Path: Common/Control
% Produces a state space n degree of freedom PID controller.
The PID controller will be of the form:
x(k+1) = a x(k) + b u(k)
y(k) = c x(k) + d u(k)
By designing in the frequency domain and converting to discrete
time using a zero-order hold. The inputs are the desired damping
ratio and undamped natural frequency of the complex mode of the
closed-loop system and the time constant of the integrator.
This system does not compensate for the phase lag of the zero order
hold and is only applicable to systems where the bandwidth is
much lower than the half-sampling frequency. The continuous time
equivalent for each axis is
Kr s u
y = Kp u + ---- u + Ki ---
s + wR s
The function converts the result to discrete time if tSamp is entered.
If only one output is requested it will return a data structure with
the matrices.
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Form:
[a, b, c, d, k] = PIDMIMO( inr, zeta, omega, tauInt, omegaR, tSamp, sType )
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Inputs
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inr (n,n) Inertia matrix
zeta (n,1) Vector of damping ratios
omega (n,1) Vector of undamped natural frequencies
tauInt (n,1) Vector of integrator time constants
omegaR (n,1) Vector of derivative term roll-off frequencies
tSamp Sampling period
sType State equation type ('Delta' or 'Z' (default))
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Outputs
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a (2n,2n) Plant matrix
b (2n, n) Input matrix
c ( n,2n) Output matrix
d ( n, n) Feedthrough matrix
k Gains
.kP Proportional
.kR Rate
.kI Integral
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Common: Control/C2DZOH Common: Control/C2DelZOH Common: Control/FResp
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