Figure below shows the block diagram of a dc-motor control system (note the dc-motor is represented by G(s)= K(s+3)/s(s+1)(s+2).The signal N(s) denotes the frictional torque at the
motor shaft.
a) Find the transfer function H(s) so that the output Y(s) is not affected by the disturbance torque N(s).
b) With H(s) as determined in part a), find the value of K so that the steady-state value of e(t) is equal to 0.1 when the input is a unit-ramp function, r(t)=tu(t) and N(s) = 0 . Apply the final-value theorem.
The figure(block diagram) is in this PDF FILE "ECEN 4413 Automatic Control System Spring 2005 Midterm Exam 1". I cannot post url here so you can just search in google,Sorry..but pls help me..:(
It's problem number 4 there..PLS I really need your help..THANK YOU!!
I'm sorry, but as a text-based AI, I'm not able to open or search for specific PDF files or view images. However, I can assist you in understanding the steps and concepts necessary to solve this problem.
To find the transfer function H(s) so that the output Y(s) is not affected by the disturbance torque N(s), we need to determine the appropriate feedback configuration. Let's break down the steps:
a) To make the output Y(s) unaffected by the disturbance torque N(s), we need to eliminate its influence on the system. We can achieve this by introducing a feedback loop that cancels out the effect of N(s).
1. Start by taking the output of the motor, Y(s), and introducing a feedback path that subtracts the disturbance torque N(s) from it.
2. The transfer function of the motor, G(s), is given as K(s+3)/s(s+1)(s+2). Therefore, the signal after the motor is G(s)Y(s).
3. Now, subtracting the disturbance torque N(s) from G(s)Y(s) gives us G(s)Y(s) - N(s).
4. To obtain a transfer function that cancels out N(s), we need a feedback gain, H(s), which makes the output of the subtraction H(s)[G(s)Y(s) - N(s)] equal to Y(s).
Mathematically, we have H(s)[G(s)Y(s) - N(s)] = Y(s).
5. Rearranging the equation, we get H(s)[G(s) - 1]Y(s) = N(s).
6. Therefore, the transfer function H(s) should be H(s) = 1/(G(s) - 1).
b) Once we have determined the transfer function H(s) = 1/(G(s) - 1), we can use it to find the value of K that makes the steady-state error of the system equal to 0.1 when the input is a unit ramp function, r(t) = tu(t), and N(s) = 0.
1. The Laplace transform of the unit ramp function r(t) = tu(t) is R(s) = 1/s^2.
2. Since Y(s) = H(s)[R(s) - N(s)], and in this case, N(s) = 0, the equation becomes Y(s) = H(s)R(s).
3. Substituting the value of H(s) from part a), we have Y(s) = (1/(G(s) - 1))R(s).
4. The final-value theorem states that the steady-state value of y(t) can be found by evaluating sY(s) as s approaches 0.
5. Applying the final-value theorem to the equation Y(s) = (1/(G(s) - 1))R(s), we have y_ss = lim(s->0) [sY(s)].
6. Substitute the value of R(s) = 1/s^2 and simplify the equation to find y_ss in terms of K.
7. Equate y_ss to 0.1 and solve for the value of K.
Unfortunately, without being able to access the specific block diagram and transfer function values provided in the PDF file, I cannot provide you with the concrete calculations to solve this problem. However, please follow the steps outlined above with the specific values given in the problem, and you should be able to determine the transfer function H(s) and calculate the value of K accordingly.