Exercise on Simulink Modeling & Stateflow

Que. 1

AIM: To develop a PID Controller for a Second Order Differential Equation along with individual gain blocks for P-I-D.

OBJECTIVES :

• To develop a model using both PID Library block and also using individual gain blocks for P-I-D.

CONDITIONS :

• Transfer Function is `20/(s^2 + 10s + 20) ` where Kp = 300, Ki = 350 & Kd = 10.

SIMULINK MODEL :

BLOCKS USED :

• Signal Generator
• Sum
• PID Controller
• Transfer Fcn
• Display
• Scope
• Gain
• Integrator
• Add

EXPLANATION :

• Before starting we first sorted out all the required blocks.
• Here we have two models one is using a PID controller and the other one is using a gain block.
• In PID Controlled Model, we have a Signal Generator whose waveform is of square type and connected to the PID controller using a Sum block and further to a Transfer Function. Here PID values are given to us.
• Through this, the function is processed and gives us the desired output.
• In Gain Block Model, we used a Signal Generator of the same square type. This block is connected with three different individual blocks represented as Kp, Ki & Kd.
• As these values are already given to us, so we connected them to a sum block. Here Ki is Integrated before connecting to a Sum block whereas Kd, goes on further to perform its integrator using a filter coefficient to get the accurate variables at the end.
• Finally, these three individual blocks are connected to a sum block which further passes the signal to a Transfer Function and we get the desired result.

RESULTS :

Model using both PID Library block & individual Gain blocks for P-I-D.

1. Scope: Model using PID Controller

2. Scope: Model using Gain Block

CONCLUSION :

As a result, we constructed a Simulink model for P-I-D using both the PID Library block and individual Gain blocks. We have an equivalent output for both, which is shown using the appropriate Display blocks.

Que. 2

AIM: To create a Simulink model for a Mass-Damper System which is governed by a second-order differential equation.

OBJECTIVES :

• To make a responsive system for a Mass-Damper System.

EQUATION :

`x¨(t) = 1/m [ f(t) - cx˙(t) - kx(t)]`

where,
x¨	Acceleration of the Mass (m)
x˙	Frequency
x	Displacement
f(t)	Forcing Function
c	Damping Coefficient
k	Spring Constant

SIMULINK MODEL :

BLOCKS USED :

• Signal Generator
• Sum
• Gain
• Integrator
• Display
• Scope

EXPLANATION :

• First, we sorted out all the required blocks.
• Here we have used a Signal Generator block as a function with a Sine waveform which is connected to a sum block that leads to a second-order differential equation.
• The Damping Coefficient 'c' with x' gives the cx' is added along with the spring constant k as kx and connected further to the sum block.
• Later we derived the values of c, k and m using the command window in MATLAB.
• Once it takes the values then it follows the Integrator process to give the desired results which are shown in the Display Block along with its Scope.

RESULTS :

Specified Value: Workspace

Scope: Displacement for a Sine Waveform

CONCLUSION :

As a result, we developed a responsive Mass Damper System for a Second-Order System that reflects the specified equation using the workspace values.

Que. 3

AIM: To create a Simulink model for a Traffic Signal Control Logic using Stateflow charts.

OBJECTIVES :

• To make use of the Stateflow chart to perform a traffic signal operation.

CONDITIONS :

1. RED light is the default entry state (Entry value at RED state is 1 & Exit Value is 0).
2. YELLOW light becomes active after 5 seconds (Entry value at YELLOW state is 1 & Exit Value is 0.
3. GREEN light becomes active after 2 seconds (Entry value at GREEN state is 1 & Exit Value is 0).
4. Signal Exits GREEN state to RED state after 5 seconds.

SIMULINK MODEL :

STATEFLOW CHART :

BLOCKS USED :

• Chart
• State
• Transition
• Constant
• Displays
• Lamps

INPUT & OUTPUT PORTS:

EXPLANATION :

• First, we sorted out all the required blocks that we will use. They are mentioned above.
• Using the Stateflow chart, we first gave its power supply to function as per the requirement.
• If the power is ON then it will show Red Light as its default entry state.
• After 5 seconds it will turn ON the Yellow Lamp and again after 2 seconds it will turn ON the Green Lamp.
• Once the operation is done, the Signal Exits the GREEN state and moves to the RED state after 5 seconds. This operation will keep on happening based on the stop time.
• Later we define the input and output ports using the symbols pane.
• In Simulink, we gave an input value to the power supply and Display at the Output along with their respective lamps. These will be ON/OFF based on the input conditions.

RESULTS :

CONDITION 1: RED light is the default entry state (Entry value at RED state is 1 & Exit Value is 0).

CONDITION 2: YELLOW light becomes active after 5 seconds (Entry value at YELLOW state is 1 & Exit Value is 0).

CONDITION 3: GREEN light becomes active after 2 seconds (Entry value at GREEN state is 1 & Exit Value is 0).

CONDITION 4: Signal Exits GREEN state to RED state after 5 seconds.

CONCLUSION :

As a result, we constructed a Simulink model for a Traffic Signal that uses the Stateflow chart to switch the lamps ON and OFF based on the given conditions.