In this paper, we present a way to create fuzzy controller from LQR method by using ANFIS toolbox of Matlab. First, after proving the ability of stability of this SIMO system under LQR method in Matlab/Simulink, we create a fuzzy controller through ANFIS toolbox of Matlab. The data, which is used to train, is collected from responses of system under LQR controller. Also, we present a hardware platform of ball and beam system. Under this fuzzy controller, control quality of ball and beam is better than under LQR controller in both simulation and experiment.

Two-linked robot arm is a popular model in both laboratory and actual industry. This is a MIMO system which has the same number of inputs and outputs. Because of the interactions between variables, normal SISO control algorithms, such as PID algorithm, do not prove their effectiveness in process of operation. In this paper, we propose using a method of sliding algorithm to control two-linked robot tracking expected trajectories. Results of controlling are proved to be successful through Matlab/Simulink.

One-wheeled self-balancing robot is a high-order SIMO system. It is developed from bicycle balancing and two-wheeled self-balancing robot by using only one wheel instead of two wheels. In this paper, we consider this model as two combined SIMO systems. Thence, a PID control structure is designed to balance this model not falling on a plane. Simulations are shown to prove again the ability of PID controllers in balancing this robot is two directions. Besides, we present a hardware platform of one-wheel self-balancing robot. Through the real model, PID control algorithm is proved to balance this object well at equilibrium point.

Rotary Inverted Pendulum (RIP) plays a vital role in control engineering. Rotary Inverted Pendulum is a complex, nonlinear, non-minimum-phase and under-actuated system which has various applications in the field of Robotics. The main contribution of this paper is to design and control RIP by using Linear Quadratic Regulator (LQR) controller for stabilization at vertically upright position - the unstable equilibrium point, and Linear Quadratic Tracker (LQT) controller for tracking the desired trajectory. Besides, stability of the closed-loop system is analyzed for ensuring the reliability of the developed controller. The simulation is carried out in MATLAB/Simulink environment, and the proposed controllers have been tested on Rotary Inverted Pendulum hardware that is designed by authors. The analysis and results conducted on the system demonstrate the performance of the control schemes, including stabilization of unstable equilibrium point, tracking the desired trajectory, and system response showing the robustness and effectiveness of methods.

The Ball and Beam system with Deviated Axis is a single input-muti output (SIMO) system commonly used in laboratories to test control algorithms. In this paper, we build and investigate an PID-GA controller in simulation and apply to real model. The controller demonstrates the ability to control the balancing statement in different desired positions. Next, we conduct a survey of the above method in the object name Ball and beam system with deviated axis through STM32F4. Through simulation and experiment, our PID controller has successfully controlled the system and GA-PID has optimize well PID parameters. In addition, the control parameters had been adjusted to verify and summerize the theoretical rules.