Develop mathematical models for each propeller set to

Question

Brushless de (BLDC) motor based propulsion system for a container vessel model

Fig. 1 shows the model scaled vessel Hoorn with twin propellers and rudder (as used in Assignment 1). The propulsion system consists of two sets of a servo amplifier, brushless dc motor, shaft and propeller. Two sets have the same specifications. More information on Hoorn is given in Appendix 1.

Each propeller set of the propulsion system as shown in Fig. 2 consists of a servo amplifier (ESCON 50/5), an EC (electronically commutated or BLCD) motor (Maxon, 136208), a gear box (110499), an encoder (137959), and a propeller. See the attached datasheets for details of the servo amplifier, EC motor and encoder.

The control voltage u_c is assumed to be in the range of 0 to 10V. The servo amplifier can be used to change the motor direction, so that the drag is positive when the motor rotates clockwise and negative when the motor rotates counter-clockwise. It is assumed that the maximum drag force is 50N and the relationship between the propeller shaft speed (ω₂) and the drag force f_x is linear, the moment of inertia for the propeller is 100 gcm². The propeller speed (ω₂) is controlled by a proportional integral derivative (PID) controller with a transfer function of U_c(s)/E(s) = K_P + K_I/S +K_Ds where K_P, K_I and K_D are the control gains of which values are assumed to be 2, 5 and 2, respectively.

1. Develop mathematical models for each propeller set to relate the control voltage u_c and v_a, v_b and v_c (and/or i_a, i_b, i_c) of the field coil, u_c and motor shaft speeds (ω₁, ω₂), and then tic and the drag force f_x. Represent the mathematical models in appropriate forms (state space model, block diagram) for programming.

2. Make a simulation program (using MATLAB or MATLAB GUI) to simulate each propeller set. Basic requirements for the MATLAB simulation program are below:

• To allow user to enter the motor parameters;
• To visualise important variables;
• To reset the graphs when the system parameters change; and
• To collect simulated data for reporting.

Hints: Before simulating the entire propeller set, please simulate the motor without load to confirm physical properties of the motor are correct based on the datasheets.

3. Make a simulation program using Simulink/GUI to simulate each propeller set. Basic requirements for the Simulink simulation program are below:

• To allow user to enter the motor parameters;
• To visualise important variables;
• To reset the graphs when the system parameters change; and
• To collect data for reporting.

4. Combine two propeller sets and develop a mathematical model for the entire propulsion system, then represent the mathematical model in appropriate forms for programming. Make a simulation program for the entire propulsion system (also refer to the information given in Assignment 1).

Hints: For each simulated scenario, you should describe the working conditions and parameters.

5. Combine the steering and entire propulsion systems (with rudder, twin motor drives and twin propellers) and the ship hull's dynamics system in Assignment I, make simulation programs for the following scenarios: a) turning by rudder only, b) turning by propellers only, c) turning by rudder and propellers, d) 20-20 zigzag test with rudder only; e) 20-20 zigzag test with propellers only; and 20-20 zigzag test with rudder and propellers.

Assignment link -

https://www.dropbox.com/s/pewqshz7oylv26w/Assignment.rar?dl=0.