Embedded Software and Motor Control Libraries for PXR40xx

Function GFLIB_ControllerPIrAW_F16
Moreover, the scaling shift cannot be a negative number, so the operation of scaling is
always to scale numbers with an absolute value larger than 1 down to fit in the range [-1,
1).
Equation GFLIB_ControllerPIrAW_Eq11
The final, scaled, fractional equation of the recurrent PI controller on a 16-bit fixed point
platform is therefore implemented as follows:
where:
Equation GFLIB_ControllerPIrAW_Eq12
• u f(k) - fractional representation [-1, 1) of the controller output
• e f(k) - fractional representation [-1, 1) of the controller input (error)
• f16CC1sc - fractional representation [-1, 1) of the 1st controller coefficient
• f16CC2sc - fractional representation [-1, 1) of the 2nd controller coefficient
• u16NShift - in range [0,15] - is chosen such that both coefficients f16CC1sc and
f16CC2sc are in the range [-1, 1)
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.
Equation GFLIB_ControllerPIrAW_Eq13
The bounds are described by a limitation element equation
GFLIB_ControllerPIrAW_Eq13. When the bounds are exceeded, the non-linear
saturation characteristic will take effect and influence the dynamic behavior. The
described limitation is implemented on 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.
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
312 Freescale Semiconductor, Inc.