A speed control for a gasoline engine is shown in Fig. 5 below.R(s) +Throttle●●1s+1910.4s +1S(b) With the smallest gain satisfying part (a):Figure 5(a) Determine the necessary gain K if the steady-state error is required to be less than 10% ofRthe reference input R(s) = where R is a positive constant.TorqueK3s +1Y(s)determine closed-loop stability of this system using Nyquist criterion (generateNyquist plot with MATLABdetermine gain and phase margins of the system using Nyquist plotWhat is the value of K that destabilizes this system (if such exists)?NOTE:part (b) can be solved graphically by clicking on the appropriate points on the generated graphmake sure that you attach the Nyquist plot with shown clicked points

Given: To find: Steady state error

Answered: A speed control for a gasoline engine…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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H.w 2: The open loop response, that is, the speed of the motor to a voltage input of 20V, assuming a system without damping is dw 20 = (0.02) + (0.06)w. dt If the initial speed is zero (w(0) = 0) ,and using the Runge-Kutta 4th order method, what is the speed at t = 0.8s? Assume a step size of h = 0.4s.
5 Problem Match the following two frequency response diagrams: -0 0.4 |G(i w)| 0.2 10 |G(i w)| 5 Response A 2 3 4 5 6 7 8 Frequency, (rad/s) Response B 5 6 7 8 Frequency, w(rad/s) 1 2 3 4 6 6 10 10 10 to two of the following ODES 1. +x+100x = u(t) 5. +100x = u(t) 9. +100x = u(t) 3. x+x+5x= u(t) 4. x+x+x= u(t) 2. x+x+25x = u(t) : 6. x + 25xu(t) 10. +25x = u(t) 7. x+5x= u(t) 8. u(t) 11. +5x= u(t) = 12. xu(t)
Given the vibrating system below: K4 Y(t) =Ysin30t where for = 30 and Y=20mm Find the following K1 K2 m C3 H C2 C1 C5 C4 1. Frequency Ratio 2. Displacement Transmissibility Ratio 3. Absolute displacement of the mass 4. Type of Damping 5. Equation of motion x(t). Assume Initial conditions for displacement and velocity 6. Graph 2 cycles of the vibrating system. You can use third party app for this. M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2=40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m
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An experiment was carried out on a SDOF system to estimate the natural frequency and damping. The time history plotted below has the response in centimetres and the time in seconds, as shown in Figure Q10 below. Estimate values for the following and choose the nearest values from the list given below: the damped natural frequency in Hz; the damping ratio using the logarithmic decrement method; and the natural frequency in rad/s. Ju(t) 2.00 AMA 1.00 0.00 0.00 Figure Q10 0.80 1.60 Select one or more: O a. 4.92 b. 0.781 c. 0.625 O d. 0.330 O e. 0.052 2.40 3.20 4.00 t
Graph/Plot the output step response from t=0 to t=10 with a 0.1-second interval.
For the system shown below, find the %OS if the input is T(t) and the output is 02(t) |N=25 =7 kg m-HD =3 N-m-s/rad Na =50 fh=15kg-m N3 25 D;=5 N-m-s/rad K=88 N-m/radr N4-100| D; = 4 N-m-s/rad ; = 8 ke-m0000 Select one: O a. %O.S 39.9 O b. %O.S=21.8 O c. %O.S 13.5 O d. %O.S =8.06 O e. %0.S= 46.7
1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally…
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 Use your knowledge of differentiation to sketch the velocity-time graph, clearly marking the critical points. Using the graph sketched in (a) above, estimate the velocity when t = 1.5 s Calculate the velocity of the function when t = 1.5 s by substituting to the velocity function. Compare this value to the value you estimated in b above.
7. What is the response to unit step function input when all initial conditions are zero. R + 2 S(S + 3) a) C(t) = 1 + 2e-t +e-2t b) C(t) = 1 – 2e-t + e2t c) C(t) = 1 – et + 2e-2t d) C(t) = 1 – 2e t + e-2t

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