Review: Linear, nonlinear and intelligent controllers for the inverted pendulum problem

A Review on the Control of Second Order Underactuated Mechanical Systems

“…The proposed controller employed the expert knowledge of the decoupled sliding mode to guarantee through simulation results a good stability and robustness. In the case of the cart-pole system, a review article has been proposed [79] which reviews all the control strategies that have been applied to control this system.…”

Modeling and Model Predictive Control (Mpc) of an Underwater Double Inverted Pendulum (Udip)

“…Such model is based on the Morison's equation and on the strip theory by means of the discretization of the links into strips. Thus, considering the model of Leabourne and Rock [8], the vector of generalized drag forces for the UDIP is given by: , (5) where v i Sk is the absolute velocity vector of the k-th strip, expressed in S i , for k = 0, ..., n s strips (considering equally discretized links) and v ee ee is the absolute velocity vector of the end-effector, expressed in S ee ; F i Sk is the drag forces vector of the k-th strip and v ee ee is the drag force vector of the end-effector, as shown below:…”

“…The results show that the MPC is capable of performing the stabilization of the DIP with a better transient response than the LQR for the cart's position. Similarly, Krafes et al [5] presented a comparison between a Proportional Integral Derivative (PID) controller and a LQR on the stabilization of a DIP. The simulations showed that both controllers can stabilize the DIP when referring to the nominal case.…”

“…However, when disturbances are added to the systems, only the LQR is able to stabilize the double pendulum. This happens because the PID is not robust to disturbances since its gain margin is negative (Krafes et al [5]). Moreover, Mohan et al [6] proposed a Modified Neuro Fuzzy Controller (MNFC) for the stabilization problem of a DIP.…”

Design Methodologies for Simple Adaptive Controllers with Applications to Spacecraft Proximity Operations

“…Use of the theorem allowed for the creation of innumerable nonlinear control laws for a wide variety of systems. Backstepping and sliding mode controllers are two popular examples [25], but the diversity and variety of controllers made using Lyapunov's stability theorem are legion, each with their own small variations for the control problem at hand. The vast amount of nonlinear controller designs present are therefore too numerous to cover here.…”