Q3 (a) Consider the transfer function system below. Y(s) s2 + 4s + 6 U(s) s3 + 6s2 + 4s + 2 Obtain a state-space representation of this system showing all intermediate steps. Briefly describe the characteristics of signal flow diagrams, and explain how you convert the state equations of a system (for example, a system like in part (a)) into a signal flow diagram. (b) It is required to design a state-feedback controller for the system defined in part (a) with the desired closed-loop poles at: (c) s = -1+ 2j; s = -5 Determine the gain values of the state feedback vector for this design.

Q3) Let x[n] have 100 samples. We want to obtain a signal with length 150 from x[n]. Draw the block diagram of your system.

a) Using a NTC thermistor with "B=4000K, resistance: 5k2 at 25°C" we want to measure the temperature of an environment in the range 50°C - 100°C. Design a suitable circuit for this purpose with "zero" output signal |v) value at 25ºC. Express the output and its temperature-sensitivity in terms of temperature (y=f(T°C) and dy/dT= f(TºC)). Roughly draw y and dy/dT for the given temperature range. (Note: For NTC: RNTC=Roexp(B(1/T-1/To))

An eight bit Successive Approximation ADC has an analog input voltage of 6.84V. Describe the steps the circuit performs to generate an eight bit digital equivalent value if the DAC in the circuit has a reference voltage of 10V.