Feedback control: Final exam project

This project will address the dynamic system and control analysis of the system proposed as "86. Automatic Weighing". The system is shown below, and the original description of the problem as proposed is attached to this document.

The requirements for this ME 344 project are as follows:

1. The system is to be built to measure rapidly varying forces, applied as shown, inferred from the position of the counterpoise, xc. Assume a sensor (not shown) will measure this distance relative to the knife edge. Because we want to understand which features in this concept may limit dynamic performance, we need to consider any physical effects that might be important and include them in the modeling and analysis. The system as conceived incorporates a feedback effect, and this needs to be recognized.

2. Only positive forces (downward) are to be considered.

3. The final model formulation should take the form of a feedback control diagram. All elements (transfer functions) of that system description need to be fully specified (as discussed during class), and your formulation should explain any assumptions made along the way.

4. The system should be evaluated by simulating the model for different types of varying forces for a range of 50 N. You will be asked below to run specific step and sinusoidal type forces with different parameters.

5. The following system parameters should be used, and those with a '?' should be determined as part of your study.

• L_b = 18 inches = length from force applied to pin A
• Beam is aluminum, 1/2 inch thick, 2 inches wide
• B_b = rotational pivot damping; tune with values from 1 to 10 Nmsec/rad to reduce oscillations (will change plant model)
• L_m = 1 inch = distance to motor CG from knife edge
• L_f = 2 inch = distance to force application point
• For PMDC (Maxon RE040): r_m = 0.032 Nm/A, R_m = 0.316?, J_m = 1.34 × 10^-5 kgm², B_m = 5.36 × 10^-6 Nmsec/rad; mass, mm = 0.48 kg (see last page of document)
• For damping on counterpoise, use b_c = 0.01 Nsec/m, but adjust as needed
• Strain-gauge leaf spring stiffness, k_b = 6250 N/m (this stiffness was chosen by determining the stiffness needed with 1 mm of deflection that would balance a 50 N applied load)
• The bridge/amplifier gain, H_b =? (this is a constant) volts/m
• m_c =? = mass of counterpoise, kg
• b_c = damping of counterpoise motion (use small value)
• GR =? = ball-screw gear ratio (think of this as how far will the counterpoise travel each revolution of shaft rotating)

What should you submit for evaluation? First and foremost, you should not present any numerical values in your submitted answers. All results should be in terms of defined system parameters.

1. Narrative to explain all the elements that follow either neatly written by hand or typeset (Word or LaTeX). Figures should be neatly sketched and labeled clearly.

2. A complete and annotated bond graph as described in class (full causality, states identified, etc.).

3. A full explanation of how the model you present can be described as a closed-loop feedback control system. In class, we described the controlled-variable as δ_b, the deflection of the strain-gauge beam, with the reference input a control reference voltage, vr, which would be zero to control δ_b at zero. You should prove to yourself this is valid.

4. A derivation of all the key transfer functions for your feedback control system model. This should be neatly written or typeset.

5. A derivation of the closed-loop transfer function (CLTF). If you use δ_b as controlled variable, you should derive δ_b/T_d, where T_d is the total disturbance torque. You should explain this as part of your model above.

6. Use your CLTF to finalize the design, which means determining the unknown parameter values. These values should be chosen such that the controlled response δ_b satisfies the requirements below. You can also solve for the response of T_c using the transfer function T_c/e_v, since you can find e_v = H_bδ_b (see hint2). Then your system measures force by F_c = T_c/L_f (you could also plot x_c = T_c/(m_cg) if you wanted to see how much the mass moves.

Please do as much as you can.

Attachment:- Assignment File.rar