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 π·(π ) = s2 +5sβ8 12 b. π·(π ) = 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. πΉ(π ) = 3.5π 2 +0.25π +2 8 b. πΉ(π ) = 4π 2 +3π β2 c. d. e. f. 7 πΉ(π ) = 3π +2 4π  3 + 4π  2 + 2 = 0 2π  3 + 4π  2 + 3π  + 2 = 0 3π  3 + 2π  2 + 3π  + 8 = 0 3. From time response first order system a. Determine the gain K, time constantπ and settling time π‘π  b. Writer the differential equation, transfer function and time response i. 4π¦Μ (π‘) + 5π¦(π‘) = 10π’(π‘) ii. 2π¦Μ (π‘) + π¦(π‘) = 4π’(π‘) iii. From the graph (1), find a and b 4. From time response second order system a. Determine πΌ. π0 . π πππ πΎ b. What is the type of this system? c. Writer the differential equation, transfer function i. 3π¦Μ (π‘) + 3π¦Μ (π‘) + 5π¦(π‘) = 10π’(π‘) ii. 12π¦Μ (π‘) + 6π¦Μ (π‘) + 15π¦(π‘) = 30π’(π‘) 15 iii. πΊ(π ) = 2 graph (1) 2π  +3π +8 iv. From the graph (2), find: Yss,Yp,M,td,tr,tp,Tp,fp and ππ 5. Examine controllability and observability of the system: 2οΉ ο©0 ο©0 οΉ Aο½οͺ , B ο½ οͺ οΊ, C ο½ ο1 0ο οΊ ο«ο­ 2 ο­ 3ο» ο« 3ο» 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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