Question

Simulink problems 

System of ODES 

Solve the system of ODEs with a suitable Simulink system. Graphically compare the Simulink solutions with the exact solutions (symbolic solution). 

y'₁ (t) = -3y₁(t) – 2y₂(t), y₁(0) = 1, 

y'₂ (t) = 4y₁(t) + 2y₂(t), y₂(0) = 1. 

Upload your Simulink model and MATLAB code with graphical output (LiveScript exported to PDF).

Answer 1

In this question, we need to solve the following ODEs with Simulink model. The ODEs are y',(t) = -3yı(t) – 2yz(t), y:(0) = 1, y'z(t) = 4y, (t) + 2y2(0), yz(0) = 1. The corresponding Simulink model is shown below

the initial condition of each integration block is considered as 1 (as per the question).

The simulink block is shown below

File Edit View Display Diagram Simulation Analysis Code Tools Help Normal untitled 2 untitled 0† 2 \dot{y1}t) y1(t) y1(t) Integrator with initial condition = 1 Gain < 3 Gain 1 Gain2 Gain3 \dot{y}(t) doty20 » 1 y2(t) y2(t) Integrator 1 with initial condition = 1 120 Ready 100% ode45^

The corresponding outputs are shown below

0.5 1. -0.5 -1.5 10 Time offset: 0

at 0 10 Time offset: 0