Industrial Process Control 1

Tutorial Questions 2: Industrial Process Control 1. Determine the system stability by root value using s-plan for following transfer function, then explain why the system is stable or not. a. 2 𝐷(𝑠) = s2 +5s−8 12 b. 𝐷(𝑠) = 2s2 +4s+6 2. Determine the system stability by Routh method (use Routh table if necessary) for following function, then explain why the system is stable or not. 3 a. 𝐹(𝑠) = 3.5𝑠2 +0.25𝑠+2 8 b. 𝐹(𝑠) = 4𝑠2 +3𝑠−2 c. d. e. f. 7 𝐹(𝑠) = 3𝑠+2 4𝑠 3 + 4𝑠 2 + 2 = 0 2𝑠 3 + 4𝑠 2 + 3𝑠 + 2 = 0 3𝑠 3 + 2𝑠 2 + 3𝑠 + 8 = 0 3. From time response first order system a. Determine the gain K, time constant𝜏 and settling time 𝑡𝑠 b. Writer the differential equation, transfer function and time response i. 4𝑦̇ (𝑡) + 5𝑦(𝑡) = 10𝑢(𝑡) ii. 2𝑦̇ (𝑡) + 𝑦(𝑡) = 4𝑢(𝑡) iii. From the graph (1), find a and b 4. From time response second order system a. Determine 𝛼. 𝜔0 . 𝜁 𝑎𝑛𝑑 𝐾 b. What is the type of this system? c. Writer the differential equation, transfer function i. 3𝑦̈ (𝑡) + 3𝑦̇ (𝑡) + 5𝑦(𝑡) = 10𝑢(𝑡) ii. 12𝑦̈ (𝑡) + 6𝑦̇ (𝑡) + 15𝑦(𝑡) = 30𝑢(𝑡) 15 iii. 𝐺(𝑠) = 2 graph (1) 2𝑠 +3𝑠+8 iv. From the graph (2), find: Yss,Yp,M,td,tr,tp,Tp,fp and 𝜔𝑝 5. Examine controllability and observability of the system: 2 0 0  A , B   , C  1 0   2  3  3 6. What is the transfer function of P, I, D, PI, PD and PID? 7. What is the advantage anddis advantage of P, I, D, PI, PD and PID? graph (2)
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