See "Linear motion control without the math" by Pramod Ranade in http://www.nxtbook.com/nxtbooks/cmp/esd0409/index.php?startid=23 (Embedded System Design Vol 22, #4, April 2009) and http://picprog.strongedge.net/step_prof/step-profile.html

pramod.ranade.c

/*
	step.c
	Program to verify new algorithm for linear acceleration.
	Author: Pramod Ranade <[email protected]>
*/

#include <stdio.h>
#if defined(_WIN32) || defined(_WIN64)
#include <io.h>
#endif
#include <stdlib.h>

#define SCAN_TIME_IN_MICRO_SEC	  	2
#define COUNT_FOR_COMPARISON		(1000000000UL / SCAN_TIME_IN_MICRO_SEC)

#define	SPEED_LIMIT					9500
#define	ACC_LIMIT					900000
#define	START_SPEED					1500
#define	DES_POS						117
#define AVAILABLE_TIME_IN_MILI_SEC	23

int OutputPinStatus = 1 ;
int g_nRisingEdgeCount = 0 ;
FILE *fptr ;

#define	MakeOutputHigh()	OutputPinStatus=1
#define	MakeOutputLow()		{PrintDebugInfo(uiDoneSteps, uiCurTimeInMicroSec, uiCurSpeedX1K);OutputPinStatus=0;}

void PrintDebugInfo (unsigned int uiDoneSteps, unsigned int uiCurTimeInMicroSec, unsigned int uiCurSpeedX1K)
{
	fprintf(fptr,"%u\t%u\t%u\n", uiDoneSteps, uiCurTimeInMicroSec, uiCurSpeedX1K) ;
}
int FpgaRunMotor (unsigned int uiDesPos, unsigned int uiStartSpeedX1K, unsigned int uiDeltaSpeedX1K, unsigned int uiTimeForAccInMicroSec, unsigned int uiTimeToStartDeccInMicroSec, unsigned int uiPeakSpeed)
{
/*
	This function performs the actions which must be done by FPGA.
	So, finally this should be converted to VHDL or Verilog code for the FPGA.
*/
	unsigned int uiDoneSteps ;
	unsigned int uiCurSpeedX1K ;
	unsigned int uiSpeedTimeProduct ;
	unsigned int uiCurTimeInMicroSec ;

	MakeOutputHigh() ;
	fprintf(fptr,"Inside FpgaRunMotor:\n") ;
	fprintf(fptr,"uiDesPos = %u\n", uiDesPos) ;
	fprintf(fptr,"uiStartSpeedX1K = %u\n", uiStartSpeedX1K) ;
	fprintf(fptr,"uiDeltaSpeedX1K = %u\n", uiDeltaSpeedX1K) ;
	fprintf(fptr,"uiTimeForAccInMicroSec = %u\n", uiTimeForAccInMicroSec) ;
	fprintf(fptr,"uiTimeToStartDeccInMicroSec = %u\n", uiTimeToStartDeccInMicroSec) ;

	uiDoneSteps = 0 ;
	uiCurSpeedX1K = uiStartSpeedX1K ;
	uiDoneSteps ++ ;
	uiSpeedTimeProduct = uiCurSpeedX1K ;
	uiCurTimeInMicroSec = 0 ;
	MakeOutputLow() ;	// first pulse output
	while(uiDoneSteps < uiDesPos)
	{
		// execute this loop after every N micro-seconds, where N = SCAN_TIME_IN_MICRO_SEC
		uiCurTimeInMicroSec += SCAN_TIME_IN_MICRO_SEC ;
		uiSpeedTimeProduct += uiCurSpeedX1K ;
		if (uiCurTimeInMicroSec >= uiTimeToStartDeccInMicroSec)
		{
			// it means deceleration is going on
			if (uiCurSpeedX1K > uiDeltaSpeedX1K)
			{
				uiCurSpeedX1K -= uiDeltaSpeedX1K ;
			}
			else
			{
				uiSpeedTimeProduct = COUNT_FOR_COMPARISON ;
				printf("\t\terror!\n") ;
			}
		}
		else if (uiCurTimeInMicroSec < uiTimeForAccInMicroSec)
		{
			// it means acceleration is going on
			uiCurSpeedX1K += uiDeltaSpeedX1K ;
		}
		else
		{
			// it means steady speed (plateau)
			uiCurSpeedX1K = uiPeakSpeed ;
		}
		if (uiSpeedTimeProduct >= COUNT_FOR_COMPARISON)
		{
			uiDoneSteps ++ ;
			MakeOutputLow() ;	// next pulse output
			printf("falling edge at step %d!\n", uiDoneSteps) ;
			uiSpeedTimeProduct -= COUNT_FOR_COMPARISON ;
		}
		else if (uiSpeedTimeProduct >= (COUNT_FOR_COMPARISON / 2))
		{
			if (!OutputPinStatus)
			{
				printf("g_nRisingEdgeCount = %d\n", g_nRisingEdgeCount) ;
			}
			MakeOutputHigh() ;
			g_nRisingEdgeCount ++ ;
		}
	}
	MakeOutputHigh() ;
	return 0 ;
}
int RunMotor (unsigned int uiStartSpeed, unsigned int uiAvailableTimeInMicroSec, int nDesPos, unsigned int uiSpeedLimit, unsigned int uiAccLimit)
{
/*
	This function performs the calculations which must be done by microprocessor.
	Finally, it calls another function FpgaRunMotor()
	i.e. it passes some parameters to FPGA and tells it to start motion.
*/
	unsigned int uiAverageSpeed ;
	unsigned int uiTimeForAccInMicroSec ;
	unsigned int uiTimeToStartDeccInMicroSec, uiRequiredAcc ;
	unsigned int uiPeakSpeed, uiDeltaSpeedX1K ;

	uiRequiredAcc = 0 ;
	if (uiAvailableTimeInMicroSec)
	{
		uiAverageSpeed = abs(nDesPos) * 1000000UL / uiAvailableTimeInMicroSec ;	// steps/sec
		if (uiAverageSpeed <= uiStartSpeed)
		{
			// no acceleration/deccelration required
			uiStartSpeed = uiAverageSpeed ;
		}
		else
		{
			uiRequiredAcc = 1 ;
		}
	}
	else
	{
		// no acceleration/deccelration required
	}
	if (uiRequiredAcc)
	{
		if (uiAverageSpeed <= ((uiSpeedLimit + uiStartSpeed) / 2))
		{
			// tri-angular profile
			uiTimeForAccInMicroSec = uiAvailableTimeInMicroSec / 2 ;
			uiPeakSpeed = ((uiAverageSpeed - uiStartSpeed) * 2) + uiStartSpeed ;
			uiRequiredAcc = (((uiPeakSpeed - uiStartSpeed) * 40000UL) / (uiAvailableTimeInMicroSec)) * 50 ;
			// please do not try to reduce above stmnt
			// becuase it results in overflow of intermediate result
		}
		else
		{
			// trapezoidal profile
			/*
				number of steps covered during acc and deacc = (Ta * (uiSpeedLimit + uiStartSpeed))
				number of steps covered during steady speed = nDesPos - (Ta * (uiSpeedLimit + uiStartSpeed))
				Ts = steady time can be computed from:
				uiSpeedLimit = (nDesPos - (Ta * (uiSpeedLimit + uiStartSpeed))) / Ts ;
				i.e.
				Ts = (nDesPos - (Ta * (uiSpeedLimit + uiStartSpeed))) / uiSpeedLimit ;
				(Ts + 2*Ta) * 1000000 = uiAvailableTimeInMicroSec ;
				Here, Ts and Ta are in seconds.
				(((nDesPos - (Ta * (uiSpeedLimit + uiStartSpeed))) / uiSpeedLimit) + (2*Ta)) * 1000000 = uiAvailableTimeInMicroSec ;
				((nDesPos - (Ta * (uiSpeedLimit + uiStartSpeed))) / uiSpeedLimit) + (2*Ta) = uiAvailableTimeInMicroSec / 1000000 ;
				multiply boths sides by uiSpeedLimit
				(nDesPos - (Ta * (uiSpeedLimit + uiStartSpeed))) + (2*Ta*uiSpeedLimit) = uiAvailableTimeInMicroSec*uiSpeedLimit / 1000000 ;
				nDesPos - Ta*uiSpeedLimit - Ta*uiStartSpeed + 2*Ta*uiSpeedLimit = uiAvailableTimeInMicroSec*uiSpeedLimit / 1000000 ;
				nDesPos - Ta*(uiStartSpeed - uiSpeedLimit) = uiAvailableTimeInMicroSec*uiSpeedLimit / 1000000 ;
				nDesPos - (uiAvailableTimeInMicroSec*uiSpeedLimit / 1000000) = Ta*(uiStartSpeed - uiSpeedLimit) ;
				Ta = (nDesPos - (uiAvailableTimeInMicroSec*uiSpeedLimit / 1000000)) / (uiStartSpeed - uiSpeedLimit) ;
				TaInUSec = (nDesPos*1000000 - uiAvailableTimeInMicroSec*uiSpeedLimit) / (uiStartSpeed - uiSpeedLimit) ;
				TaInUSec = (uiAvailableTimeInMicroSec*uiSpeedLimit - nDesPos*1000000) / (uiSpeedLimit - uiStartSpeed) ;
			*/
			uiPeakSpeed = uiSpeedLimit ;
			uiTimeForAccInMicroSec = (uiAvailableTimeInMicroSec*uiSpeedLimit - nDesPos*1000000) / (uiSpeedLimit - uiStartSpeed) ;
			uiRequiredAcc = (((uiSpeedLimit - uiStartSpeed) * 40000U) / uiTimeForAccInMicroSec) * 25 ;
			// please do not try to reduce above stmnt
			// becuase it results in overflow of intermediate result
			if (uiRequiredAcc > uiAccLimit)
			{
				// handle this error condition
				// TBD
			}
		}
		uiTimeToStartDeccInMicroSec = uiAvailableTimeInMicroSec - uiTimeForAccInMicroSec ;
		uiDeltaSpeedX1K = SCAN_TIME_IN_MICRO_SEC * uiRequiredAcc / 1000 ;
		if (!uiDeltaSpeedX1K)
		{
			uiDeltaSpeedX1K = 1 ;
		}
		// do something to set/clear direction pin here
		FpgaRunMotor(abs(nDesPos), uiStartSpeed * 1000, uiDeltaSpeedX1K, uiTimeForAccInMicroSec, uiTimeToStartDeccInMicroSec, uiPeakSpeed * 1000) ;
	}
	else
	{
		// run steady at uiStartSpeed for N steps and then stop
		// do something to set/clear direction pin here
		FpgaRunMotor(abs(nDesPos), uiStartSpeed * 1000, 0, 0, uiAvailableTimeInMicroSec, uiStartSpeed * 1000) ;
	}
	fprintf(fptr,"Required acceleration = %u Steps/sec/sec\n", uiRequiredAcc) ;
	return uiRequiredAcc ;
}

int main (int argc, char* argv[])
{
	unsigned int uiStartSpeed = START_SPEED ;
	unsigned int uiAvailableTimeInMiliSec = AVAILABLE_TIME_IN_MILI_SEC ;
 	int nDesPos = DES_POS ;
	unsigned int uiSpeedLimit = SPEED_LIMIT ;
	unsigned int uiAccLimit = ACC_LIMIT ;
	int k ;

	if ((argc < 2) || (argc > 7))
	{
		printf("Syntax: step outputfilename [AvailableTime] [DesPos] [StrtSpeed] [SpeedLimit] [AccLimit]\n") ;
		return 1 ;
	}
	fptr = fopen(argv[1], "wt") ;
	if (fptr == NULL)
	{
		printf("Could not open file %s\n", argv[1]) ;
		return 2 ;
	}
	for(k = 2 ; k < argc ; k ++)
	{
		switch(k)
		{
			case	2	:
					uiAvailableTimeInMiliSec = atoi(argv[k]) ;
				break ;
			case	3	:
					nDesPos = atoi(argv[k]) ;
				break ;
			case	4	:
					uiStartSpeed = atoi(argv[k]) ;
				break ;
			case	5	:
					uiSpeedLimit = atoi(argv[k]) ;
				break ;
			case	6	:
					uiAccLimit = atoi(argv[k]) ;
				break ;
		}
	}
	fprintf(fptr,"\n\t\tProfile Generation Algorithm Test Program\n")	;

	fprintf(fptr,"\nSpeed Limit in Steps/Sec is:%u",uiSpeedLimit) ;
	fprintf(fptr,"\nAcceleration Limit in Steps/Sec/Sec is:%u",uiAccLimit) ;
	fprintf(fptr,"\nStart Speed in Steps/Sec is:%u",uiStartSpeed ) ;
	fprintf(fptr,"\nDesired Position (Number of Steps) is:%u",nDesPos ) ;
	fprintf(fptr,"\nAvailable time in mili seconds is:%u\n\n",uiAvailableTimeInMiliSec ) ;

	RunMotor(uiStartSpeed,(uiAvailableTimeInMiliSec * 1000),nDesPos,uiSpeedLimit,uiAccLimit) ;

	fclose(fptr) ;
	return 0;
}