Hello,

i need help in my homework in automatic control. i tried to solve the problem, but i dont know how to start. maybe you can give me a hint? Thanks in advance

Assume that xc(t) = 1u(t), where u(t) is a step function, i.e., u(t) = 1 for all t ≥ 0 and u(t)=0 for all t<0.
1) For system x ̇ = −0.02x + 0.1V + d, design an open loop controller
V (t) = F1xc(t)
where F1 is a constant.

a) Find F1 such that limt→∞(x(t)−xc(t))=0 when d=0, a=0, and b=0.
b) Where is the pole of the controlled system when d = a = b = 0? Is the pole location affected by the choice of the control law parameter F1?
c) What is the settling time of the closed-loop system when d = a = b = 0 (i.e., three times the time constant when d=a=b=0)?
d) Find an expression for the tracking error xe = (x − xc) as a function of d, a, and b.

 

Nice of you to type out the whole question, but you have to make an attempt to solve it. THEN we push you in the right direction.

 

i dont want u to solve the problem!!! I just want a hint to start!! because i am totally new in this topic and dont know how the start solving the problem. thats my first homework

ok, i already solved (a), but which equotations should i use for (b) and (c)?

 

i don't have the solution for c) and d) yet. can nobody help me?

 

Might be worth checking the original problem statement. What are a & b for instance? They don't get a mention in the function .....??