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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.
1.Write a single line Verilog statement that declares a 12-bit by16-word memory called mem1. 2. Write a single line Verilog statement that assigns the fifth word of mem1 the decimal value 127 on the positive edge of the signal clock.
A Thevenin equivalent can also be determined from measurements made at the pair of terminals of interest. Assume the following measurements were made at the two external terminals a, b of a circuit.
Design a filter that satisfies the following requirements: 1 input is a current source ranging from 4 mA to 20 mA with a source resistance of 10 ohms. 2 THe filter must output a voltage ranging from 2v to 10 v.
trace how the electrons and holes move through the device under the two different biasing conditions. Explain how these three devices work in terms of holes and electrons.
Drift velocity the actual (physical) velocity of electrons along the wire. Transmission velocity the rate at which information can be transmitted electronically using conducing wires. How is it possible that the transmission velocity is so much faste..
Identify the type of cable that is permitted in single- and multifamily dwelling units but that cannot be used underground, nor in buildings that are more than three stories above grade, nor in commercial garages, motion picture studios, theaters,..
The core is made of cast steel. Find the MMF required to get an air gap flux of 60,000 lines. The cross sectional area of the center section and air gaps is 4 in^2. The remaining sections have a cross sectional of 6 in^2.
What is the smallest number of samples that could be collected in order to know for sure whether or not the 1000Hz component is present? Assume you are using a Rectangular window.
The data rate of a continuous-phase FSK modulated signal is 100 kbps. What is the minimum frequency separation that can maintain orthogonality between the two tones (sinusoidal carriers)
A simple voltmeter with a full-scale reading of 50(V) is required. Use a d'Arsonval movement with a rating of 20(mV) at 1 (mA). Calculate the value of the voltmeter resistor, Rv, required to achieve these design specifications.
Given N-type silicon sample with uniform donor doping of (a) Nd= 1018/cm3 , (b) Nd= 1019/ cm3 and (c) Nd= 106/cm3, calculate the Fermi levels at room temperature assuming full ionization for all cases.
1- Use the half-reaction method to balance the equation Ca(s) +Cl2(g) --> CaCl2(s). 2-A sample of sodium chloride, NaCl, weighing 0.0678 g is placed in a 25.0-mL volumetric flask. Enough water is added to dissolve the NaCl, and then the flask is ..
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