1. Using Hebbian-type of learning rule to obtain a Hopfield network which can memorise the following two patterns: [1 -1 -1 1 -1 1], [1 -1 1 -1 -1 1] a)

5.) A force of 500 N is required to open a process control valve. What area of diaphragm will be needed with a diaphragm actuator to open the valve with a control gauge pressure of 70 kPa? (20 pts)

2.) Consider a Pt resistance sensor that requires long leads to operate. To compensate for the changes in the resistance of long leads, the sensor can be connected to a Wheatstone bridge (as R1, see picture) using long leads (1,2,3) of same dimensions and material. They will all be subject to the same change in resistance (AR) due to temperature. If we consider lead #1 in series with R3 and lead #3 in series with R1, for R1 = R3 (and hence R2 = R4),starting from the general Wheatstone bridge output expression: \mathbf{V}_{\bullet}=\mathbf{V}_{\mathbf{A B}}-\mathbf{V}_{\mathbf{A D}}=\mathbf{V}_{\mathbf{2}}\left(\frac{\mathbf{R}_{\mathbf{1}}}{\mathbf{R}_{\mathbf{1}}+\mathbf{R}_{\mathbf{2}}}-\frac{\mathbf{R}_{\mathbf{3}}}{\mathbf{R}_{\mathbf{3}}+\mathbf{R}_{\mathbf{4}}}\right) show that the Wheatstone bridge cancels the effects of temperature on the long leads. In other words, show that V. = 0 when temperature varies and affects the resistance of the long leads.

3.) A diaphragm pressure gauge employs four strain gauges to monitor the displacement of the diaphragm. The four active gauges form the arms of a Wheatstone bridge, in the way shown in Fig. 3.23 b (see class notes too). The gauges have a gauge factor of 2.1 and resistance 120 Q. A differential pressure applied to the diaphragm results in two of the gauges on one side of the diaphragm being subject to a tensile strain of 1.0 x 10^-5 and the two on the other side a compressive strain of 1.0 x 10^-5 . The supply voltage for the bridge is 10 V. What will be the voltage output from the bridge? (20 pts) (Answer is 0.21 mV, but you need to show the work to get to this.)

A 220 V, three-phase, 6-pole, 60 Hz induction motor is running at a slip of 2.5%, and delivers5 kW to its load. The rotational losses are 500 W. Find O The speed of rotation magnetic field produced by the stator in rps; The speed of rotation magnetic field produced by the rotor in rps; The frequency of the voltage induced in the rotor; The slip speed in rps; The mechanical speed of the rotor in rpm; The load torque; 2) The converted power; The airgap power; ) The induced torque; The rotor copper losses.

2. This is a 3 DOF planar robot with 3 rotational joints. Derive the transformation matrix between the end-effector and the base of the robot coordinate systems. Assume the y and z axes orientations at every joint (y axis is given) and draw your assumptions in the free body diagram. Your assumptions will vary from your fellow students, if there is an intentional match both parties will receive zero marks! (a) DH (b) Three-link, nonplanar manipulator.

7.) A small permanent magnet motor has a torque constant kr=0.1 Nm/A and a back e.m.f.constant ke-2.50 V/krpm. The total internal resistance is R=15 2. Determine the torque for maximum power and the maximum rotational speed if the applied voltage is V=5V. (25pts)

In El 02.04, which of the follow is the time constant? \text { a. } \frac{R_{1}}{L}+\frac{R_{2}}{L} \text { b. } \frac{L}{R_{1}}+\frac{L}{R_{2}} \text { c. } \frac{1}{R_{1}}+\frac{1}{R_{2}} \text { d. } \frac{L R_{2}}{R_{1}}+\frac{L R_{1}}{R_{2}}

3. Consider frames {0}, {1} and {2} shown below. Assume that no rotation is allowed around Y axis and the maximum angle each axis can rotate at each time is 90 degrees. a. Find the homogeneous transformation matrices ⓇH, and¹H₂. b. Find H, using the relationship: "H₂="H,¹H₂. Z₁4 1m 1m Z₁ Z₂ Assume positive or negative rotations about the axes. You must write the transformation equations.

A 208V Y-connected synchronous motor is drawing 50 A at unity power factor from a 208Vpower system. The field current flowing under these conditions is 2.7 A. Its synchronous reactance is 1.6 N. Assume a linear open-circuit characteristic. Find V, and E, for these conditions.'A Find the torque angle ð. What is the static stability power limit under these conditions? O How much field current would be required to make the motor operate at 0.80 PF leading? What is the new torque angle in part (d)?

4. As shown in the following figure, it is an ABB IRB140 industrial robot. It has six DOF and all the major dimensions are given. The last three axes intersect with each other and have the common origin located at the centre of axis 5. Please derive the transformation matrix between the end-effector (6) and the base of the robot coordinates systems {0} using the homogenous transformation method. Assume the axes orientations at every joint and draw your assumptions in the free body diagram. Your assumptions will vary from your fellow students, if there is an intentional match both parties will receive zero marks! The link lengths are given in the diagram. You may use MATLAB for matrix multiplications. 670 Te 70 380 65 810 486 1092 712 352 151