Parameters
Presets
PID Gains
Proportional gain Kp
2.00
Integral gain Ki
0.50
Derivative gain Kd
0.50
Plant (2nd-order)
Natural freq. ωn
1.00 rad/s
Damping ratio ζ
0.50
Input & Simulation
Input type
Simulation time
20.0 s
—
Overshoot [%]
—
Settling time (2%) [s]
—
Rise time [s]
—
Steady-state error
Response y(t) & Setpoint r(t)
Control signal u(t)
Theory
PID control law:
$$u(t)=K_p e(t)+K_i\int_0^t e(\tau)\,d\tau+K_d\frac{de}{dt}$$2nd-order plant:
$$\ddot{y}+2\zeta\omega_n\dot{y}+\omega_n^2 y=\omega_n^2 u$$Discrete-time simulation (Euler method, $\Delta t=0.01$ s) with anti-windup integrator.
CAE application: Initial gain design for hydraulic actuators, temperature controllers and robotic arm position control. Useful for Ziegler-Nichols pre-check and cross-validation against MATLAB/Simulink models.