THE USE OF MATLAB AND SIMULINK AS A TOOL FOR CONTROL SYSTEM DESIGN Rajeh Rajaman ME 43 Deartment of Mechancal Engneerng Unerty Of Mnneota OBJECTIVES Lab objecte To learn the ue of Matlab and Smuln a tool for mulaton and control ytem degn To dentfy the arameter of a ehcle model n Smuln To degn a controller for a ehcle followng alcaton and ealuate t erformance through mulaton
SIMULINK Seeral tutoral on Smuln are aalable, a referenced n the lab handout Quc hand-on oerew of Smuln n cla LONGITUDINAL CONTROL Longtudnal control control of the longtudnal moton of the ehcle.e. t eed, acceleraton or t dtance from another ehcle throttle and brae are the control nut Eamle of longtudnal control alcaton crue control adate crue control collon aodance ehcle latoon n automated hghway ytem
ADAPTIVE CRUISE CONTROL Etenon of the regular crue control ytem MOTIVATION Hghway Safety About 4,000 eole de n traffc accdent annually Oer 90 % of accdent occur due to human error Vehcle falure and road condton account for le than 0% of all accdent Hghway Congeton Traffc congeton a gnfcant - and growng - roblem n the country major metrooltan area Roadway eanon unlely to ole the congeton roblem Increae n traffc demand contnue to outace ncreae n caacty Road buldng tycally cot $30 mllon er mle er lane of hghway Automaton technologe can lay a ey role n addreng afety and moblty 3
Longtudnal Control Oerall objecte Mantan dered acng from target ehcle (ehcle followng) or mantan dered eed (eed control) Derable cloed-loo ecfcaton for ehcle followng nddual ehcle tablty trng tablty autonomou oeraton robutne SPECIFICATIONS Inddual ehcle tablty If the recedng ehcle not acceleratng, the acng error hould conerge to zero Strng tablty If recedng ehcle acceleratng/ deceleratng, acng error could be non-zero need to enure that acng error attenuate a t roagate along the trng of ehcle (.e. a t roagate utream toward the tal of the trng) 4
NOTATION Conder a trng of 3 car that are ung adate crue control L de 3 Sacng error e.g. L de L de CONTROL ARCHITECTURE Control ytem dered accel Uer Controller fault meage Indeendent degn of lower controller Bandwdth of lower controller condered n degn of uer controller Lower Controller throttle brae 5
UPPER CONTROLLER Model ued for degn Uer controller degned ung de Dered acceleraton the control nut Model ued for analy Robutne of the uer controller analyzed ung de where the tme contant due to a lag n tracng the dered acceleraton CONSTANT SPACING POLICY Inddual ehcle tablty Sacng error hould conerge to zero f the recedng ehcle not acceleratng A mle PD controller can guarantee ehcle tablty 0 0 a Lde t 0 Stable! 6
7 CONSTANT SPACING POLICY For the econd car, the acng error gen by L de Hence the tranfer functon relaton between lead car acceleraton and acng error of econd car ) ( ) ( Hence acng error of econd car conerge to zero f lead car mong at contant eed CHARACTERISTIC EQUATION P C y u L de e de PC L ) (
8 CONSTANT SPACING POLICY If recedng ehcle not acceleratng, acng error conerge to zero If recedng ehcle acceleratng/ deceleratng, acng error non-zero howeer, we need to enure that acng error attenuate a t roagate along the trng of ehcle ecfcaton of attenuatng error roagaton: th roerty of attenuatng error roagaton called trng tablty CONSTANT SPACING POLICY Strng tablty L ) ( ) ( 0
CONSTANT SPACING POLICY Bode lot of ( ) ( ) 0 0 0 0-0 - 0-3 0-0 - 0 0 0 0. 3 Magntude alway eceed, no matter what alue are ued for and PRELAB Wrtten hand n requred. Reew ue of the bloc n Smuln ecfed on age (no wrtten hand-n for th ta) Oen the Smuln ehcle model gen to you on the cla web te and reew t (no wrtten hand-n for th ta) Decrbe a rocedure for how you wll determne the tme contant of the ehcle model durng the lab (Hnt: Reew the ytem dentfcaton rocedure of Lab 6). Show how acng error wll be defned n Smuln tartng from the ehcle model roded to you. Determne alue of the roortonal and derate gan that you wll ue n a PD controller o a to achee a bandwdth of 6 rad/ and a damng rato of 0.707. Ue the nomnal econd order ehcle model for your degn. 9
TASKS IN LAB Imlement the rocedure you deeloed for dentfyng the tme contant of the ehcle model. Sae your data and calculate the tme contant. The abolute oton of the three car are aalable a gnal n the gen Smuln rogram. Defne acng error for car and 3 n the Smuln bloc dagram ung the dfference between thee oton and a dered alue for the nter-ehcle acng. Imlement a PD controller n Smuln ung the gan you calculated n re-lab. Smulate the erformance of th controller. Aume that the frt (lead) ehcle moe at a contant eed of 30 m/. Aume that there an ntal error n acng between the lead and the econd ehcle of meter and that the dered acng 0 meter. Aume that the thrd ehcle ha zero ntal acng error. Smulate and how the erformance of the ytem to thee ntal condton. TASKS IN LAB Net, aume that the ntal acng error are zero. Aume that at econd, the lead ehcle begn to accelerate wth a contant acceleraton of m//. What the teady tate error n acng for ehcle and 3? Doe the ue of PID control hel to reduce th acng error to zero? Net, aume that the lead ehcle ha an ntal eed of 30 m/, an ntal acceleraton of zero, and after econd t ha a dered acceleraton of n( t) wth = 5.5 rad/. Smulate the erformance of your PD controller. Comare the acng error of car and 3 and determne whch acng error bgger. Comment on how the acng error wll roagate f there were a trng of ACC ehcle wth the ame control law. 0