The swerve response of finand spin-stabilized projectiles to control mechanism inputs is sometimes not intuitive. This paper seeks to explain the basic parameters that govern the swerve of projectiles excited by control inputs. By modeling the overall effect of a generalized control mechanism as a nonrolling reference frame force applied to a point on the projectile, general expressions for swerve are obtained in terms of basic vehicle parameters. These compact expressions are used to show that maximum swerve response for a fin-stabilized projectile is achieved when the force is applied near the nose of the projectile, whereas maximum swerve response for a spin-stabilized projectile is achieved when the force is applied near the base of the projectile.

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) March 20052. REPORT TYPE AUTHOR(S)Douglas Ollerenshaw * and Mark Costello † 5f. WORK UNIT NUMBER PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Department of Mechanical Engineering Oregon State University Corvallis, OR 97331 PERFORMING ORGANIZATION REPORT NUMBER SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army Research Laboratory ATTN: AMSRD-ARL-WM-BC Aberdeen Proving Ground, MD 21005-5066 SPONSOR/MONITOR'S REPORT NUMBER(S)ARL-CR-558 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited.13. SUPPLEMENTARY NOTES * Graduate research assistant † Associate professor, member ASME ABSTRACTLaunch uncertainties in uncontrolled direct-fire projectiles can lead to significant impact point dispersion, even at relatively short range. A model predictive control scheme for direct-fire projectiles is investigated to reduce impact point dispersion.The control law depends on projectile linear theory to create an approximate linear model of the projectile and quickly predict states into the future. Control inputs are based on minimization of the error between predicted projectile states and a desired trajectory leading to the target. Through simulation, the control law is shown to work well in reducing projectile impact point dispersion. Parametric trade studies on an example projectile configuration are reported that detail the effect of prediction horizon length, gain settings, model update interval, and model step size. iii

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) March 20052. REPORT TYPE AUTHOR(S)Douglas Ollerenshaw * and Mark Costello † 5f. WORK UNIT NUMBER PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Department of Mechanical Engineering Oregon State University Corvallis, OR 97331 PERFORMING ORGANIZATION REPORT NUMBER SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army Research Laboratory ATTN: AMSRD-ARL-WM-BC Aberdeen Proving Ground, MD 21005-5066 SPONSOR/MONITOR'S REPORT NUMBER(S)ARL-CR-558 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited.13. SUPPLEMENTARY NOTES * Graduate research assistant † Associate professor, member ASME ABSTRACTLaunch uncertainties in uncontrolled direct-fire projectiles can lead to significant impact point dispersion, even at relatively short range. A model predictive control scheme for direct-fire projectiles is investigated to reduce impact point dispersion.The control law depends on projectile linear theory to create an approximate linear model of the projectile and quickly predict states into the future. Control inputs are based on minimization of the error between predicted projectile states and a desired trajectory leading to the target. Through simulation, the control law is shown to work well in reducing projectile impact point dispersion. Parametric trade studies on an example projectile configuration are reported that detail the effect of prediction horizon length, gain settings, model update interval, and model step size. iii

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) March 20052. REPORT TYPE AUTHOR(S)Douglas Ollerenshaw * and Mark Costello † 5f. WORK UNIT NUMBER PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Department of Mechanical Engineering Oregon State University Corvallis, OR 97331 PERFORMING ORGANIZATION REPORT NUMBER SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army Research Laboratory ATTN: AMSRD-ARL-WM-BC Aberdeen Proving Ground, MD 21005-5066 SPONSOR/MONITOR'S REPORT NUMBER(S)ARL-CR-558 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited.13. SUPPLEMENTARY NOTES * Graduate research assistant † Associate professor, member ASME ABSTRACTLaunch uncertainties in uncontrolled direct-fire projectiles can lead to significant impact point dispersion, even at relatively short range. A model predictive control scheme for direct-fire projectiles is investigated to reduce impact point dispersion.The control law depends on projectile linear theory to create an approximate linear model of the projectile and quickly predict states into the future. Control inputs are based on minimization of the error between predicted projectile states and a desired trajectory leading to the target. Through simulation, the control law is shown to work well in reducing projectile impact point dispersion. Parametric trade studies on an example projectile configuration are reported that detail the effect of prediction horizon length, gain settings, model update interval, and model step size. iii