Instrucdons:. You have 45 minutes to complete this quiz. Namg :. You MAY use your formula sheet.. You MUST show your work in your bookl"t SA.,l: I #l 2otl F^\ Inglnecflns 1 - (2 marks) The following two systems are similar except that a unity gain has been removed? Draw the equivalent block diagrams ofeach SFG:. do not include any umty gain blocks. do not leave any negative signs in any ofthe system blocks SFG #I D -F SFG#2 -B D -F Block Diag #1 Block Diag #2 U v \ /..L(2mafts) #lyn= Use block diagram manipulation (ifnecessary) to solve the transfer firnctions YAJ. Ac A.t*l AStecFas)(-cu)(\rcn) #2YN: (1+ne)(l +er-.b).t J /-0marks) Kct bely A gymnast uses her eyes, brain, and stomach muscles to balance (maintain angle 0 = 0) on a beam. -urtemal Draw the feedback control system. Label ALL blocks and signals (input, output and al1 states). Use meaningful names. ol( lf co/,lbtn > D.rirJ Ar\'
4 - (1 marks) For the SFG shown below, specify all the forward path gains Pl...Pn in terms of G & H.,/: f.il Pl : \lruzq: Uq(JE P2= G6 r r{: yr= 5 - (1 marks) For the SFG shown above, specifu all the loop gains L1...Ln. Lt= -G,Ff, L2= O.H. L3: - G.Hr La: - GlHq Ls: - Gt Hs L6= Gof{,S$:H,{Hs (i)..---,6- (1 marks) For the SFG shown above, compute tlle determinant A in terms of L & P. ^: l- L;L;L,-L* Ls-Lt, * L,L.+ L,L.,, t L,Lr+ LzL\ + L2L5 L3Lr Lt u.ut 7 - (1 marks) Forthe SFG shown above, ""J" A1= t ^2: l-lflr-lt +LzL.l the sub-determinant A1...An in terms of L & P. f F= {: * 8 - (l marks) For the SFG shown above, specis the transfer function YAJ. Expand all terms into G & H except for A. A is assumed to be the same as in Q5. Y/U = GtGLGrG\Gs r Gn(t- G"tt no,hr+g1h1-g"gr t1"hr) A
Instructions:. You have 45 minutes to complete this quiz- Name :. You MAY use your formula she t.. You MUST show your work in your bookl"a SA.{: #2 *l firsmcsrne 1 - (1 marks) Converthe following system into its simplest possible mechanical equivalent. Label the circuit with appropriate mechanical symbols (F, V M, B, K). Rr L ) 'dl: rjl '/t 2 - (1 marks) Write the formula for each of your mechanical symbols (R Y M, B, K) in terms of the electrical symbols above (I, Y C, R, L). 3 - (1 marks) IG) u(s) 4 - (1 marks) r 1T It IJ= ZR t' I / r\ T 1t -- '1L (s+l)(s+2)(s+3) {= Cr* C,Cr.4-C,*Cr - ConVerthe following transfer function into the time domain..s -is 1-.s+ Sketch the poles and zeros. What is the order of the system? Is it stable? C,c.+ C.cr+C1Cl C,+ C, ffi: $rt) " fjl(r) - rojt"rt order= 1 @t, o, t(circle answer) stable =@ no (circle answer)
5 - (1 marks) 6 - (1 marks) For the following system, compute ( (zeta) and orn as a firnction of K. What value of K results in critical damping? /-- E: /'Jt+r tr:ffi Note that when K<0, the system tums into a positive feedback system. Sketch the NAIURAL resoonsewhenk:-0.5. K: o 7 =FFbl,l ot/e{^b""^pt"j 7 - (l marks) Use the Routhe-Hurwitz criteria to detemrine the values of K for which the svstem is stable. I 2 [rk K > -1, t*k 8 - (l marks) Compute the rise and settle time of the following system. I(1) _ s+45 U(s) "'*3"*9 T,= {.?,\ : T,: \,G-I S \-/' 9 - (1 marks) Compute the DC gain, Final Value of the impulse response, and percentage Koc = FV= 0J = overshoot. f a 16,X70
Instructions : #3 -Fall20l4. You have 45 minutes to complete this quiz. Name : o You MAY use your fomula sheet. o You MUST show your work in yow booklet. SAi: 1 - (l marks) For the following CLOSED-LOOP transfer function, fill in the block diagram. K(s + 5) Y - (s2+2s+2) U, l_1-- K(s+5) (s+ 1)(s2 +2s+2) 2 - (1 marks) Re-draw the system as a signal flow graph. Label ALL signals and systems. Zetos: - 5+t,z+')>+7 5+l 3 - (1 marks) For the above system, compute the OPEN-LOOP poles and zeros. eoles: -[, -l*j 4 - (1 marks) Compute the assymptotes ofthe root locus. t -l 1- An5( 6 Pet,Arrv : ) ) -l-j AssymptoteAngles: t 1O' Assymptote Centre: 5 - (1 marks) For a.ll COMPLEX poles-and./or zeros, compute the departure and/or arrival angles. Departure Angles: Arrival Angles: lt' " NlA 6 - (1 marks) Compute the breakpoints for all positive K values, if any exist. Hint: s3+9s2+15s+9: (s+7)(s- I +0.6j)(s- 1-0.6j) Break points: No^ a
7 - (1 marks) Is this system stable for all positive values of K? If so compute the maximum K value. Stable for all K>0?: NJ" MaximumK: 8 - (1 marks) Sketch the root locus. Draw the assymptotyes using a dotted line. 9 - (1 marks) l0 - (1 marks) Compute the frequency of oscillation when the system is MARGINALLY STABLE.. If the system is marginally stable for a positive K value, use that value.. Otherwise, use the negative K value.. Do not compute both!. Soecifu the units. Frequency: 3 -yt Use the Ziegler-Nichols Method to compute PID control gains for the system. Kp= 7 Ki= z.\b Kd: Q,195
Instructions : a o o You have 45 minutes to comdlete this outz. You MAY use your formulaaheet. You MUST show your work in your booklet. For the following open-loop transfer function: KGH: #4 -Fall20l4 lo81s + looy (s + 10)2(s2 + 1600s + 106) Name: *l SAJ: I lginsottts 1 - (1 marks) Write it in the correct form for drawing a Bode Plot. l+ Vtao KGH= lc'l) (ffi( +V,*,p)(t* %*"lff 2 - (2 marks) Draw the associated Nyquist contour in the s-domain. Transform any points that do not appear on the Bode Plot, into the u*jv domain. :@ 3 - (2 marks) 4 - (2 marks) 5 - (2 marks) 6 - (3 marks) On the attached Bode Papeq draw the magnitude plot. On the attached Bode Paper, draw the phase plot. On the anached Nyquist Paper. draw the Nyquist plot. Determine the gain margin, phase margin and cross-over ftequency. Gain Margin:?n ),9 Phase Margin: 45' Cross-Over Frequencv: l6,d -l 5
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-1 1 2 3 4 5 6 7 10 10 10 10 10 10 10 10-45.0-90.0-135.0-180.0-225.0-270.0-315.0-360.0
-120-60 0 db +60