A High-Efficient Finite Difference Method for Flexible Manipulator with Boundary Feedback Control

The paper presents a high-efficient finite difference method for solving the PDE model of the single-link flexible manipulator system with boundary feedback control. Firstly, an abstract state-space model of the manipulator is derived from the original PDE model and the associated boundary conditions of the manipulator by using the velocity and bending curvature of the flexible link as the state variables. Then, the second-order implicit Crank-Nicolson scheme is adopted to discretize the state-space equation, and the second-order one-sided approximation is used to discretize the boundary conditions with excitations and feedback control. At last, the state-space equation combined with the boundary conditions of the flexible manipulator is transformed to a system of linear algebraic equations, from which the response of the flexible manipulator can be easily solved. Numerical simulations are carried out to simulate the manipulator under various excitations and boundary feedback control. The results are compared with ANSYS to demonstrate the accuracy and high efficiency of the presented method.

Controller Tuning and Robustness Testing of Attitude Control Laws for a CubeSat Mission

The purpose of this project was to create a test environment that can be used to test different controllers and their robustness. In this report, the equations of motion were derived using kinematics, with attitude quaternions, and spacecraft dynamics, with angular velocity and acceleration. The equations were combined and placed into the form of a linearized state-space equation. The different control methods being investigated, Linear Quadratic Regulator (LQR) for the reaction wheel model, and the Bdot with bias controller, were explained and the block diagram for each was shown. To setup the test, the tolerances for the roll, pitch, and yaw, and their rates, were taken from the mission requirement for the ESSENCE mission. The attitude tolerance being ±0.5deg and the angular rates requirement being ±0.05deg/s. Then the test setup was further explained. The test is broken up into different scripts and steps: 1. Main run function for simulation. Initializes simulation parameters. 2. Build state-space equation and calculate constant gain matrix. 3. Randomize initial conditions and pass onto simulation. 4. Post-processing and plot generation. 5. Statistics generation. This robust testing environment was used to test 5 different controllers for the reaction wheel model. Each controller was tested for 200 different simulations, in which the initial attitude, initial angular rates, and the center of mass were randomized. The first controller was successful for 198/200 simulations, where the only failure came from over-saturating the reaction wheels. The next three controllers had a perfect record and were successful for all 200 simulations each. The last controller, had only 71 successful simulations in the set, and a sample of one of the failed simulations was further investigated to see how it failed.

Controller Tuning and Robustness Testing of Attitude Control Laws for a CubeSat Mission

The purpose of this project was to create a test environment that can be used to test different controllers and their robustness. In this report, the equations of motion were derived using kinematics, with attitude quaternions, and spacecraft dynamics, with angular velocity and acceleration. The equations were combined and placed into the form of a linearized state-space equation. The different control methods being investigated, Linear Quadratic Regulator (LQR) for the reaction wheel model, and the Bdot with bias controller, were explained and the block diagram for each was shown. To setup the test, the tolerances for the roll, pitch, and yaw, and their rates, were taken from the mission requirement for the ESSENCE mission. The attitude tolerance being ±0.5deg and the angular rates requirement being ±0.05deg/s. Then the test setup was further explained. The test is broken up into different scripts and steps: 1. Main run function for simulation. Initializes simulation parameters. 2. Build state-space equation and calculate constant gain matrix. 3. Randomize initial conditions and pass onto simulation. 4. Post-processing and plot generation. 5. Statistics generation. This robust testing environment was used to test 5 different controllers for the reaction wheel model. Each controller was tested for 200 different simulations, in which the initial attitude, initial angular rates, and the center of mass were randomized. The first controller was successful for 198/200 simulations, where the only failure came from over-saturating the reaction wheels. The next three controllers had a perfect record and were successful for all 200 simulations each. The last controller, had only 71 successful simulations in the set, and a sample of one of the failed simulations was further investigated to see how it failed.

Pemodelan dan simulasi boost converter menggunakan Python

Pada Paper ini dirancang model boost converter untuk charging kapasitor pada robot sepak bola beroda. Kapasitor pada kondisi ini digunakan untuk menyimpan energi pada sistem penendang robot. Karena sistem penendang membutuhkan energi yang tinggi, tegangan yang digunakan untukmengisi kapasitor harus tegangan tinggi. Oleh karena itu, pada paper ini akan dibahas pemodelan boost converter dengan tegangan output 350V.Pemodelan akan menggunakan metode averaging untuk membuat 2 persamaan dari 2 kondisi boost converter menjadi 1 persamaan state-space yang mewakili seluruh kondisi dari boost converter tersebut.Dengan memasukkan parameter-parameter yang telah dihitung ke dalam persamaan state-space tersebut akan diuji respon dari sistem boost converter dengan menggunakan simulasi python. Pada kondisi awal boost converter akan disimulasikan menggunakan critical value dari setiap komponen dari hasil perhitungan. Selanjutnya, beban kapasitor akan dirubah menjadi 4700µF sesuai dengan kapasitor yang digunakan pada robot. Dari simulasi tersebut didapatkan bahwa boost converter dengan tegangan output 350V dan menggnakan beban kapasitor 4700uF mampu menuju keadaan stabil pada waktu 0.6 s. In this paper, a boost converter model is designed for charging capacitors on wheeled soccer robots. Capacitors in this condition are used to store energy in the robotic kicking system. Because the system requires high energy, the voltage used to charge the capacitor must be high. Therefore, this paper will discuss the boost converter modeling with 350V output voltage. The modeling will use the averaging method to create 2 equations from 2 boost converter conditions to 1 state-space equation that represents all conditions of the boost converter. By entering the calculated parameters into the state-space equation, the response of the boost converter system will be tested using python simulation. In the initial conditions, the boost converter will be simulated using the critical value of each component from the calculation results. Furthermore, the capacitor charge will be changed to 4700µF according to the capacitor used in the robot. From the simulation, it was found that the boost converter with an output voltage of 350V and using a 4700uF capacitor load was able to go to a stable state in 6s.

A Non-Iterative Integration Scheme Enriching the Solution to the Coupled Maglev Vehicle–Bridge System

A non-iterative integration scheme is presented in this study to enrich the solutions to the coupled equations of the maglev vehicle–bridge system. The proposed integration scheme is composed of two integration methods aiming at providing the solutions to equation of motion and state-space equation. First, the equation of motion of the simply supported girder bridge is transformed by the modal superposition method. Then the state-space equation is used to describe the motions of both the vehicle and the suspension control system, with the associated matrices assembled using the fully computerized approach. By adopting this integration scheme, only pure vector calculations arise in the solution process, regardless of the existence of time-dependent displacement and velocity on the right-hand sides of the two coupled equations. The proposed integration method is of the second-order accuracy with and without damping. Being equipped with adequate numerical dissipation and dispersion, the method also possesses the characteristic of little computing errors, as can be achieved through the use of different pairs of parameters. Finally, numerical simulations have been conducted to assess the influence of different feedback gains, three types of bridges with different lengths, and guideway irregularity on the maglev vehicle–bridge system.

Active Disturbance Rejection Control for Double-Pump Direct-Driven Hydraulics

As a result of the energy crisis and further development of the electro-hydraulic actuator, double-pump direct driven hydraulics (DDH) was brought forward, which mainly comprises a servo motor, double fixed displacement pumps, a differential cylinder, a low-pressurized tank and auxiliary valves. To address the problems caused by uncertain parameters and unknown external disturbances of DDH, this paper proposed a control method adopting active disturbance rejection control (ADRC). Firstly, a mathematical model, including a DDH unit and a micro-crane, was created and modelled in MATLAB/Simulink. Further, the model was verified by measurement. After that, the state-space equation model of the system was derived based on its mathematical model and a third-order ADRC was designed using the constructed system state-space equation. Additionally, tracking-differentiator (TD) was employed to process the input signal transiently to avoid unnecessary oscillations, and the extended state observer (ESO) was used to accurately estimate the influence of the uncertainty and compensate by nonlinear feedback control law (NFCL). Moreover, the proposed ADRC or Proportional–Integral–Differential (PID) control was combined with the mathematical model of a micro-crane. Finally, the simulations were performed under varying loads, and the system position tracking performance were analyzed and compared. The results show that the ADRC can sufficiently suppress the unknown external disturbance, has the advantages of robustness, and improves the position tracking precision.

Stability Analysis for Milling Process with Variable Pitch and Variable Helix Tools by High-Order Full-Discretization Methods

Chatter is one of the significant limitations in the milling process, which may cause poor surface quality, reduced productivity, and accelerated tool wear. Variable pitch and variable helix tools can be used to suppress regenerative chatter. This study extends the high-order full-discretization methods (FDMs) to predict the stability of milling with variable pitch and variable helix tools. The time-periodic delay-differential equation (DDE) with multiple delays is used to model the milling process using variable pitch and variable helix tools. Then, the DDE with multiple delays is reexpressed by the state-space equation. Meanwhile, the spindle rotational period is divided into many small-time intervals, and the state space equation is integrated on the small-time interval. Then, the high-order interpolation polynomials are used to approximate the state term, and the weights related to the time delay are employed to approximate the time-delay term. The second-order, third-order, and fourth-order extended FDMs (2nd EFDM, 3rd EFDM, and 4th EFDM) are compared with the benchmark in terms of the rate of convergence. It is found that the 2nd EFDM, 3rd EFDM, and 4th EFDM converge faster than the benchmark method. The difference between the curves obtained by different EFDMs and the reference curve is very small. There is no need to extend hypersecond FDMs to analyze the stability of milling with variable pitch and variable helix tools.

Random Vibration Analysis of Coupled Three-Dimensional Maglev Vehicle-Bridge System

This paper presents a framework for the linear random vibration analysis of the coupled three-dimensional (3D) maglev vehicle-bridge system. Except for assembling the equation of motion of vehicle only via the principle of virtual work, the fully computerized approach is further expanded to assemble the governing equation of fluctuating current via the equilibrium relation. A state-space equation couples the equation of motion of the vehicle and the governing equation of fluctuating current. The equation of motion of a real three-span space continuous girder bridge is established by using finite element methods. A separated iteration method based on the precise integration method and the Newmark method is introduced to solve the state-space equation for the maglev vehicle and the equation of motion for the bridge. Moreover, a new scheme to application of the pseudoexcitation method (PEM) in random vibration analysis is proposed to maximize the computational efficiency of the random vibration analysis of the maglev vehicle-bridge system. Finally, the numerical simulation demonstrates that the proposed framework can efficiently obtain the mean value, root mean square (RMS), standard deviation (SD), and power spectral density (PSD) of dynamic response for the coupled 3D maglev vehicle-bridge system.