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.
   [a, b, c, d, k] = PIDMIMO( inr, zeta, omega, tauInt, omegaR, tSamp, sType )

   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))

   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



Common: CommonData/SwooshWatermark
Common: Control/C2DZOH
Common: Control/C2DelZOH
Common: Control/FResp
Common: Control/GND
Common: Control/GSS
Common: Control/ND2SS
Common: Control/S2Damp
Common: Control/SS2ND
Common: Control/SizeABCD
Common: Control/TrnsZero
Common: Control/WPZ
Common: Control/WReson
Common: Control/ZFresp
Common: General/CellToMat
Common: General/MatToCell
Common: General/Watermark
Common: Graphics/LogLimit
Common: Graphics/NewFig
Common: Graphics/Plot2D
Common: Graphics/PltStyle
Common: Graphics/TextS
Math: Linear/ColCompR
Math: Linear/DelLZ
Math: Linear/IsZero
Math: Linear/RowCompU

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