Question

FIGURE 2.23 2.18 Find state-space equations to describe the pendulum systems in Fig. 2.24. The systems are useful to model one- or two-link robotic manipulators. If e, 81, and O2 are very small can you consider the two systems as linear? m 1 " m2 ult) - mg (a) FIGURE 2.24

Please show how to solve b) step by step. please to include the parameter u(t)

Answer 1

for mass 2. en 128 --Mngh2O2-modd ,+UCH) & m2 122 82 + mphid20, + magh202 = u(t) - 02 + vrt 2 + 02-(t). ] 3 no2 (a) Taking More about pivot and applying Neuton's law we hau. 18 - – mgnsind auf S. since o is very smal : Sino- - to fingle = 6(H) [= ml2 me2 tinglo - o ult) 1 2 8 + 80 ) for Moss - 1,8; - -m, gd, 0,-maghio, -m{1,10 +1202) di ra, 1, ² i + m2 70+ m2 1502 + (rm, than 2) gh, 0,20 - (m, tm20 + Mzd2l02 + (mitme) gd; 920