Question

For a double pendulum, is it possible to implement a PID controller or any controller to control the motion to something that can be calculated?

Answer 1

Ans. et 1/ a move cranes are in ΟΥ For a double pendulum 18 posseble to emplement PID ( Proportional integral desrivative) controller to control motion → To heavy and bulky loads overload used through the overhead space facelety instread of through aisles the floor The natural sway of cravers payload is safety problem which require by control engeweers. Let us dexcuss au optimized mathematical model of a double penduan overhead Crane schenne Mathematical model - a huge good research with control N Trolley mi > o, 1 L2 Hook on - mz payload m. Fug. shows double pendulum type system parts trolley , hook and having three

Three coordinate narriables which are sho.com un payload xa and o the figure. The length of cables hung below the trolley the hook h and he respectively. The other parameter loiko force F. (conrol input) trolley mass and payload payload mass me and ale mo are defeined. make (Q) (b ) Cables are (C) and certain assumptrom Smooth motion of trolley mass less and raged Hook cable payload modelled as point mass The equation of metron be written as by Lagrange's d (94) ETE dt oqi can method OL gqi Ly Lagrangian function qis generalized coordenate (x, 0,,O2 here) Hon conservative force. Ti →

LE K-P k= energy a = system we can Total könetic of mechanical system. potential energy of the write the uation of motion of motion of system (mam, twy) ä + (m, 4m2) L, ö, uso, try to copla -(mam) La sind, -m Lasing ZF as (M, M2) L,ä copo, + (m, + m2) 2² 6 t ml, Leo h) - 2 + m2 Lil Or Bin (on-02) tim, m) 2 g sind, zo 212 Måly si caso at my 2202 + m₂ 4hë eas Cool mahho sin (0-0) + mghsmo, zo 3 Control schomes Schome L- Three PID controllons The control of double pendulum depends on PID .controllers for eachy objective а

The forst PID controller ugod for accurate positionning of the ofrolley The other 2 PID controllers are used to eliminate of Cillation and sway of the hook and payload respectively, Block doagram ult) + >O + PIDI Oz position reference {pioak ay Trolley displacement | Payload auti-swing controller a Hook sway angle O= payload sway angle Hook auti swing controller Plo-ok P1 р. and pp Schame 2 One controller for possitioning two controller for double pendulan The two PID controller which are edeninating Oscillation are replaced by controllers. used for two PD Block deagradu Os shown as

a Uct) 5 PID 4 Controlled force O Reference position PDI Payload Anti Swing controller PD 2 controller Block diagsam Hook anti-swing