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Embedded Software and Motor Control Libraries for PXR40xx

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Proportional-Integral (PI) algorithm according to the equations below. The PI algorithm<br />

is implemented in the parallel (non-interacting) <strong>for</strong>m, allowing the user to define the P<br />

<strong>and</strong> I parameters independently without interaction.<br />

An anti-windup strategy is not implemented in this function.<br />

The PI algorithm in the continuous time domain can be described as:<br />

where<br />

Equation GFLIB_<strong>Control</strong>lerPIp_Eq1<br />

• e(t) - input error in the continuous time domain<br />

• u(t) - controller output in the continuous time domain<br />

• K P - proportional gain<br />

• K I - integral gain<br />

Equation GFLIB_<strong>Control</strong>lerPIp_Eq1 can be described using the Laplace trans<strong>for</strong>mation<br />

as follows:<br />

Equation GFLIB_<strong>Control</strong>lerPIp_Eq2<br />

The proportional part of equation GFLIB_<strong>Control</strong>lerPIp_Eq2 is trans<strong>for</strong>med into the<br />

discrete time domain simply as:<br />

Equation GFLIB_<strong>Control</strong>lerPIp_Eq3<br />

Trans<strong>for</strong>ming the integral part of equation GFLIB_<strong>Control</strong>lerPIp_Eq2 into a discrete time<br />

domain using the Bilinear method, also known as trapezoidal approximation, leads to the<br />

following equation:<br />

where T s [sec] is the sampling time.<br />

Equation GFLIB_<strong>Control</strong>lerPIp_Eq4<br />

<strong>Embedded</strong> <strong>Software</strong> <strong>and</strong> <strong>Motor</strong> <strong>Control</strong> <strong>Libraries</strong> <strong>for</strong> <strong>PXR40xx</strong>, Rev. 1.0<br />

Chapter 4 API References<br />

Freescale Semiconductor, Inc. 277

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