Design of Parameter Adaptive Fuzzy Controller for the Planar Double Inverted Pendulum

The double inverted pendulum is a multivariable, nonlinear control system. The fuzzy controller of double inverted pendulum is studied in the paper. The mathematical model is gained by the Lagrange equation and the controllability of double inverted pendulum system in unstable equilibrium point is analyzed. On the base of above, the fuzzy controller for double inverted pendulum is designed by the fuzzy control theory. The dimensions and control rules of the fuzzy controller are depressed by designing a fusion function using the optimization control theory. Simulation and real-time control results prove that the fuzzy controller is effective and feasible.

To achieve a better robustness and get a static response of a certain target missiles in longitudinal control, a mathematical model of target missiles is established. The uncontrolled trajectory, the predetermined trajectory and the requirements of the predetermined trajectory are analyzed next. Then the trajectory instruction angle is designed to ensure the stable flight of the target missiles system. To solve the problem that the PID controller cannot adjust parameters online and the output is easy to be disturbed by external noise, the fuzzy adaptive PID control is designed. It enhanced the robustness of the target missiles by fuzzy control, and also has a good response by using PID control. The simulation experiments show the fuzzy adaptive control system can track the predetermined trajectory rapidly and smoothly, and the static error and overshoot were significantly reduced. When the system are affected by noise, the fuzzy adaptive PID control can achieve a good robustness than traditional PID controller.

In this design, through the analysis of the physical model of the linear double inverted pendulum, the motion equation of the system is obtained by using the classical Newtonian mechanical formula, and the obtained equation is linearized at the stable point, and the state space model of the system is obtained. In order to realize the stable control of the trolley position and the secondary linkage in the linear inverted pendulum system, the linear quadratic optimal controller is used in this design to obtain an excellent output response. In order to design the optimal state feedback control matrix K, the shortcomings of weight matrices Q and R in general LQR control design that depend on experience selection and trial and error are overcome. This design attempts to apply PSO algorithm to LQR controller parameter optimization. PSO algorithm is applied to optimize Q parameters and R parameters of LQR weighting matrix of linear quadratic optimal controller, and K matrix is obtained. The matrix is applied to a fuzzy PID controller designed by the fusion algorithm to overcome the disadvantage that a single PSO cannot adapt itself. Finally, a comparative simulation study is carried out in the Simulink environment of Matlab software toolbox, which verifies the effectiveness of the fuzzy PID controller based on particle swarm optimization algorithm, laying a theoretical foundation for the practical application of the inverted pendulum system, and has certain application value.

Realizing balance control of single inverted pendulum without mathematic model by reinforcement learning has gained great success. However, further applying it to the multilevel inverted pendulum faces problems such as curse of dimensionality and difficulty in convergence. In this paper, we propose a hierarchical reinforcement learning algorithm to control parallel double inverted pendulum. Firstly, control of single inverted pendulum is learned by Q-learning algorithm. Then the learned control states of single inverted pendulum are used to direct control process of parallel double inverted pendulum so that the double one is controlled.

In this paper a fuzzy optimal control for stabilizing an upright position a double inverted pendulum (DIP) is developed and compared. Modeling is based on Euler-Lagrange equations. This results in a complicated nonlinear fast reaction, unstable multivariable system. Firstly, the mathematical models of double pendulum system are presented. The weight variable fuzzy input is gained by combining the fuzzy control theory with the optimal control theory. Simulation results show that the controller, which the upper pendulum is considered as main control variable, has high accuracy, quick convergence speed and higher precision.

Inverted pendulum is a highly unstable, nonlinear and an under-actuated system. Its dynamics resembles many real-time systems such as segways, self-balancing robots, vertical take-off and landing aircraft (VTOL) and crane lifting containers etc. These real-time applications demand the need of a robust controller. In literature, many different control strategies have been discussed to stabilize an inverted pendulum, out of them, the most robust being fuzzy control and sliding mode control. The former is difficult to tune and has a problem of rule explosion for multivariable system, whereas the latter has a problem of discontinuity and chattering. To address the issues in fuzzy controller, a novel robust linear quadratic regulator (LQR) based adaptive-network fuzzy inference system (ANFIS) controller is proposed and implemented on the stabilization of x and x-y inverted pendulums. These pendulums differ from each other in degrees-of-freedom, complexity of the mathematical model and their respective degree of under-actuation. The proposed controller is able to solve the problem of robustness in the LQR controller as well as the difficulty in tuning along with rule explosion in fuzzy controller. Furthermore, the designed controller is tested for different pendulum masses and the results show that as compared with conventional PID controller, the proposed controller gives better performance in achieving lesser overshoot and settling time along with better robustness properties.

A fuzzy controller design using linguistic control rule adjustment is proposed. The proposed adaptive law, which results from the direct adaptive approach, is used to indirectly regulate the output fuzzy variables in the fuzzy controller according to the prelabelled rules. The main advantage of the proposed method is that the determination of rule selection is formed by an analytical parameter equation with multiple input variables of the fuzzy controller. Practically, it is not easy to characterise the linguistic control rules and their membership function distribution without expert knowledge, especially in those cases when the input state variables of the fuzzy controller are increased. The rules are first labelled, then an adaptive law is used to tune the injected parameters in the IF-part to appropriately determine each output fuzzy variable under situations of lack of any knowledge of the plant. The derivation result shows that the proposed adaptive fuzzy controller is stable in the Lyapunov sense. Finally, a nonlinear system simulation example is applied to verify the effectiveness and the ability of the proposed fuzzy controller.

Abstract- This paper introduces a linear structure of wind turbine, operator and the pitch angle controller. Then, a new method of adaptive fuzzy on the variable speed wind turbines was provided and it was compared with PID and Fuzzy Logic Control ler and the simulation results were analyzed. So when the results of each simulation using PID and Fuzzy controllers and adaptive fuzzy PID controllers provided, the observed advantages and disadvantages of the rotor speed and wind turbine power can be introduced. It can be seen that in PID method the high overshoot is discussed as a disadvantage while it is overcome by using fuzzy controller and overshoot will decrease. The time of reaching to a sustained speed increases slightly and in adaptive fuzzy PID controller, the less overshoot has provided a good and effective performance for system response. The use of adaptive fuzzy PID controller causes the system does not have any steady-state error and at all moments of time, the response rate is better than PID and fuzzy controller. The importance of the amount of overshoot and rate fluctuations is that by reducing these parameters in addition to reducing the cost of preventive care, maintenance and depreciation, the fluctuations in electricity generated by induction generator also greatly reduced.

Research on A Fuzzy Adaptive PID Control Method for Four Rotor UAV Control System With the continuous improvement of national living standards, people have higher and higher requirements for the reliability of power supply. The emergence of unmanned aerial vehicle inspection technology provides a new idea to solve the contradiction between the increasing equipment scale and the increasing inspection requirements. However, at present, the stability of the traditional proportion integration differentiation (PID) control system of the four rotor unmanned aerial vehicle (UAV) is not high enough. During the inspection, there are accidents of drones hitting power equipment from time to time. In view of the above problems, this paper studies the fuzzy adaptive PID control method to support the stable flight of four rotor UAV. The principle of fuzzy control is analyzed. The fuzzy control method and PID control method are deeply integrated. A fuzzy adaptive PID control system is designed. The universe and membership function of the relevant control parameters of the system are formulated. The tuning rules of fuzzy adaptive PID control system are formulated. Finally, the improved control system is simulated. The simulation results show that the fuzzy adaptive PID control algorithm can effectively improve the stability, reliability and emergency ability of UAV. This method can effectively improve the adaptability of UAV to perform complex missions in complex environments. The research results have guiding significance for expanding the application field of UAV.

Artificial intelligence methods such as fuzzy logic and particle swarm optimization (PSO) have been applied to maximum power point tracking (MPPT) for solar panels. The P-V curve of a solar panel exhibits multiple peaks under partial shading condition (PSC) when all modules of a solar panel do not receive the same solar irradiation. Although conventional PSO has been shown to perform well under uniform insolation, it is often unable to find the global maximum power point under PSC. Fuzzy adaptive PSO controllers have been proposed for MPPT. However, the controller became computation-intensive in order to adjust the PSO parameters for each particle. In this paper, fuzzy adaptive PSO-based and conventional PSO-based MPPT are compared and evaluated in the aspect of design and performance. A simple fuzzy adaptive PSO controller for MPPT was designed to reach the global optimal point under PSC and uniform irradiation. The controller combines the advantages of both PSO and fuzzy control. The fuzzy controller dynamically adjusts the PSO parameter to improve the convergence speed and global search capability. Since tuning of the PSO parameter is designed to be common for all particles, it reduced the computation complexity. The fuzzy controller’s rule base is designed to obtain a fast transient response and stable steady state response. Design of the fuzzy adaptive PSO-based MPPT is verified with simulation results using a boost converter. The results are evaluated in comparison to the results using a conventional PSO controller under PSC. Simulation shows the fuzzy adaptive PSO-based MPPT is able to improve the global search process and increase the convergency speed. The comparison indicates the settling time using the fuzzy adaptive PSO-based MPPT is 14% faster under PSC on average and 30% faster under uniform irradiation than the settling time using the conventional PSO. Both the fuzzy adaptive and conventional PSO controllers have similar output power tracking accuracy.

In the off-grid microgrid cluster, the energy storage device is mainly charged and discharged to maintain the stability of the bus voltage and the system power balance. Generally, the voltage and current double closed-loop control and fuzzy control are adopted for the energy storage converter. The traditional double closed-loop control parameters and the scale factor and quantization factor in fuzzy control cannot be adjusted in real time during system operation, resulting in slower dynamic response and weak anti-interference ability of the system. In response to the above problems, this paper proposes an adaptive genetic fuzzy double closed-loop control, which can adjust the PI control parameters in real time by adjusting the quantization factor and the scale factor to optimize the control effect. The simulation platform is built in MATLAB/Simulink and the simulation results show that the adaptive genetic fuzzy double closed-loop control combines the advantages of fuzzy and PI control. Under different working conditions, the system has not only a fast dynamic response, small overshoot, and strong anti-interference ability but also good robustness.

Direct adaptive fuzzy position controller for an electropneumatic actuator: Design and experimental evaluation

This paper illustrates a Comparative study of highly non-linear, complex and multivariable Inverted Pendulum (IP) system on Cart using different soft computing techniques. Firstly, a Fuzzy logic controller was designed using triangular and trapezoidal shape Membership functions (MF's). The trapezoidal fuzzy controller shows better results in comparison to triangular fuzzy controller. Secondly, an Adaptive neuro fuzzy inference system (ANFIS) controller was used to optimize the results obtained from trapezoidal fuzzy controller. Finally, the study illustrates the effect of variation in shape of MF's on Performance parameters of the IP system. The results shows that ANFIS controller provides better results in comparison to both fuzzy controller.

The greenhouse environment is a complex nonlinear time-varying system. It is difficult to establish accurate mathematical model. Adaptive fuzzy control does not rely on the mathematical model of the controlled object, and has the advantages of adaptive learning algorithm. The learning algorithm is to rely on the data information to adjust the parameters of fuzzy logic system. So we can adopt direct adaptive fuzzy control to control the greenhouse environment temperature. Through the MATLAB simulation, we simulate the control effect of fuzzy controller in different working conditions. The results show that the fuzzy adaptive controller can meet the requirements of the greenhouse environment temperature control.

The linear fusion function is constructed on the basis of LQR control in this paper. Therefore it is possible to decrease the dimensions of fuzzy controller input variables and reduce the rules for fuzzy control. The fuzzy controller based on fusion function is applied to the approximate linear model of double inverted pendulum, and the experimental results show that the system's response rate is well improved and the robustness is also enhanced.