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**Q1:**Q.3 A process consists of two stirred tanks with input Q and outputs T1 and T2 (see Figure).See Answer**Q2:**Q.4 An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t=0, the set point is increased at the rate of 0.5 mA/min. If the current settings are K₂= 2, t=1.5 min, Tp=0.5 min. (a) Generate the controller response in Simulink. (b) Repeat part (a) for a PI controllerSee Answer**Q3:**A control system has the following transfer functions: Gc = Kc, GvGp = 1/(s+1) (0.5s+1)2See Answer**Q4:**Question 5 Determine the controller gain (Kc) for a proportional-only feedback controller for the system comprising the following elements that ensures a gain margin of at least 2 and a phase margin of at least 30°. Plot the controlled and uncontrolled closed-loop response of the system to a unit-step change in set- point. Gc= Kc; Gp = 50 30s +1' G₂ = 0.016 3s +1' Gm = 1 10s + 1See Answer**Q5:**Consider a weight held in place by a spring. Initially suspended at rest, the height ofThe spring constant is kThis represents how "stiff" the spring is and is constant. The frictional losses areisthe weight is x=0The mass of the weight ismcharacterized by the constant b . The force applied to the weight after t=0 f(t) . This leads to the ODE m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=f(t) 2. (65 points) Imagine the spring is vertical. The weight is held by a platform atx=0 initially. If m=0.1kg , b=0.1 kg/ s , and k=1.0 kg/s . The platformis removed at t=0 O What are the initial conditions for this system? b. (15 points) What is the new steady-state position? That is, where willt - o ? Show this using the final-value theorem.the mass settle as c. (15 points) What is the maximum distance the mass will move from itsinitial position? (Hint: what is the force applied to the weight?)(15 peints) Whatvalue vwill recuultming d. (15 points) What spring constant value will result in the system comingto (and remaining within) 1% of its new steady-state position withoutovershooting that value as quickly as possible? e. (15 points) Imagine the spring system is now horizontal.represents how far the spring is from its resting position. If 1 N of forceis instantaneously transferred to the weight (in thedirection)described above att=0 ,what is the response? That is, what isx(t) when the weight is flicked with 1 N of force? Assume the weightis only free to move in one direction.See Answer

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