MODELLING AND SIMULATION OF MARINE SYSTEMS ASSIGNMENT -

LEARNING OUTCOMES -

1. Apply engineering principles in theoretical modelling of marine systems.

2. Apply simulation techniques, including numerical methods and block diagrams, in development of computer simulation programs for marine systems.

3. Develop MATLAB programming skills for simulation of marine systems.

4. Develop Simulink programming skills for simulation of marine systems.

5. Use computer simulation programs to learn behaviour and characteristics of the simulated marine systems under varying conditions.

TASK - SIMULINK PROGRAMMING AND DYNAMIC SIMULATION ASSIGNMENT

Description - In this assignment you need to develop mathematical models, block diagrams and to make Simulink simulation program/s for dynamic systems (see the attached sheets). The main tasks are to:

1. Apply engineering principles to derive mathematical models for dynamic systems with relevant assumptions and represent the mathematical models in appropriate forms for programming with Simulink;

2. Write codes of function/s and script files for the dynamic systems using Simulink;

3. Run the simulation programs under various conditions;

4. Visualise simulated results;

5. Evaluate the simulation programs; and

6. Write an individual short report to present solutions and simulated results.

Task Length - Sufficient to describe dynamics of the systems, working conditions, simulated scenarios and simulated results with selection of appropriate numerical integration methods.

Problems for Simulink Programming Assignment -

Problem 1 - Motor Control Systems

The parameter values for a certain armature-controlled motor are

• Motor constant and back-emf constant K_I = K_b = 0.2 Nm/A
• Damping coefficient b = 2.25x10^-4 Nms/rad
• Armature resistance R_a = 1.15 ?
• Armature inductance L_a = 4.25x10^-3 H
• Moment of inertia of rotor J = 5.5x10^-4 kgm2

where b and J include the effect of the load. The load torque is zero

(1) Develop equation/s to relate the motor speed and armature voltage v_a (of which maximum value is 48 V). Write a transfer function ?(s)/Va(s) and state space model.

(2) Use Simulink to obtain a plot of the step response of the motor torque and speed if the applied voltage is v_a = 10 V. Determine the peak value of the motor torque.

(3) Now suppose that the motor torque is limited to one-half the peak value found in part (2). Use Simulink to obtain a plot of the step response of the motor torque and speed if the applied voltage is v_a = 10 V.

(4) The motor speed is controlled by a PID controller G_c(s), i.e. G_c(s) = K_P + K_I/s + K_Ds, as arranged in Figure 1, make a Simulink model to simulate the closed-loop system. Plot the motor speed (and desired speed), armature current and motor torque versus time. You will need to select appropriate values of control gains K_P, K_I and K_D. K_a is the gain of the servo amplifier, is assumed to be 4.8. Notes: Use K_P as you number in the list.

(5) The motor position (in the range of 0 to 360 degrees) is controlled by a PID controller, i.e. G_c(s) = K_P + K_I/s + K_Ds, as arranged in Figure 2, make a Simulink model (by modifying the Simulink model in (4)) to simulate the closed-loop position control. Plot the motor shalf position, amarture current, and motor torque versus time. You will need to select appropriate values of control gains KP, KI and KD. Ka can be the same with that in (4). Notes: Use KP as y ou number in the list.

Problem 2: Pressure process system

Figures 3 and 4 show a picture and schematic diagram of a multivariable process system, including two processes level and pressure. The pressure process system for this assignment includes a storage tank with an inlet pipe, drain pipe, pump to circulate/feed water acting as an actuator, controller (PC) and signal conditioning unit. The storage tank has an inner diameter of 18cm.

Figure 4 Schematic diagram of Delorenzo pressure process system (via the level process system) using the pump as an actuator (abbreviations: PT = pressure transmitter, PC = Pressure controller):

The variables and their ranges are below:

• u₁ input voltage of the pump, 0V to 10 V;
• h is the level of the liquid in the tank in the range of 0 to 10cm;
• H_max is the maximum height of the tank, H_max = 15cm;
• q_in inlet flowrate, 0 litre/hour to 300 litre/hour;
• q_out the outlet flowrate through the drain valve which has a valve constant K_v = 0.0025 m²/s; it is assumed that q_out = K_vh where h is the level [m]; and
• P is the process pressure (the pressure of the compressed air), in the range of 0 to 2.5 bars (0 to 250 kPa).

Notes: The air valve is closed when the lelve is zero cm, and pressure P is zero (bar).

1. Develop equations to relate the pump input voltage u₁ and the level h(t); and the develop equation to relate the pressure and the pump input voltage u₁. Represent the equations in appropriate form for programming.

2. Make Simulink simulation programs to simulate the system with different simulated scenarios to examine the relationship between the pump input voltage and pressure and level (Hints: consider different values of K_v, and different values of pump input voltage).

3. If the pressure process system is controlled by a PID controller with the transfer fundction of G_c(s) = K_P + K_I/s + K_Ds as shown in Figure 5 (P_d is the desired pressure, P is the process pressure/process variable). Suggest a set of control gains as K_P = your number in the list, K_I = 2.5, and K_D = 4, then make simulation program to examine whether the procces pressure will be maintained as desired.

Attachment:- Assignemnt File.rar