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### hw8

Course: HW 599, Fall 2009
School: Kentucky
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Word Count: 306

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Wednesday, Due February 20 EE/MFS599 D(s) = 1/s T s HW#8 W(s) + + Gc (z) G zoh(s) 10 s+6 Y(s) 1. a) b) c) Ts = 10 msec Re-write the problem so it is completely in the s-domain Make the disturbance zero and let Gc(s) = K. Find the sensitivity of Y(s)/W(s) to the gain K for both the open-loop and unity feedback case when the nominal value is K=100 and the input is a unit step. Predict how the steady-state...

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Wednesday, Due February 20 EE/MFS599 D(s) = 1/s T s HW#8 W(s) + + Gc (z) G zoh(s) 10 s+6 Y(s) 1. a) b) c) Ts = 10 msec Re-write the problem so it is completely in the s-domain Make the disturbance zero and let Gc(s) = K. Find the sensitivity of Y(s)/W(s) to the gain K for both the open-loop and unity feedback case when the nominal value is K=100 and the input is a unit step. Predict how the steady-state response will change if K increases by 10% for both the openloop and closed-loop configurations. 2. a) Let the disturbance be a unit step (constant). Design a Robust digital compensator, Gc(z), which will meet the following specifications 1. Closed-loop system is stable 2. ts due to a step is less than 2 seconds 3. ess due to a step is zero 4. Mp < 5% (remember Mohannad's 4.32% means = 0.707 5. Steady-state error due to constant the disturbance d(t)=u(t) is minimized b) Use Simulink to verify your design (in the s-plane using Gc(s)). Initially, set the disturbance to zero and measure your transient (ts and Mp) and steady-state error specs. Then, set the disturbance to a unit step and verify that its effect is negligible c) Your book discusses the case when your disturbance occurs at the output. I made the statement in class that the model we use is the same as the model in the book if we simply put GzohG(s) as a p...

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Kentucky - EEMFS - 599
Due Wednesday, January 30 You may use Matlab/simulink wherever applicable 1. a)EE/MFS 599HW #3Plot the step responses of the following first order systems with a transmission zeroes. Can you see the effect of the zero? How about on part ii)? i)
Kentucky - HW - 599
Due Wednesday, January 30 You may use Matlab/simulink wherever applicable 1. a)EE/MFS 599HW #3Plot the step responses of the following first order systems with a transmission zeroes. Can you see the effect of the zero? How about on part ii)? i)
Kentucky - EEMFS - 599
Due Wednesday, February 6thEE/MFS 599HW #5You may use Matlab/Simulink wherever applicable 1. Consider the standard, unity-feedback closed loop control system shown below where G(s) = 10/[sq(s+1)(s+9)]W(s)+ -Gc(s)G(s)Y(s)a) Let q=0 (
Kentucky - HW - 599
Due Wednesday, February 6thEE/MFS 599HW #5You may use Matlab/Simulink wherever applicable 1. Consider the standard, unity-feedback closed loop control system shown below where G(s) = 10/[sq(s+1)(s+9)]W(s)+ -Gc(s)G(s)Y(s)a) Let q=0 (
Kentucky - EEMFS - 599
Due Monday, February 11EE/MFS 599HW#6In our controls system lab, we have a DC Servo motor called the Motomatic. We would like to design a controller for this DC servo using the following block diagram:I= F C onstant + aRa + I aL a V out
Kentucky - HW - 599
Due Monday, February 11EE/MFS 599HW#6In our controls system lab, we have a DC Servo motor called the Motomatic. We would like to design a controller for this DC servo using the following block diagram:I= F C onstant + aRa + I aL a V out
Kentucky - EEMFS - 599
Due Wednesday, February 20EE/MFS599D(s) = 1/s TsHW#8W(s) + + Gc (z)G zoh(s)10 s+6Y(s)1. a)Ts = 10 msec Re-write the problem so it is completely in the s-domainSolution: Gzoh = 1/[(Ts/2)s+1] = 1/[0.005s+1]b)Make the disturbance
Kentucky - HW - 599
Due Wednesday, February 20EE/MFS599D(s) = 1/s TsHW#8W(s) + + Gc (z)G zoh(s)10 s+6Y(s)1. a)Ts = 10 msec Re-write the problem so it is completely in the s-domainSolution: Gzoh = 1/[(Ts/2)s+1] = 1/[0.005s+1]b)Make the disturbance
Kentucky - EEMFS - 599
Due Wednesday, January 30 You may use Matlab/simulink wherever applicable 1. a)EE/MFS 599HW #3Plot the step responses of the following first order systems with a transmission zeroes. Can you see the effect of the zero? How about on part ii)? i)
Kentucky - HW - 599
Due Wednesday, January 30 You may use Matlab/simulink wherever applicable 1. a)EE/MFS 599HW #3Plot the step responses of the following first order systems with a transmission zeroes. Can you see the effect of the zero? How about on part ii)? i)
Kentucky - EEMFS - 599
Due Wednesday, February 13EEMFS 599HW #161. Given the following digital control system for a servo with open-loop transfer function G(s) = 10/(s(s+8):T W(s) + G c (z) G zoh(z)s10 s(s + 8)Y(s)a) b)Find an S-domain model for the open-lo
Kentucky - HW - 599
Due Wednesday, February 13EEMFS 599HW #161. Given the following digital control system for a servo with open-loop transfer function G(s) = 10/(s(s+8):T W(s) + G c (z) G zoh(z)s10 s(s + 8)Y(s)a) b)Find an S-domain model for the open-lo
Kentucky - EE - 571
EE571 - Solution to HW#18w + K (s+2)(s+3)(s+5) y1. a) System:s3Char. Equation: 1+GH = 0 = s +10s +31s+(30+K). Our Routh Array looks like:3 21 101031-1( 30 + K ) 1031 30 + K 0s s s2 1 030 + KThus, to be stable the Routh Array canno
Kentucky - EE - 571
EE571 Solution to HW#25 1. a) Realize the following compensators using op-amps, 1 F capacitors, and resistors: i)SF : G 1 W (s) 1 14 -1/s 1 5 Y (s)Gc (s) = 5(s+6)/(s+20) =5[1 +-14/(s+20)](note: all capacitors are 1 F )25 1M O mC p-A p kt. 1/5
Kentucky - EE - 19
EE571 - Solution to HW#19 1. a) Use all 10 rules to plot the root locus of GH=K/(s (s+3)(s+8) 10 rules:1. Starts @ open loop poles @ K=0 which are s=0,0,-3,-8 2. Ends @ open loop zeroes @ K= which are s=, 3. # of branches = n which is 4 4. R.L. is sy
Kentucky - EE - 571
EE571 - Solution to HW#19 1. a) Use all 10 rules to plot the root locus of GH=K/(s (s+3)(s+8) 10 rules:1. Starts @ open loop poles @ K=0 which are s=0,0,-3,-8 2. Ends @ open loop zeroes @ K= which are s=, 3. # of branches = n which is 4 4. R.L. is sy
Kentucky - EE - 571
EE571 Objective: - To obtain a model for the Motomatic using frequency response methods Pre-Lab: (Counts as HW#27 - Due Monday, December 10)Experiment #6 (Counts as HW#27+28)For the remaining two experiments, we will operate the motomatic in velo
Kentucky - EE - 571
Solution to HW#22 1.a) Design a PD (ultimate lead compensator) to meet the transient specs given in problem 2 on HW21.Sol'n: Desired dominant poles are at s=-4+j4 and s=-4-j4. The angle of deficiency is still the same as it was for the lead design:
Kentucky - EE - 571
Objective:EE571 Experiment #4 (Counts as HW#16 and 17) 1. To design a Full-order Observer for the Motomatic 2. To design an Improved Observer for the MotomaticPre-Lab: (Counts as HW#16 - Due Monday, November 3) We are indeed fortunate to have a t
Kentucky - EE - 571
Objective:EE571 Experiment #5 (Counts as HW#23+24) 1. To design classical, root-locus based compensators for the Motomatic 2. To implement these designs and measure performance specsPre-Lab: (Counts as HW#23 - Due Wednesday, Nov. 19 Recall from L
Kentucky - EE - 571
EE571 - HW#20 1. a)i)Sketch the root locus for the following open-loop pole-zero configurations for GH(s):j ii) jj iii)-4-4-4b)Use the property of symmetry (if applicable) to help you sketch the root locus for the following open-loo
Kentucky - EE - 571
Prelab is due Monday, Sept. 29EE571Experiment #2 (Counts as HW#9 and 10)Objective: The objective of lab 2 is to: 1) complete our measurements of the MOTOMATIC internal parameters; 2) To obtain a state vaiable model of the MOTOMATIC. Prelab (Cou
Kentucky - EE - 571
EE5712 ohm iL1 iL2 2 ohm + -Solution to HW#121/2 H1/4 Hw(t)1a)Let the state variables be iL1 and iL2. Therefore, vL1 / L1 2( vL1) 2( iL1 iL2 + 0.5w) 2 2 1 &amp; x= = 4( vL2) = 4( iL1 iL2 + 0.5w) = 4 4 x + 2 w vL2 / L2 Ne
Kentucky - EE - 571
EE571 Solution to HW#1 1. a) Find the state variable model of the form&amp; x = Ax + Bw, x( 0+ ) for the following electrical network:1 ohm+iL1 0 u(- t)+ w ( t) u( t)Amp sVc -1 /3 F2 o hm s 1 /2 H(Hint: Let x = v C ) iL (make sure
Kentucky - EE - 571
EE571 Solution to Prelab 1 1a) To find tp, we need to take dy/dt and set equal to zero:dy = n e - n t (cos d t + dt ( n -1 - 2sin d t) - e -w n t (- d sin d t +- d )sin d t = ( n - d1 - 2cos d t) = 0)cos d t + ( d1 - 2)cos d t
Kentucky - EE - 571
EE571 1a) The solution is x(t) = eA(t- t 0 )Solution to HW#7x( t 0 ) +et0tA(t- )Bw( )d . To evaluate eAt, first lets find the eigenvalues of A:s + 4 2 4 2 A= sI A = = s2 + 8s + 12 = ( s + 2)( s + 6) = 0 s1 = 2 and s2 = 6 2 4 2 s
Kentucky - EE - 571
Due Wednesday, October 8EE571HW#121. a) b) Uncontrollable systems often arise when we have a great deal of symmetry in our system. Uncontrollable systems can also occur if we have have two energy storage elements which can be combined into one
Kentucky - EE - 571
Due Wednesday, September 24 1.EE571HW#8Since it is football season, you have decided to invest in a satellite dish. Rather than pay for a DSS system, you decide to build your own and borrow signals from a variety of satellites. Thus, you must d
Kentucky - EE - 571
Last HW! 0. 1. a)EE571HW#31Sign-up and perform lab 6 it is due on Wednesday, as well. From the Bode Plot below, find G(s), the open-loop transfer function (assume H(s)=1)Bode Plot for HW#31 40200 Gain dB -20-40 -1 1010010 Frequen
Kentucky - EE - 571
Note: All HW's and Solutions are on the web at http:/www.engr.uky.edu/csl/ee571 Due Wednesday, September 3rd EE571 Our HW Theme is: The State Variable Model and You 1. a) HW#1&amp; Find the state variable model of the form x = Ax + Bw, x ( 0 ) for the
Kentucky - EE - 571
Due Wednesday, December 11EE571Solution to HW#311. a)From the Bode Plot below, find G(s), the open-loop transfer function (assume H(s)=1)0 dB/dec 40Bode Plot for HW#3020-20 dB/dec0 Gain dB -20 -40 dB/dec-40 -1 1010010 Freque