified Nyquist criterion, including dead time.
Open calculator →Root Locus Calculator for Closed-Loop Poles
Calculate the root locus of G₀(s) with breakaway points, imaginary-axis crossings and asymptotes, and follow the closed-loop poles as gain increases.
Open calculator →Closed-Loop Step Response Calculator with PID
Simulate the step response of a control loop with P, PI, PD or PID controller and get overshoot, rise time, settling time and steady-state error.
Open calculator →Hurwitz Stability Criterion Calculator
Check closed-loop stability with the Hurwitz criterion: enter the characteristic equation coefficients and get the Hurwitz matrix and all determinants.
Open calculator →PID Tuning Calculator: Ziegler–Nichols and CHR
Calculate P, PI and PID settings from the inflection tangent (K_S, Tu, Tg) or oscillation test (K_crit, T_crit) by Ziegler–Nichols, CHR, Samal and Kuhn.
Open calculator →Magnitude and Symmetric Optimum Tuning Calculator
Calculate P and PI controller settings by magnitude optimum and Kessler's symmetric optimum with K_PR, Tn, damping, phase margin, overshoot and settling time.
Open calculator →PT2 Overshoot Calculator – First Peak Value
Calculate the first peak of an underdamped second-order (PT2) step response from damping ratio, initial value and final change.
Open calculator →PT1 Time Constant Calculator from a Step Test
Calculate the time constant of a PT1-like process from one measured point, the final value and the elapsed time.
Open calculator →PID Controller Output Calculator for an Error Ramp
Calculate the P, I and D contributions and the output of a PID controller from initial error, current error and sampling interval.
Open calculator →PD Controller Output Calculator for an Error Ramp
Calculate the output of a proportional-derivative (PD) controller from two error readings and their sampling interval.
Open calculator →PI Controller Output Calculator
Calculate the time-dependent output of a proportional-integral (PI) controller for a constant control error.
Open calculator →Dead Time Step Response Calculator
Calculate when and at what level an input step appears at the output of a pure dead-time (transport delay) element.
Open calculator →PTn Step Response Calculator
Calculate and plot the step response of a cascade of n identical first-order lags at a selected time.
Open calculator →P Controller Output Calculator
Calculate the output of a proportional controller from controller gain, instantaneous control error and bias.
Open calculator →I Controller Output Calculator
Calculate the time-dependent output of a pure integral controller from integral time, constant control error, duration and initial output.
Open calculator →Steady-State Error Calculator for P Control
Calculate the steady-state error between setpoint and measured value after a setpoint step from controller and process gain.
Open calculator →P Controller with PT1 Process: Step Response Calculator
Calculate the measured output after a setpoint step for a closed loop of a proportional controller and a first-order process.
Open calculator →PT2 Step Response Calculator
Calculate the time response of an underdamped second-order (PT2) element from gain, damping, natural time, step height and time.
Open calculator →PT2 Frequency Response Calculator: Amplitude and Resonance
Calculate the steady output amplitude of a second-order system under sinusoidal excitation from gain, damping, natural time, amplitude and frequency.
Open calculator →Damping Ratio from Decay Curve Calculator
Calculate the damping ratio of an underdamped second-order system from two measured oscillation amplitudes and their separation.
Open calculator →PT2 Natural Time from Oscillation Peaks Calculator
Calculate the natural time T₀ of an underdamped second-order model from damping ratio and the timing of same-direction peaks.
Open calculator →PT2 Settling Time Calculator for a Tolerance Band
Calculate a conservative settling time after which an underdamped second-order response stays inside a relative tolerance band.
Open calculator →PT1 Step Response Calculator
Calculate the instantaneous output of a first-order lag from gain, time constant, step height and observation time.
Open calculator →First-Order Plus Dead Time Step Response Calculator
Calculate the step response of a first-order process with time constant and dead time at a selected instant.
Open calculator →PT1 Frequency Response Amplitude Calculator
Calculate the steady output amplitude of a first-order system under sinusoidal excitation from gain, time constant, input amplitude and frequency.
Open calculator →Phase Margin Calculator for PT1 with Dead Time
Calculate the phase margin at gain crossover of an open loop with proportional controller and first-order process with dead time.
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