Weclome to ME859 Nonlinear Systems and Control

Presentation (10 minutes) schedule:

Monday April 26: Papers 1, 2, 3, 4, and 9.
Wednesday April 28: Papers 5, 6, 7, and 8.
Friday April 30: Papers 10, 11, 12, and 13.

4-5 papers will be presented in a class at the last week of the class. Each presenter will have 10 minutes for presenting the paper and 2 minutes for answering questions.
Please send me a list of four papers you want to review via email. I will assign two papers back to you considering your choices. Review the two papers according to the suggested criteria in syllabus.

Paper 1: Minimizing the Phase Drift of a MEMS Oscillator by Scott Strachan.

Abstract: This paper attempts to minimize the phase drift of a MEMS oscillator subject to small electronic and thermal noise by finding optimal operating points of its feedback components. The oscillator of interest is implemented as a biased mechanical resonator in a closed loop with 3 electronic compenents: an amplifier, a phase shifter, and an amplitude limiter, which, in this case, is a hard saturator. Using a general model, we find a differential equation approximating the noise-induced dynamics of the phase and from this estimate an optimal amount of phase shifting and amplitude limiting for miniminal phase drift. The main result of this work is that, despite the inability to provide a rigorous solution without a detailed model, a likely minimal phase drift is obtained by setting the phase shifter to $\frac{\pi}{2}$ and the hard saturator so that the nominal amplitude operates at or near the saddle node bifurcation in the transition from softening to hardening in the amplitude response curve.

Paper 2: Linearization and Sliding Mode Control for Robotic Arm by Elbeskri A.M.

Abstract: Even though the control systems have been improved but model uncertainties (modeling error) still have great effect on the system performance. In this paper, I will design a simple sliding mode controller support by state feedback linearization to reduce tracking error in the task Space of four link Puma 560 robotic manipulator. MATLAB simulation will be provided to show the results.

Paper 3: Design and Analysis of Actuated Seat for Cerebral Palsy Research by M. Cody Priess.

Abstract: The focus of this work was the design and analysis of an actuated seat for use in cerebral palsy research. A conceptual design was produced for the seat which would allow rotations to occur on the pitch and roll axes. The dynamics of the seat were analyzed using the Lagrange mechanics and the non-linear equations of motion were derived. Using these equations along with analysis tools for multi-link robot systems, different position-control schemes such as PD or Passivity-based control were explored and the stability of the system was analyzed. Finally, a passivitybased control scheme was selected and implemented, and the response of the physical seat using this control was compared
to the simulated response. It was found that passivity control produced excellent tracking of a sinusoidal trajectory in simulation, and matched very closely with the experimental response.

Paper 4: Rumor Control by Julian von Eye

Abstract: Using a system of equations similar to the evolution of an epidemic like model, the ability to control rumor propagation in small-world networks will be analyzed. Under what conditions this system is bounded will be investigated. These results will be interpreted and discussed to see if and how it can be applied to the real world.

Paper 5: Stability Analysis of Vibrating String Subjected to Sequential Constraint Applications at One Boundary by Assaad Abbass.

Abstract: In this paper we investigated the effect of a sequentially applied constraint at one boundary on the stability of string initially vibrating in the fundamental mode. The constraint is represented by moving scabbard which moves axially along the mean position of the string. The application of the constraint causes work done on the system and this work done could be negative or positive depending on time of the application of the constraint and on the traveled distance of the constraint. The work done decreases or increase the total energy of the system. Hence, the application of the constraint can be implemented as positive or negative damping element. The stability is investigated by choosing the energy expression of the system after application of constraint as Lyapunov candidate function. Thus, the system can be asymptotically stabilized and brought to the equilibrium position over a period of time by using an actuator at on boundary to move the constraint and takes the energy out.

Paper 6: Impedance Controllers Exposed to Nonlinear External Forces by Paul Strefling.

Abstract—It is known that the stability and performance properties of impedance and admittance controllers are complementary in their application. A hybrid system, originally proposed by Ott, Mukherjee and Nakamura [1] was developed to allow continuous switching between both controllers to maximize their performance; interpolating between the two yielded a controller that outperformed impedance and admittance
controllers operating in a stand alone, independent installation. The motivation behind this paper is to investigate the nonlinear behavior of external forces generated from the environment into the system on the impedance controller. With a successful analysis of the impedance controller, future topics will include a similar analysis on the admittance controller and finally the coupling of them.

Paper 7: Coordinated Formation Control for Heterogeneous Multi-Robot Systems by Yunyi Jia.

Abstract: The paper proposes a coordinated formation control method for heterogeneous multi-robot system. The model of heterogeneous multi-robot system is built first. A coordinate reference transformation is used to transform the problem into a tracking problem and a consensus problem. Afterwards tracking and consensus control laws are designed and the stability of the system is analyzed. Simulation results illustrate the effectivenessand correctness of system.

Paper 8: Nonlinear Orientation Estimation Using Low Cost Sensors by Jianguo Zhao.

Abstract—As the advancement of microelctromechanical system (MEMS) technology, lots of low cost motion sensors, including accelerometers, gyroscopes, and magnetometers, are widely available nowadays. Accompany with the low cost nature, each sensor also suffers from low-resolution and high noise. To overcome such disadvantage, this project aims to combine those motion sensors to build a sensor system which can robustly estimate the orientation of a rigid body. Based on a combination of a tri-axis accelerometer, tri-axis gyroscope, and a tri-axis magnetometer, the nonlinear extended Kalman filter is used to perform the desired orientation estimation. The filter will be established based on both Euler angle and quaternion parameterizations of orientation. Simulations are performed to evaluate the filters’ performance. Preliminary experimentalsetup is also described.

Paper 9: Design of power electronics DC to DC converters using nonlinear systems strategies by Jorge G. Cintron-Rivera.

Abstract— Nonlinear behavior is present in all power electronics converters. The sources of Nonlinearity in power electronics are primarily due to the switching components, such as transistors and diodes, and most importantly the control input is a nonlinear pulse-width function. When designing a power converter it is a common practice to linearize the transfer function to come with an average linear system, which is easy to deal with. Since power electronics converters are rich in nonlinearity, it would be wise to analyze and design them using nonlinear system theory. This paper shows how to design a DC to DC converter using nonlinear systems, with this strategy important characteristics are modeled, such as voltage and current ripples. When linearization is preformed these important behaviors are lost. Phase-plane portraits, bifurcation, Lyapunov stability equations, passivity, etc. are key worlds in the nonlinear design of a power converter.

Paper 10: Nonlinear Ship Control by Azizah Muhammad.

Abstract— This paper investigates the control of an ocean vehicle, which involves making the vessel follow a desired trajectory. There are many types of ocean vehicles, but for simplicity, this paper considers slow-moving surface ships in calm waters. Lyapunov stability theory is used to design an observer-based controller. The observer-based controller estimates the unknown state of the system. The author uses SIMULINK to test the reliability of the design. It is found that nonlinear control theory – rather than performing linearization on a nonlinear system and applying linear theory – works well in this case.

Paper 11: Nonlinear Feedback Control of the Acrobot Robot Arm by Michael Farmer.

Abstract: The acrobot is an underactuated, two linkage, robot arm. This paper examines the nonlinear dynamics of the acrobot. We will also investigate the control difficulties and control stragegies involved in the acrobotproblem.

Paper 12: Nonholonomic Wheeled Mobile Robot Control using Feedback Linearization by Jerome Yancy.

The problem of motion planning and control of nonholonomic wheeled mobile robots has attracted the interest of researchers in view of its academic challenges. The purpose of this project is to evaluate the motion control problem of wheeled mobile robots (WMRs) in environments without obstacles. Using WMRs, it will be shown that dynamic feedback linearization is an efficient design tool to solve the trajectory tracking problem. To assess the quality of the proposed controller, several simulations will be ran to validate the control design.

Paper 13: Vehicle Speed Feedback Linearization Control by Xuefei Chen.

Abstract: This paper describes the application of feedback linearization techniques to control the cruise speed of an automobile. The objective of the vehicle cruise control is to maintain the speed at a set-up value by providing proper traction force for different road conditions and different wind disturbance, etc. The vehicle dynamic model is simplified for analysis purpose. The result shows the feedback linearization controller provides good dynamics performance for the automobile.

Please submit your pdf version of the project paper via email to the instructor.
Exam #2 will be given on Monday April. 19th. The scope will cover material upto lectures on April 12th.

Read again on the overall description about the project from syllabus.
Project submission deadlines:

Abstract submission deadline: Friday March 19.
First submission deadline: Monday April 12.
Presentation: Monday April 26, Wednesday April 28, Friday April 30.
Review submssion deadline: Friday April 30.
Final submission deadline: Monday May 3.