c) The electron concentration in a piece of Si maintained at 300K under equilibrium conditions is 105/cm³. What is the hole concentration?

5. Represent the following system in state-space form. Write A, B, C and D clearly in your answer. d³y d²y dt3 - +5y=2u dt²

3. Find the transfer function H(s) and frequency response H (w) of the following system whose differential equation is given by d¹y d³y +3. dy +5 dt4 dt3 dt - d²u du 4y = - 5 dt² dt

1. Consider a plant that you want to control. The input u(t) and output y(t) of the plant are related by y(t) = 7 u(t) + w(t) where w(t) is an additive disturbance at the output which is bounded by -0.5 w(t) ≤0.5 for all time t. You want to build a controller so that the output follows a constant reference signal r(t) = where -15 ≤≤ 15. You will consider both open-loop and closed-loop for this problem. a) Sketch the block diagram of the plant. b) Please build an open-loop controller that sets the output to 7, assuming the disturbance is ignored. Please show your controller both as an equation and a block diagram. c) Say that you use the open-loop controller in part b, but now the disturbance w(t) is present. What is the maximum possible magnitude of error in the output for the reference signal? Suppose you have designed a feedback control for the plant where the controller has the form u(t) = K(r(t) − y(t)). Here K is the gain constant of the controller that you will design. d) Please…

2. Suppose the Laplace transform of a causal signal x(t) is given by s² +2 X(s) = S³ + 1 Using the lookup tables for standard Laplace transforms and the Laplace transform properties, find the Laplace transforms of the following signals. You do not need to simplify the expressions. a) x₁(t) = e² x(t) + 38(t − 1) − (t − 2)² u(t − 2) b) x2(t) = x(2t - 1) + et u(t − 2)

Please explain in detail the steps to solve this. Thank you

6. Answer the following questions. Take help from ChatGPT to answer these questions (if you need). But write the answers briefly using your own words with no more than two sentences and make sure you check whether ChatGPT is giving you the appropriate answers in our context. a) What is the difference between a regulator and a servo system? Which is harder to build? b) What are the advantages and drawbacks of manual control systems over automatic ones? c) Does transfer exist for the non-linear systems? d) Explain the convolution property of the Laplace transform. e) What are the advantages of using state-space representation?

4. Find the differential equation of the following system whose transfer function is given by S+3 H(s) = s3 +3s+2

Preliminary Laboratory (Prelab) Work Complete the following tasks in the space provided below for the circuit shown in Figure 2. 1. Use voltage division to compute the phasor voltages VR and Vc assuming nominal values of R = 1000[2], C = 0.01[u], and a cosinusoidal time-domain source voltage signal given by equation 5 below. Voltage division must be used to receive any credit. (10 points) equation (5) Vs(t) = VRMSCOS(ct + 0) = 5cos(@t + 0) = 5cos(62832t + 0) = 5cos(62832t) [V] =VRMSCOS(2лft + 0) = 5cos[2л(10000)t + 0] = 5cos[2л(10000)t] [V] 2. Compute the phasor current, Is. (3 points) 3. Calculate the complex power, S, active power, P, and reactive power, Q, for the circuit. (4 points) 4. Construct the phasor diagram for the circuit, and show mathematically that the phasor (vector) sum of the phasor voltages VR and Vc is equal to Vs. (3 points) Agilent 33210A (BECC4242) or Vs Keysight 33500B (BECC4261) Function Generators Is R w + VR Vc + + Zc V out =Vc Figure 2: RC circuit connected…