Embedded Software and Motor Control Libraries for PXR40xx

Function GFLIB_ControllerPIr_FLT
4.48.3 Return
The function returns a single precision floating point value, representing the signal to be
applied to the controlled system so that the input error is forced to zero.
4.48.4 Description
The function GFLIB_ControllerPIr_FLT calculates a standard recurrent form of the
Proportional-Integral controller, without integral anti-windup. The continuous time
domain representation of the PI controller is defined as:
Equation GFLIB_ControllerPIr_Eq1
The transfer function for this kind of PI controller, in a continuous time domain, is
described using the Laplace transformation as follows:
Equation GFLIB_ControllerPIr_Eq2
Transforming equation GFLIB_ControllerPIr_Eq2 into a discrete time domain leads to
the following equation:
Equation GFLIB_ControllerPIr_Eq3
where Kp is proportional gain, Ki is integral gain, Ts is the sampling period, u(k) is the
controller output, e(k) is the controller input error signal, CC1 and CC2 are controller
coefficients calculated depending on the discretization method used, as shown in Table
4-61.
Table 4-61. Calculation of coefficients CC1 and CC2 using various discretization methods
Trapezoidal Backward Rect. Forward Rect.
CC1= K p+K IT S/2 K p+K IT S K p
CC2= -K p+K IT S/2 -K p -K p+K IT S
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
302 Freescale Semiconductor, Inc.