The inverted pendulum represents many real-world systems.Examples include the Segway, the human posture systems, thelaunching of a rocket, and so on. Basically, any system thatrequires vertical stabilization has dynamics that are similar to aninverted pendulum.
The system in this example consists of an invertedpendulum mounted to a motorized cart. The invertedpendulum system is an example commonly found in control systemtextbooks and research literature. Its popularity derives in partfrom the fact that it is unstable without control, that is, thependulum will simply fall over if the cart isn't moved to balanceit.
We will consider a two-dimensional problem where the pendulum isconstrained to move in the vertical plane shown in the figurebelow. For this system, the control input is theforce that moves the carthorizontally and the outputs are the angular position of thependulum and the horizontal positionof the cart .
- Problem Statement The Inverted Pendulum Represents Many Real World Systems Examples Include The Segway The Human Postu 1 (7.5 KiB) Viewed 27 times
We need to define a PID controller for theinverted pendulum system. More specifically, the controller willattempt to maintain the pendulum vertically upward when the cart issubjected to a 1-Nsec impulse.
Under these conditions, the criteria are:
A PID controller for the system has to be defined that should beable to cater the above-mentioned requirements scenarios.
Steps:
First, define the transfer function of the invertedpendulum.
Add the PID controller (Kp, Ki, Kd) in feedback to the invertedpendulum.
Show the impulse response anddisplay the characteristics such as settling timeand peak response.
If the system is not stable, begin to modifythe parameters of PID controller.
You can set the parameters as you want.
Then, again show the impulse response to checkthe characteristics.
F O 1 M Ꮎ m, I X