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1.1 INTRODUCTION

• CONTROL - Using artificial means to manipulate the world - with a particular goal.

• Continuous - the values to be controlled change smoothly. e.g. the speed of a car

• Discrete - The value to be controlled are easily described as on-off. e.g. the car motor is on-off (like basic pneumatics). NOTE: all systems are continuous (Except for Heisenberg’s electrons) but they can be treated as discrete for simplicity.

• Linear - Can be described with a simple differential equation (not a very accurate explanation).

e.g. a car can be driving around a track and can pass same the same spot at a constant velocity. But, the longer the car runs, the mass decreases, and it travels faster, but requires less gas, .......... etc. Basically, the math gets tougher, and the problem becomes non-linear.

- This is the preferred starting point for simplicity, and a common approximation for real world problems.

• Non-Linear - Not Linear. This is how the world works, but is very complicated. Especially when trying to do mathematical approximations. (Note: if the coefficients in a differential equation change it is non-linear)

• Temporal/sequential - the controller must not just keep track of things that changes, but it must know the time, or how long since something happened.

• e.g.

non-linear - as rocket approaches sun, gravity increases, so control must change.

linear - We are driving the perfect car with no friction, with no drag, and can predict how it will work perfectly.

discrete - “When I do this, that always happens!” For example, when the power is turned on, the press closes!

How to tell the difference? An elevator is the perfect example.

Discrete

1. The elevator must move towards a floor when a button is pushed.

2. The elevator must open a door when it is at a floor.

3. It must have the door closed before it moves.

etc.

Linear (our approximation commonly used in industry) NOTE: each floor will have a certain motor position, and we know what that position is.

1. If the desired position changes to a new value, accelerate quickly towards the new position.

2. As the elevator approaches the correct position, slow down.

Non-linear (not yet common in industry) e.g. Fuzzy logic, Neural Networks, Adaptive Control

1 Accelerate slowly to start.

2. Decelerate as you approach the final position.

3. Allow faster motion while moving.

4. Compensate for cable stretch, and changing spring constant, etc.