Mechatronics Modelling and Control

Assessed Matlab Practical 3 – Control of robotic arm Aim: To control the pitch attitude of a robotic arm.

To turn the robotic arm, a servo actuator motor is used to apply Torque, T that will rotate the robotic arm.

The angular position of the robotic arm is govern by the.

T ??J

d2?

dt2

??B d?

dt

Where ??is the robotic arm angular positon, J is the moment of inertia of the robotic arm and B is the coefficient of damping primarily due to friction in the gears. T is the torque applied to move the robotic arm.

1. Show that if the output is angular velocity (?). The equation that models the movement of the antenna is a first order differential equation. What is the gain, Ka and time constant Ta? Hence write down the Transfer Function, ?(s)/T(s).

2. Enter the transfer function ?(s)/T(s) into Matlab and use the LTIview facility to plot a time response of the robotic arm when a constant torque (T = 10Nm) is applied assuming angular velocity, ? as the output in deg/s. What is the steady state velocity? What is the 95% settling time?

30%

3. The robotic arm is controlled via a motor which adjust the Torque as the robotic arm turns to a desired angle.

A 0-10v volts control signal is used to drive the motor and turn the robotic arm between angles of 0 to 90°. The diagram bellow shows the transfer function of the motor and the robotic arm.

Hence determine the value of the encoder gain Kc, if the input voltage range from 0 to 10V correspond to the output angles ranging from 0 to 90°. Use block manipulation and LTI viewer to measure the percentage overshoot and tmax of the control loop assuming a step input u of 5V.

What is the position of the robotic arm assuming this step input?

Hence determine the value of the encoder gain Kc, if the input voltage range from 0 to 10V correspond to th

20%

4. Hence determine the undamped natural frequency and damping constant for a 5V input.

5. Determine the closed loop transfer function of the robotic arm motor control loop.

40%

J = 0.314 N.m.s^2/deg

B = 0.039 N.m.s/deg

Kt = 0.343 N.m/A

Kv = 0.035 V.s/deg

Question 1

Value for Ka =

Value for Ta =

Question 2

- ?ss = deg/s

- t95% = /sec

Question 3

Kc =

tmax = /sec

??????????deg

% overshoot =

Question 4

K =

?n

Undamped natural frequency =

Question 5

S2 S1 S0

Num coeff

Deno coeff

Conclusion

Which of the following statements are true or false?

1. Increasing the rate gyro gain can remove overshoot from the system.

2. Increasing the encoder gain can decrease the position range of the robotic arm.

3. Induction motor is suitable for controlling the position of the robotic arm.

4. Increasing the signal voltage decreases the angular velocity of the robotic arm

5. Increasing the torque gain can increase the overshoot.

Assessed Matlab Practical 3 – Control of robotic arm Aim: To control the pitch attitude of a robotic arm.

To turn the robotic arm, a servo actuator motor is used to apply Torque, T that will rotate the robotic arm.

The angular position of the robotic arm is govern by the.

T ??J

d2?

dt2

??B d?

dt

Where ??is the robotic arm angular positon, J is the moment of inertia of the robotic arm and B is the coefficient of damping primarily due to friction in the gears. T is the torque applied to move the robotic arm.

1. Show that if the output is angular velocity (?). The equation that models the movement of the antenna is a first order differential equation. What is the gain, Ka and time constant Ta? Hence write down the Transfer Function, ?(s)/T(s).

2. Enter the transfer function ?(s)/T(s) into Matlab and use the LTIview facility to plot a time response of the robotic arm when a constant torque (T = 10Nm) is applied assuming angular velocity, ? as the output in deg/s. What is the steady state velocity? What is the 95% settling time?

30%

3. The robotic arm is controlled via a motor which adjust the Torque as the robotic arm turns to a desired angle.

A 0-10v volts control signal is used to drive the motor and turn the robotic arm between angles of 0 to 90°. The diagram bellow shows the transfer function of the motor and the robotic arm.

Hence determine the value of the encoder gain Kc, if the input voltage range from 0 to 10V correspond to the output angles ranging from 0 to 90°. Use block manipulation and LTI viewer to measure the percentage overshoot and tmax of the control loop assuming a step input u of 5V.

What is the position of the robotic arm assuming this step input?

Hence determine the value of the encoder gain Kc, if the input voltage range from 0 to 10V correspond to th

20%

4. Hence determine the undamped natural frequency and damping constant for a 5V input.

5. Determine the closed loop transfer function of the robotic arm motor control loop.

40%

J = 0.314 N.m.s^2/deg

B = 0.039 N.m.s/deg

Kt = 0.343 N.m/A

Kv = 0.035 V.s/deg

Question 1

Value for Ka =

Value for Ta =

Question 2

- ?ss = deg/s

- t95% = /sec

Question 3

Kc =

tmax = /sec

??????????deg

% overshoot =

Question 4

K =

?n

Undamped natural frequency =

Question 5

S2 S1 S0

Num coeff

Deno coeff

Conclusion

Which of the following statements are true or false?

1. Increasing the rate gyro gain can remove overshoot from the system.

2. Increasing the encoder gain can decrease the position range of the robotic arm.

3. Induction motor is suitable for controlling the position of the robotic arm.

4. Increasing the signal voltage decreases the angular velocity of the robotic arm

5. Increasing the torque gain can increase the overshoot.

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