Homework Automatic Control/Open loop controller

Discussion in 'Homework Help' started by Luksch, Apr 18, 2013.

1. Luksch Thread Starter New Member

Apr 18, 2013
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0
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.

2. #12 Expert

Nov 30, 2010
16,705
7,355
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.

3. Luksch Thread Starter New Member

Apr 18, 2013
5
0
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)?

Last edited: Apr 19, 2013
4. Luksch Thread Starter New Member

Apr 18, 2013
5
0
i don't have the solution for c) and d) yet. can nobody help me?

5. t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Might be worth checking the original problem statement. What are a & b for instance? They don't get a mention in the function .....??