1. Given a system transfer function G(s) = 3s^3 + 2s^2 + s / s^6 + 4s^5+ 3s^4 + 2s^3 + s^2 + 2s + 6 Determine the steady state response of the system to an excitation: 8sin2t + 15sin3t 2. Construct root loci for (i) s^3 + s^2 + (K+2)s + 3K = 0 (ii) s^4 + 6s^3 + 9s^2 + K(s^2 + 4s + 5) = 0 (iii) s^3 + 5Ks^2 +10 = 0 (iv) s^5 + 2s^4 + 3s^3 +2s^2 + s + K = 0 3. Show that the system with rate feedback in Fig. P6.8a may be reduced to system shown in Fig. P6.8b 4. A linear control system is described by G(s) =10^4(s+1) / s^2 + 110s + 10s^3 (i) obtain Bode magnitude and phase plots (ii) calculate G(s) for w=50 and 1000 rad/s 5. Draw a generic block diagram of a closed loop controls system and describe each of the blocks. Document Preview:

Assignment: Control System Q 1. Q 2. Q 3. Q 4.Assignment: Control System Q 5. Q 6.Assignment: Control System Q 7. Q 8. Q 9.

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1. Give a way to multiply two complex numbers together using fewer than four integer multiplication operations.

2. How much storage would be used by the FFT' if we didn't circumvent the storage-management problem with the perfect shuffle?

 

 

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1. How does a profit-maximizing firm that is operating in a competitive labor market respond to an increase in the wage rate? A. The firm will demand less capital due to the substitution effect. B. The firm will demand more labor due to the substitution effect. C. The firm will produce less output due to the scale effect. D. The firm will demand more capital due to the scale effect. E. The firm will demand more labor due to the scale effect. 2. Labor demand is more elastic A. the greater is the supply elasticity of capital. B. the greater is the elasticity of substitution between labor and capital. C. the greater is the elasticity of demand for the firm’s output. D. the greater is labor’s share in total costs. 3. What is the most accurate description of the value of a worker to the firm? A. The wage. B. The firm’s total output when holding capital fixed. C. The firm’s average product when holding capital fixed. D. The dollar value of the worker’s output. E. The dollar value of the average worker’s output.

 

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1 Homework stifles the thrill of learning in the mind of the student. 2 It instills an oppressive learn-or-else discipline. 3 It quenches the desire for knowledge and the love of truth. For these reasons 4 homework should never be assigned. (Colman McCarthy, “Homework’s Tyranny Hobbles Promising Minds”)

 

 

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1. How would you modify the HRP exercise 1, algorithm to produce allocations that add up to 0, where

2. Can you think of an easy way to incorporate expected returns in the HRP allocations?

exercise 1

Given the PnL series on N investment strategies:

(a) Align them to the average frequency of their bets (e.g., weekly observations for strategies that trade on a weekly basis).

(b) Compute the covariance of their returns, V.

(c) Identify the hierarchical clusters among the N strategies.

(d) Plot the clustered correlation matrix of the N strategies.

 

 

 

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