MMAN3200 Linear Systems and Control Lab 1: Lab Report Assessment Sheet Term 2, 2025

MMAN3200 Introduction 

Complete the questions below based on your own analysis and any measurements and observations undertaken during the Lab 1 session. Please consult the accompanying Background Information Sheetand Activity Sheetfor additional information. Note that only direct answers to the questions are required (with working out shown); no formal report or long written answers are needed. Typed work is strongly preferred; however, neat handwritten working with typed final answers is acceptable. Submit your report as a PDF file via Moodle. The marks allocated for each question are indicated in square brackets.

1.Modelling [5 marks] 

For this Modelling part, provide all answers using symbolic representation (no numerical substitutions). 

1. Using the law of motors and the law of generators, derive the two governing differential equations of the QUBE's electromechanical system. For this, you may lump all mechanical components into a single mass moment of inertia. Assume the drag in the motor can be modelled as a viscous friction coefficient 𝑏, which applies a torque proportional to shaft speed.
2. By combining the differential equations derived above, and assuming zero initial conditions, obtain the transfer function of the system relating the voltage 𝑣𝑚 (input) to the rotational displacement of the motor (output), i.e., 𝜃𝑚(?)/𝑉𝑚 (?).
3. Based on the transfer function obtained above, obtain another transfer function expressing instead the motor rotational speedas the output, i.e., Ω𝑚(?)/𝑉 𝑚 (?).
4. Simplify the two transfer functions above by assuming the inductance of the electrical circuit is negligible. What is the order of the two models after this simplification?