Chapter 5, Problem 6CP

Design a proportional derivitivecontroller for a plant orsystemthat satisfies the following specifications : 1. is steady-state error is less than 2 % for a ramp input.   2.) Damping ratio (zeta) is greater than 0.7have determined the   3. Once youvalue of kp and kd, then plotthe response of the compensated(with controller) and uncompensated( without the controller, only the plantsystem using MATLAB.

Example 2 The particle has a mass of 0.5 kg and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on the particle when 0 = 30°. The rod is rotating with a constant angular velocity 2 rad/s. Assume the particle contacts only one side of the slot at any instant. B =2 rad/s 0.5 m 0.5(9.81)N r F 30° N

A gas turbine cycle has two stages of compression, with an intercooler between the stages. Air enters the first stage at 100 kPa, 300 K. The pressure efficiency of 82%. Air exits the intercooler at 330 K. Calculate the temperature at the exit of each compressor stage and the total specific work required.

For problem 13, your answer should be the same as problem 12. Calculate the flow velocity and the heat transfer/area of the outer surfaces for both duct geometries to see the performance difference of the two designs.

One end of a thin uniform rod of mass m and length 31 rests against a smooth vertical wall. The other end of the rod is attached by a string of length 1 to a fixed point O which is located a distance 21 from the wall. A horizontal force of magnitude F₁ is applied to the lower end of the rod as shown. Assuming the rod and the string remain in the same vertical plane perpendicular to the wall, find the angle 0 between the rod and the wall at the position of static equilibrium. Notes: This quiz is going to walk you through a sequence of steps to do this. It won't give you the answers, but it will hopefully get you to see how to approach problems like this so that you have a working reference/template in the future. This is actually a modified version of a problem from the textbook (6.3). Note that in that problem, is not actually given. It has been introduced for convenience as we move through solving the problem, and should not show up in the final answer. DO NOT DO PROBLEM 6.3. It is…

v

13.64 The shaft shown in Sketch h transfers power between the two pulleys. The tension on the slack side (right pul- ley) is 30% of that on the tight side. The shaft rotates at 900 rpm and is supported uniformly by a radial ball bearing at points 0 and B. Select a pair of radial ball bear- ings with 99% reliability and 40,000 hr of life. Assume Eq. (13.83) can be used to account for lubricant clean- liness. All length dimensions are in millimeters. Ans. Cmin = 42,400 N.

A 4 inch wide, 12 inch tall cross section beam is subjected to an internal shear of 5.5 kips. What is the maximum transverse shear stress in the beam in psi if this bending is about the x axis?

A Brayton cycle produces 14 MW with an inlet state of 17°C, 100 kPa, and a compression ratio of 16:1. The heat added in the combustion is 960 kJ/kg. 0.7 MW of heat transferred from the turbine to the environment. What are the highest temperature and the mass flow rate of air? Assume cold air properties.