In this paper, explicit model predictive controller is applied to an inverted pendulum apparatus. Explicit solutions to constrained linear model predictive controller can be computed by solving multi-parametric quadratic programs. The solution is a piecewise affine function, which can be evaluated at each sample to obtain the optimal control law. The on-line computation effort is restricted to a table-lookup. This admits implementation on low cost hardware at high sampling frequencies in real-time systems with high reliability and low software complexity. This is useful for systems with limited power and CPU resources.
An efficient feedback scheduling scheme based on the proposed Feed Forward Neural Network (FFNN) scheme is employed to improve the overall control performance while minimizing the overhead of feedback scheduling which exposed using the optimal solutions obtained offline by mathematical optimization methods. The previously described FFNN is employed to adapt online the sampling periods of concurrent control tasks with respect to changes in computing resource availability. The proposed intelligent scheduler will be examined with different optimization algorithms. An inverted pendulum cost function is used in these experiments. Then, simulation of three inverted pendulums as intelligent Real Time System (RTS) is described in details. Numerical simulation results demonstrates that the proposed scheme can reduce the computational overhead significantly while delivering almost the same overall control performance as compared to optimal feedback scheduling
As a key type of mobile robot, the two-wheel mobile robot has been developed rapidly for varied domestic, health, and industrial applications due to human-like movement and balancing characteristics based on the inverted pendulum theory. This paper presents a developed Two-Wheel Self-Balanced Robot (TWSBR) model under road disturbance effects and simulated using MATLAB Simscape Multibody. The considered physical-mechanical structure of the proposed TWSBS is connected with a Simulink controller scheme by employing physical signal converters to describe the system dynamics efficiently. Through the Simscape environment, the TWSBR motion is visualized and effectively analyzed without the need for complicated analysis of the associated mathematical model. Besides, 3D visualization of real-time behavior for the implemented TWSBR plant model is displayed by Simulink Mechanics Explorer. Robot balancing and stability are achieved by utilizing Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR) controllers' approaches considering specific control targets. A comparative study and evaluation of both controllers are conducted to verify the robustness and road disturbance rejection. The realized performance and robustness of developed controllers are observed by varying object-carrying loaded up on mechanical structure layers during robot motion. In particular, the objective weight is loaded on the robot layers (top, middle, and bottom) during disturbance situations. The achieved findings may have the potential to extend the deployment of using TWSBRs in the varied important application.