- A Special Case Of The Two Functions Is The Following System Sometimes Called A Negative Feedback Control System A R S 1 (94.82 KiB) Viewed 31 times
- A Special Case Of The Two Functions Is The Following System Sometimes Called A Negative Feedback Control System A R S 2 (290.58 KiB) Viewed 31 times
A special case of the two functions is the following system, sometimes called a negative feedback control system: a R(S) G(s) C(s) H(S) By defining a variable e(s) at the output of the summation block, the two governing equations for this system are: e(s) = R(S) - C(s)H(s) C(s) = e(s)G(S) Substituting for the 1st equation into the 2nd yields: C(s) = [R(s) - C(s)H(s)]G(s), or C(s) = R(s)G(s) - C(s)H(s)G(s) This can be rewritten as: C(s) + G(s)H(s)C(s) = R(s)G(s), or C(s)[1+G(s)H(s)] = R(S)G(s), or C(s) R(S) G(s) 1+G(s)H(s) This general approach can be used to find the transfer function of other systems with feedback control as well.
s general approach can be used to find the transfer function of other systems with feedback control as well. blem IV: (35 points) (10 points) Find the transfer function of Figure 2 above in the s-domain (i.e., find the transfer function C(s)/R(s) for the Simulink model of Figure 2). Put your answer in the form of (s+a)(s+b), etc., where a and b are constants (potentially complex). Scan your handwritten work and include it in your lab report. By looking at the roots in the denominator, briefly explain (2-3 sentences) why (in the time domain) the system is "uncontrolled". (5 points) Build the model in Simulink. Using the pulse generator, build an impulse function by having one pulse of amplitude 1000 and width 1 ms used as the disturbance. Run the simulation for 10 seconds. Indicate (1 sentence whether the variable c(t) (which represents the position of the ball bearing mass in the time domain) due to the impulse goes back to zero, or whether c tends to move away from zero (exponentially or cyclically) as time increases. (10 points) Modify the Simulink model to look like Figure 3 below. A controller is implemented in Figure 3, which hopefully will stabilize the system. You will need to replace the value of k in the block "controller gain" with an actual value. Rerun the simulation of Figure 3 with various integer values of k, and see whether c tends to move away from zero as time increases. For those values of k where c returns towards zero, we can say that the controller has stabilized the system. Find the range of integer values of k which, in fact, stabilize the system. Stable, as defined for this problem, implies that the ball's position tends towards a certain fixed finite position without going towards + oo as time goes towards co. (10 points) Find the transfer function of the new Simulink model in Figure 3 below, using the average value of k you found from part 3 above (round it to the nearest integer). Put your answer in the form of (s+a)(s+b), etc., where a and b are constants (potentially complex). Scan your handwritten work and include it in your lab report. By looking at the roots in the denominator, briefly explain (2-3 sentences) why (in the time domain) the system is now "controlled" when k is properly selected. (If necessary, use the "roots” function in Matlab). a a