Filtered PID Control Simulation with Delay

Filtered PID Controller Simulation for an Arbitrary Rational System with Delay

The system is modeled as a rational function with delay:

\[ G(s)=\dfrac{Y(s)}{U(s)}=\dfrac{N(s)}{D(s)}e^{-\tau s} \]

where you enter the numerator and denominator coefficients (in descending powers of \(s\)) and the delay \(\tau\). A unity feedback is assumed in closed-loop form.

The filtered PID controller is given by:

\( U(s)=K_p\,E(s)+\dfrac{K_i}{s}\,E(s)+K_d\,\dfrac{F\,s}{s+F}\,E(s) \)

where \(F\) is the derivative filter parameter and \(e(t)=\mathrm{Reference}\,-\,y(t)\).

System Transfer Function Numerator Coefficients: (For instance, for \(2s+3\) enter \(2,3\))

Denominator Coefficients: (For \(s^2+5\) enter \(1,0,5\).)

Delay (τ in sec):

PID Gains Proportional (\(K_p\)): Integral (\(K_i\)): Derivative (\(K_d\)): Derivative Filter (\(F\)):

Reference Signal Reference Type:

Amplitude:

Simulation Settings Duration (sec): Time Step (sec):

Closed-loop Control (PID):

\(u_\mathrm{max}\): \(u_\mathrm{min}\):

Saturation: