Embedded Software and Motor Control Libraries for PXR40xx

Transforming equation GFLIB_ControllerPIrAW_Eq2 into a discrete time domain leads
to the following equation:
Equation GFLIB_ControllerPIrAW_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 the controller
coefficients calculated depending on the discretization method used, as shown in Table
4-67.
The output signal limitation is implemented in this controller. The actual output u(k) is
bounded not to exceed the given limit values UpperLimit, LowerLimit. This is due to
either the bounded power of the actuator or to the physical constraints of the plant.
Table 4-67. 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
Equation GFLIB_ControllerPIrAW_Eq13
The bounds are described by a limitation element equation
GFLIB_ControllerPIrAW_Eq4. When the bounds are exceeded, the non-linear saturation
characteristic will take effect and influence the dynamic behavior. The described
limitation is implemented in the internal controller accumulator (limitation during the
calculation). Therefore, if the limitation occurs, the controller output is clipped to its
bounds and the wind-up occurrence of the accumulator portion is avoided by saturating
the actual sum.
Note
All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PIAW_R_DEFAULT_FLT macro.
As the PI controller also contains the integration part, the output
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
Chapter 4 API References
Freescale Semiconductor, Inc. 315