What is a Linear Inverted Pendulum

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What is a Linear Inverted Pendulum

The linear inverted pendulum (or linear pendulum, lin. pen for short) is a classical physics experiment used to explain the control theory and system dynamics. Therefore, it has been used as one of the primary systems used to test and compare control strategies. In an inverted pendulum system, which is an open-loop unstable system, it is desired to stabilize the system by reciprocating motion to stabilize it. It is also used as a common method for testing control algorithms.

Applications and Examples

Although the linear inverted pendulum looks like a classic pendulum control mechanism, it is a tool that helps in many controls and training. We can have the opportunity to examine many events today through this pendulum system. The system is used actively especially in education. In this system, students learn how the vertical bar at the end of the movable arm stays in balance. However, this robot is very useful for familiarizing with many industrial components such as servo motors and their drivers, different type of encoders, linear or rotary motors, and slide springs. If we need to talk about the examples of a linear inverted pendulum, we should mention the examples that we come across quite often in our daily life. Examples include the human stance system, segway, and rocket launch. So basically, any system that needs a vertical balance has dynamics like an inverted pendulum. Let us briefly explain the example of the human posture. A person standing upright moves like an inverted pendulum with their feet pivoting. It is the muscular system that balances the human body. That's why we can topple over if we don’t constantly make small movements (even though we don’t do it consciously).

Figure 1 - Segway, balancing the stickwith a finger and linear pendulum resembles a similarbalance application (image in courtesy of Automatic Control Lab of the Schoolof Electrical Engineering, KTH)

Linear Inverted Pendulum Experiment System

The arm of the inverted pendulum is fixed to a moving cart and this cart can only move horizontally. At this cart, there is the freely rotating pendulum arm with a mass of 'm' and a length 'l'. The important point here is that the car is limited to linear movements and is subject to the force that causes or prevents the movement. This reflects the control system and is an example commonly used in textbooks. This example shows that it is caused by a system that is unstable without control. Because the pendulum will fall if the cart is not moved to balance it.

This robot provides a control-ready experience with a durable linear DC servo motor and industrial servo motor driver. Cart position feedback (along all the movement axis) is obtained using a non-contact magnetic encoder with very high sensitivity and high speed.

Figure 2 - Free body diagram of thelinear pendulum. Proportions of the items are not in scale.


The controller should control the position of the cart very fast and very precisely. Special control techniques such as LQR or scheduled PID should be utilized in the controller. With this robot, students will be able to progress in undergraduate, graduate, and architectural courses, as well as in research projects related to advanced control and mechanical systems.

The linear inverted pendulum example, which is very common in control and balance topics, is also encountered in our daily lives. Therefore, it is the explanatory robot that attracts the attention of students. It is an easy-to-use tool with many features.

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