We present an inverted pendulum design using readily available V-slot rail components and
3D printing to construct custom parts. To enable the examination of different pendulum
characteristics, we constructed three pendulum poles of different lengths. We implemented
a brake mechanism to modify sliding friction resistance and built a paddle that can be
attached to the ends of the pendulum poles. A testing rig was also developed to consistently
apply disturbances by tapping the pendulum pole, characterizing balancing performance.
We perform a comprehensive analysis of the behavior and control of the pendulum. This
begins by considering its dynamics, including the nonlinear differential equation that
describes the system, its linearization, and its representation in the s-domain. The primary
focus of this work is the development of two distinct control modes for the pendulum: a
velocity control mode, designed to balance the pendulum while the cart is in motion, and a
position control mode, aimed at maintaining the pendulum cart at a specific location. For
this, we derived two different state space models: one for implementing the velocity control
mode and another for the position control mode. In the position control mode, integral action
applied to the cart position ensures that the inverted pendulum remains balanced and
maintains its desired position on the rail. For both models, linear observer-based state
feedback controllers were implemented. The control laws are designed as linear quadratic
regulators (LQR), and the systems are simulated in MATLAB. To actuate the physical
pendulum system, a stepper motor was used, and its controller was assembled in a DIN rail
panel to simplify the integration of all necessary components. We examined how the
optimized performance, achieved with the medium-length pendulum pole, translates to poles
of other lengths. Our findings reveal distinct behavioral differences between the control
modes
