An Analytical Formula for Optimal Tuning of the State Feedback Controller Gains for the Cart-Inverted Pendulum System

Fuzzy Swing Up Control and Optimal State Feedback Stabilization for Self-Erecting Inverted Pendulum

“…In work of S. Chaterjee and S.K. Das (2018), disturbance was given in the 65.2 second and stabilized in the 68 second [5]. They used optimal tuning of state feedback controller gain with dominant pole structure.…”

“…Problems of an inverted pendulum stabilization had been attracting many control system engineers and researchers for years [1]- [3]. Since an inverted pendulum is typically nonlinear, high order, multivariable and unstable, then many efforts to achieve balancing condition were proposed [4], [5]. Also, due to its nonlinearity and instability, balancing capability is the important platform to demonstrate various control applications such as running and biped walking robot, Segway riding and propeller rocket operation [6]- [8].…”

Stabilization of the Cart–Inverted-Pendulum System Using State-Feedback Pole-Independent MPC Controllers

“…On the other hand, there are many proposed (MPC or non-MPC) linear explicit control schemes (ECS) to stabilize the CIP system, where the control input is evaluated directly in a single step and applied at the same time on the cart control input. These ECS include the coincident pole placement (CPP) [ 17 ], dominant pole placement (DPP) [ 18 , 19 ], two proportional-integral-derivatives (TPID) [ 20 , 21 , 22 , 23 ], and linear quadratic regulator (LQR) [ 22 , 23 , 24 ]. From the linear control theory point of view, the design task to satisfy some prescribed time (i.e., steady-state and transient) response performance may be regarded as a pole placement problem, especially when using CPP, DPP, and LQR methods.…”

“…In order to obtain the best possible performance, the optimal choice of the SFC gains needs to be addressed. An important contribution in this line for pole-dependent non-MPC SFC controllers is attributed to the authors of [ 17 ], who proposed an analytical formula for optimal tuning of the SFC gains for the CIP system. In the derivation of the formula, the authors promote a priori a coincident-pole structure, which has a single tuning parameter (see Appendix C ) for the closed-loop poles before maximizing the worst gain margin associated with the CIP output signals.…”

Observer Design for an Inverted Pendulum with Biased Position Sensors

“…The analysis of the mathematical models of inverted pendulums and the design of control laws can be done with computational [5,6] and imitational methods [7,8] based on the equations of motion. The advantage of the control law design methods that use the differential equations of motion are high accuracy and numerical stability of the resulting solutions [9], ability to analyze the behavior of the system with varying physical parameters. Analytic solutions can also be used for a parametric identification of the system.…”