Reduced-dimensional fuzzy controller design based on fusion function and application in 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.

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.

The presented stair climbing device (SCD) allows consideration of applications like stair-climbing wheelchairs and assistive robots. It can be considered as a wheeled double inverted pendulum which goes through different contact situations during the stair-climbing. The derived hybrid dynamic model covers the whole stair-climbing functionality. A model analysis is shown from the control point of view whereat the state transition “lift-off” is described in detail considering conditions and limits for successful transition. Presented simulation results give an insight into system properties. The “lift-off” simulation is compared with measurements of the real SCD prototype.

We discuss the optimality and computational efficiency of sampling based motion planning (SBMP), which calculates dynamically precise and approximately optimal state transitions using arbitrarily selected nonlinear control system models. To ensure high optimality and computational efficiency, SBMP requires an approximately uniform state sampling function, though the non-linearity of the system models does not allow a perfect function. We propose linear prediction-based uniform state sampling (LPUSS) that samples approximately uniform state points while ensuring a dynamically correct state transition profile with a small calculation cost. LPUSS samples a state by using the given non-linear control system model after determining the input values by using a local linear transition model. We developed a mechanical motion planning system using LPUSS, articulated body algorithm, and parallel computing techniques. To validate LPUSS, we conducted experiments on double, triple, and sixtuple inverted pendulum models. LPUSS showed better optimality and computational efficiency with the double and triple inverted pendulum models, compared with randomized kinodynamic planning (RKP), which is based on rapid random tree (RRT), and our previously proposed rapid semi-optimal motion-planning method in which state sampling is based on uniform inputs. In particular, compared with our previous method, LPUSS was respectively 130 times and 3,000 times faster on double and triple inverted pendulum models under the condition of the same optimality. LPUSS found an approximately optimal swing up motion for the sixtuple inverted pendulum model within 40 minutes. According to our survey, there is no other optimization method that is applicable to higher than quadruple inverted pendulum models with standard constraints.

The following paper is the first part of our investigation into the feasibility of arm-free paraplegic standing. A novel control strategy for unsupported paraplegic standing which utilizes the residual sensory and motor abilities of the thoracic spinal cord injured subjects is proposed. The strategy is based on voluntary and reflex activity of the paraplegic person's upper body and artificially controlled stiffness in the ankles. The knees and hips are maintained in an extended position by functional electrical stimulation (FES). The analysis of a linearized double inverted pendulum model revealed that with properly selected ankle stiffness the system can be easily stabilized. We developed a closed-loop double inverted pendulum model including a neural system delay, trunk muscles dynamics, body segmental dynamics and linear quadratic regulator (LQR) optimal controller. Through simulations of the closed-loop model two different strategies for disturbance rejection were explained. We investigated the capability of the closed-loop model to reject disturbances, imposed at the ankle joint (in anterior and posterior directions) for various stiffness levels and neural system delays in the presence of biomechanical constraints. By limiting permissible excursions of the center of pressure, we found out that the length of the foot is the most important constraint, while the strength of the trunk muscles is not of major importance for successful balancing. An ankle stiffness of approximately 10 Nm/degree suffices for arm-free standing of paraplegic subjects.

Deals with the modeling of a flexible inverted pendulum. The mathematical model of the controlled object used is a simplified one, which is approximated by rigid links and springs. The possibility of driving a simplified model of the flexible inverted pendulum using a double inverted pendulum with an elastic joint is studied. The experimental results show that the simplified model is sufficient to describe the flexible inverted pendulum, but with some modeling and identification errors. These uncertainty will excite the vibration. An H/sub infinity / control to stabilize the flexible inverted pendulum using the simplified model is presented. >

Mathematical models and parameters with high accuracy are required for the swing-up control of a double inverted pendulum. This study proposes a mechanical structure of a double inverted pendulum having excellent matching characteristics with a mathematical model. The implementation of a parameter estimation method based on nonlinear optimization, which is essential for swing-up control, is also proposed. The proposed structure of a double inverted pendulum eliminates backlash using the direct drive of a BLDC motor, minimizes the unmodeled frictional force through bearing cleaning and oiling, minimizes unnecessary load torque using the double support of a timing pulley shaft and power transmission through a coupling, and constrains the pendulum rotation to one degree-of-freedom by adopting a dual-bearing joint. In addition, both 3D printing and CNC milling are appropriately used to satisfy the requirements for each mechanical part. The swing motion of the manufactured double inverted pendulum is measured using the lab-built light-weight rapid control prototyping 02 (LW-RCP02). The proposed parameter estimation method based on nonlinear optimization is implemented to match the response trajectory of the actual double inverted pendulum with that of a Simulink model implemented as an S-function. Finally, the effectiveness of the proposed double inverted pendulum design and parameter estimation method is confirmed by showing that the mathematical model that, based on the parameters estimated using the proposed method, accurately describes the response characteristics of the double inverted pendulum.

In this study, interval type2 fuzzy logic (IT2FL) and PID controller is designed for swing-up position control of double inverted pendulum (DIP) system. The double inverted pendulum system consists of two rigid bars connected by a revolute joint. Mass of the revolute joint is included in the dynamic model.Rigid bars in the system are assumed to experience planar motion. The pendulum system is connected to the base by means of a revolute joint. Torque provided through a motor mounted to the base is used for position control of the system. PID (Proportional-Derivative-Integral) and interval type2 fuzzy logic controllers are developed by using the same performance criteria for position control of double inverted pendulum system. IT2FL controller is similar with type1 fuzzy logic controller. IT2FL system provides soft decision boundaries, whereas a type-1 fuzzy logic system provides a hard decision boundary. Membership function in interval type2 fuzzy logic set as an area called Footprint of Uncertainty (FOU) which limited by two type1 membership function those are upper membership function (UMF) and lower membership function (LMF).System behaviour is obtained by computer simulation using developed controllers respectively. Computer simulation results are compared in order to evaluate applicability of developed controllers. MATLAB/Simulink software is used in computer simulations.

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.

A new type of adaptive neural network fuzzy controller based on the stability for the double inverted pendulum control problem is introduced. The method uses a fusion function to reduce the dimension of the system, reducing the number of input variables to solve the fuzzy rule explosion problem. In order to optimize and amend the front-part and later-part parameter of Takagi-Sugeno fuzzy model, a mixed algorithm of backward propagation (BP) and least square method (LSE) algorithm are used. Using the collected original input and output data to establish adaptive neural network fuzzy inference system (ANFIS), and to control the double inverted pendulum system. Simulation results show that the controller is better than the other controller.

In this paper, adaptive network based fuzzy inference system (ANFIS) was used in control applications of different type nonlinear systems as interval type-2 fuzzy logic controller (IT-2FL). Two adaptive network based fuzzy inference systems were chosen to design type-2 fuzzy logic controllers for each control applications. Membership functions in interval type-2 fuzzy logic controllers were set as an area called footprint of uncertainty (FOU), which is limited by two membership functions of adaptive network based fuzzy inference systems; they were upper membership function (UMF) and lower membership function (LMF). The double inverted pendulum, a single flexible link and a flexible link carrying pendulum systems were used to test the performances of designed interval type-2 fuzzy logic controllers. System behaviours were defined by Lagrange formulation and MATLAB/SimMechanics computer simulations. The performances of the proposed controllers were evaluated and discussed on the basis of the simulation results. An experiment set up of flexible link carrying pendulum system was built and used to verify the performance of IT-2FL controller. Key words: Adaptive network based fuzzy inference system, interval type-2, inverted pendulum, a single flexible link, control, simulation.

According to the Lagrange equation, the mathematical model for the double inverted pendulum is first presented. For the fuzzy controller, the dimension of input varieties of fuzzy controller is depressed by designing a fusion function using optimization control theory, and it can reduce the rules of fuzzy sharply, `rule explosion' problem is solved. The result shows that the LQR-Fuzzy logic controller not only has quite good stability, but also be able to make the cart of the pendulum moving to the designed in advance place along the orbit.

A fuzzy controller for stabilizing parallel-type double inverted pendulum system is presented, based on the single input rule modules (SIRMs) dynamically connected fuzzy inference model. By using the SIRMs and the dynamic importance degrees, the angular controls of the two pendulums and the position control of the cart are done entirely in parallel and the priority orders of the three controls are automatically adjusted according to control situations. Simulation results show that the fuzzy controller with a simple and intuitive structure can stabilize completely a parallel-type double inverted pendulum system within 10 seconds. This is the first result for a fuzzy controller to realize complete stabilization of a parallel-type double inverted pendulum system.

A new fuzzy controller for stabilization of parallel-type double inverted pendulum system

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.