Complete notes of the lectures

Page 1

INTRODUCTION TO THE COURSE Introduction to a controlled system Controlling a system means that we are able to make the system follow a specific and determined law of motion. Let’s remember that generate a law of motion means generate a coordinate which is depending on time: 𝑥(𝑡). Let’s point out that a law of motion is different from a trajectory because a trajectory is related to space: 𝑧(𝑥, 𝑦) where 𝑥 and 𝑦 depend on time: 𝑥(𝑡) and 𝑦(𝑡). Anyway, in general we can think of adding a controller to our mechanical system because we would like that it follows a specific law of motion. Another reason that we can think of is regarding the capability of reducing the external excitations. Nowadays we cannot make the system follows a specific law of motion neither a specific trajectory if we don’t use any type on controller. Control system have a lot of pros, one of the main one is the fact that they are easy to modify, thus adding a controller to our mechanical system means increasing its flexibility. As changing law of motion brings us t o change the mechanical system, also changing the controller or the parameters of the controller leads us have a different controlled system with respect to the one that we had previously. Let’s point out the fact that when we are discussing about a contro lled system we don’t have only the controller and the mechanical system but we also have an actuator and eventually we could also have a sensor (this is not obliged, it depends on the type con controller as we are going to see later on). Thus, this type of system needs actually more components but it's more flexible. Our goal is to learn how to choose or decide the actuators and controller of the controlled system the suits the best in order to obtain a specific law of motion. This way of…