Question

For the given RC circuit shown below, ys the output, and ut) is the input. Values of the components are marked on schematic i) Derive the system differential equation and transfer function Y(s)/U(s) ii) Choose voltage across capacitors as states and derive the state equations and state matrices (A, B, C,and D). iii) Validate the states by deriving the transfer function from state matrices. iv) Choose a different set of states and derive a different state equation and state Matrix values v) Confirm the states by deriving the transer function from the states. (SHOW DETAILS OF WORK.) (七 LC ult)

Answer 1

ut) is input 2-R u(t) At Node ,8 KC dt 天 权 śubsitthing

u(s) V,(, ove state dt 2P 2- RC dt 收(t) ARC duzst)

32t C OPC 2KC -1 -1 C(ST-A) t+D uS)

V,L be the state vaxinbles 근R u (t 2 U(t) v,(et) 2 RC

ry (t) - 1. ( 2 R ) - 2 Diffe、ent ating above eAⓑ P.C RC y(+) = -@ v,(t)- 丁7 ( 2C) OFt

姒 , s-그 RC 2 RC 2亿"c FC RC ZRC 2 ze 2 RC

RC