Control Systems Question?

Question

Ok, I want to understand this, I have the answer but I need to know why we got that answer, if we have a closed loop system with a given transfer function:

G(s) = 10 / (s+11)

What is the steady state output of the system when an input of:

2 cos (2t - 45)

is presented to the system.

the answer I have is 1.79 cos (2t - 55.3)

Please Explain, Thanx in advance.

Answer 1

The input is specified in the time domain. Convert it to something usable in the frequency domain (convert it to a function of s).

Multiply G(s) times the input, and finally transfer the result back into the time domain. That should be equal to your answer.

Answer 2

the errors to which you referr to is termed offset. An On/Off administration is via no skill in a delicate state as its administration sign is the two On or Off and therfore motives the recommendations-set fee to consistently be in the two an up vogue or down vogue. Proportional structures generate a administration sign (corrective action) it is predicated on the quantity of deviation from set component (the quantity of errors) it is further approximately via making use of a metamorphosis in equipment stability (replace in load). there's a fixed relationship between the quantity of deviation and the consequent corrective administration sign that could desire to be considered a earnings fee it is larger with the deviation to compute the quantity of administration sign. This multiplier creates a proportional reaction to an volume of deviation from setpoint. >>>Why does sturdy state errors take place in a proportional administration equipment? <<< because of the reality if the quantity of deviation modifications in an attempt to does the quantity of administration sign. Its like a weigh being located on a spring. Initally it bounces up and down and settles out with a elementary compression for a given volume of load (weight) . If the spring tries to return to its unique lenght much less stress is generated to counter the burden. subsequently the spring keeps to be compressed jointly as a weigh is located on it. The proportional equipment reponds to boot the placement the quantity of deviation creates a proportional administration respnse for a given load. keep the burden the comparable and attempt to regulate the quantity of deviation and you to boot mght replace the quantity of administration sign. On Off administration differs in that there via no skill a genuine stability acheived between load and the administration and teh equipment is operated indoors a suitable deadband decision of PV.