![]() The sum of the torques of the car body mass center is as follows: Using Newton’s second law, the force of the vertical direction of the car body is as follows: According to the revolver force equation can be obtained in the following according to the Newton’s law and the rotational torque formula :Īmong them, is the displacement of the car body centre of gravity relative to the ground, ![]() The two wheels are regarded as the research object, Figure 1 is a diagram revolver force analysis. This paper separates the wheel from the pendulum analysis first in the process of modeling, and then it deduces the dynamics state equation of the two-wheeled self-balancing robot through the simultaneous two parts. The two-wheeled and self-balancing robot can be regarded as the vehicle-mounted inverted pendulum, so the dynamic system analysis process is more complex. The two-wheeled and self-balancing robot structure is mainly composed of the body and the two wheels, and the robot is the coaxial two wheels, driven by the independent motor the parameters of quality, moment of inertia, and radius of the two wheels are regarded as the same, so the body center of gravity is inverted above the axletree and it keeps balance through sports. The Dynamics Model of the Two-Wheeled Self-Balancing Robot ![]() This method has better control effect by simulation tests and comparison. It gains the global optimal solution of matrix and of the LQR controller so as to design the optimal state feedback control matrix and overcome the disadvantages of relying on the experience and the trial and error in the selection of matrix and of the general LQR control design, making up for the inadequacy of big workload. In view of the mathematical model of the system, LQR controller is designed based on the particle swarm optimization and makes full use of the searching capability of the particle swarm algorithm to optimize the matrix and matrix of the LQR controller. This paper concerns the self-designed and two-round self-balancing robot as the research object, which uses the Newtonian mechanics equation method and the linear method near the balance point to establish the linearized mathematical model of the system. However, the parameters are difficult to adjust, and it is easy to fall into the local optimization. ![]() The genetic algorithm is successfully applied to the parameter optimization of the LQR controller of the inverted pendulum system, and it achieves the good control effect. The optimal LQR controller is designed on the basis of establishing the system structure model the correctness and effectiveness of the LQR controller are verified, but it is difficult to determine the weighted matrix and. The two-wheeled and self-balancing robot control system based on the fuzzy control can overcome the instability and nonlinear nature of the system, but it relies on the expert’s experience too much. Since 1980s, the scholars of various countries have conducted the system research on the two-wheeled self-balancing robot. Because it has the advantages of simple structure, stable running, high energy utilization rate, and strong environmental adaption, it has the broad application prospects whether in the military field or in the civilian field. The two-wheeled and self-balancing robot belongs to a multivariable, nonlinear, high order, strong coupling, and unstable essential motion control system, and it is a typical device of testing various control theories and control methods therefore, the research has great theoretical and practical significance. The simulation experiments prove that the LQR controller improves the system stability, obtains the good control effect, and has higher application value through using the particle swarm optimization algorithm. This paper uses the particle swarm algorithm to optimize the parameter matrix of LQR controller based on the LQR control method to make the two-wheeled and self-balancing robot realize the stable control and reduce the overshoot amount and the oscillation frequency of the system at the same time. The dynamics model is established in view of the self-designed, two-wheeled, and self-balancing robot.
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