Gp4_Chapter 7

# Gp4_Chapter 7 - EE2010 Systems and Control(Chapter 7 Open...

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EE2010 Systems and Control (Chapter 7) 7-1 An open-loop control system utilizes an actuating device to control the process directly without using feedback/device Consider the following transfer function of a motor, Open Loop and Closed Loop Control Actuator Desired output response Output Process ) ( t v in ) ( t v b Js K s V s V s G in ) ( ) ( ) ( K : constant; b : frictional constant; J : motor shaft inertia; v ( t ) = ( t ): angular velocity; v in ( t ): input voltage Motor Open Loop Control

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EE2010 Systems and Control (Chapter 7) 7-2 How can these values be different? Different values of K , J and b gives rise to different velocity profiles, v ( t ) 0 5 10 15 5 10 15 20 25 Step Response Time (sec) Angular Velocity K = 50, J = 5, b = 5 K = 40, J = 5, b = 2 K = 50, J = 5, b = 2 b Js K s V s V s G in ) ( ) ( ) ( How do we control the velocity of the motor? How can we keep the shaft rotating steadily at a certain velocity? 300 rpm? 500 rpm? 1000 rpm? What are the difficulties with keeping the angular velocity constant?
EE2010 Systems and Control (Chapter 7) 7-3 How do we know what voltage to input into the motor to get a velocity of 300 rpm? 500 rpm? 1000 rpm? What happens if the load at the end of the shaft changes? After some time of operation, the bearings in the motor wears out and friction increases, what happens then? Open loop motor Motor ) ( t v in ) ( t v b Js K s V s V s G in ) ( ) ( ) (

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EE2010 Systems and Control (Chapter 7) 7-4 Suppose the transfer function, Then, the steady state gain is G (0) = K / b . If desired speed, v ( t ) = 300 rpm, what should v in ( t ) be? If all parameters are known precisely with K = 50, J = 5 and b = 2. Then if v in ( t ) = 12 V, the steady state motor speed will be 300 rpm, since steady state output = steady state gain × input = 25 × 12 = 300 rpm However, if b is not known precisely and b is in fact b = 2.5 (instead of b = 2), then for v in ( t ) = 12 V, steady state output = 20 × 12 = 240 rpm Thus open loop control is sensitive to modeling errors! No longer the desired speed! Problems with Open Loop Control b Js K s V s V s G in ) ( ) ( ) (
Systems and Control (Chapter 7) 7-5 Suppose we now have operational or environmental (external) uncertainties, e.g., load on the shaft increases, bearings wear out, etc Motor v in ( t ) v ( t ) External factors We can easily see that without feedback, there is no control over the external factors Example: When the bearings wear out, parameter, b will change. Motor will continue to operate with this change and has no means of making any corrections Thus, velocity fluctuates with fluctuating external conditions Uncontrollable external factors! Big problems with fluctuating external conditions!

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Gp4_Chapter 7 - EE2010 Systems and Control(Chapter 7 Open...

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