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1. Consider the LQR minimization problem
J = ∫o∞ (mx2(t)+u2(t))dt; m>o
and constraint:
x.(t) = ax(t)+µ(t); y(t) = x(t)
a. Is the system controllable? Observable?
b. Find the optimal state feedback. Solve the ARE for two possible solutions. Which is the positive definite solution?
c. Verify that selecting the positive definite solution of ARE in (ii) gives a stable response by analyzing the optimal closed-loop g coefficient for optimal state equation x*(t) = gx*(t).
d. Explain how the time constant of the optimal closed-loop system varies with parameter m. In your answer concentrate on the speed with which the state x(t) decays to zero starting from some arbitrary initial condition x(0) = xo (e.g. the time constant of the response) and on the peak value of the optimal control signal u(t) i.e. maxt≥o |u(t)|.
e. Compare the two parameters (time constant and the maxt≥0 |u(t)| in relation to the real physical limitation on the maximum magnitude of the optimal control.
A shunt regulator utilizing a zener diode is biased on through a 100 resistor. Determine the change in the regulated output voltage for the two situations below: a) VI changes +2.0 V, ILoad constant b) ILoad changes +100 mA, VI constan..
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Eble Company proposes to invest $6 million in a new type of text printing equipment. The fixed costs are $1 million per year. The equipment is expected to last for 5 years. The manufacturing costs per hammer is $1. Calculate the break-even volume ..
A student designs a zener shunt regulator to produce a regulatedoutput of 10 V using a zener diode specified to have a 10V drop ata test current of 25mA. Incremental resistance of the zener is 10ohm and minimum diode current =2mA.
Design a passive RC low pass filter with a cutoff frequency of 100Hz using a 4.7 uF capacitor. a) draw a schematic showing your filter while designating all component values and labeling the input and output voltage
A certain engine lathe can be purchased for $330,000 and depreciated over three years to a zero salvage value with the SL method. This machine will produce metal parts that will generate revenues of $220,000 (time zero dollars) per year.
At oneparticular quiescent operating point, a BJT produces a 300 mAchange in collector current for a 0.1 volt change in thebase-emitter voltage. What is gm for thistransistor in millisiemens
A current I = 20
(1) If the frequency was changed, what would happen to the current in a circuit Explain increase or decrease. (2) If you have R = 2 K ohm, Xc = 3 K ohm, XI = 4 K ohm . Find the G, Bc, BI, Yt anf Zt.
A slotted line is used to measure the voltage maximums and voltage minimums on a transmission line with a characteristic impedance of 50 . The voltage maximum is measured as 7.5 V and the minimum is 5 V. The line is terminated with a purely resist..
The RS-232 serial port on a personal computer is transmitting 2400-bit/sec data using a polar NRZ line code that has a peak value of 12 V. Assume that binary 1's and 0's are equally likely to occur.
A small gasoline engine can put out 18,000 N-m/min of mechanical power. The engine is used to drive an electrical generator that is 80 percent efficient. 1 N-m = 2.78 X 10-4 W-h. Find the output of the generator in Watts.
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