Control of Nonlinear Mechatronic Systems

This dissertation is divided into four self-contained chapters. In Chapter 1, an adaptive nonlinear tracking controller for kinematically redundant robot manipulators is presented. Past research efforts have focused on the end-effector tracking control of redundant robots because of their increased dexterity over their non-redundant counterparts. This work utilizes an adaptive full-state feedback quaternion based controller developed in [1] and focuses on the design of a general sub-task controller. This sub-task controller does not affect the position and orientation tracking control objectives, but instead projects a preference on the configuration of the manipulator based on sub-task objectives such as the following: singularity avoidance, joint limit avoidance, bounding the impact forces, and bounding the potential energy. In Chapter 2, two controllers are developed for nonlinear haptic and teleoperator systems for coordination of the master and slave systems. The first controller is proven to yield a semi-global asymptotic result in the presence of parametric uncertainty in the master and the slave dynamic models provided the user and the environmental input forces are measurable. The second controller yields a global asymptotic result despite unmeasurable user and environmental input forces provided the dynamic models of the master and slave systems are known. These controllers rely on a transformation and a flexible target system to allow the master system\u27s impedance to be easily adjusted so that it matches a desired target system. This work also offers a structure to encode a velocity field assist mechanism to provide the user help in controlling the slave system in completing a pre-defined contour following task. For each controller, Lyapunov-based techniques are used to prove that both controllers provide passive coordination of the haptic/teleoperator system when the velocity field assist mechanism is disabled. When the velocity field assist mechanism is enabled, the analysis proves the coordination of the haptic/teleoperator system. Simulation results are presented for both controllers. In Chapter 3, two controllers are developed for flat multi-input/multi-output nonlinear systems. First, a robust adaptive controller is proposed and proven to yield semi-global asymptotic tracking in the presence of additive disturbances and parametric uncertainty. In addition to guaranteeing an asymptotic output tracking result, it is also proven that the parameter estimate vector is driven to a constant vector. In the second part of the chapter, a learning controller is designed and proven to yield a semi-global asymptotic tracking result in the presence of additive disturbances where the desired trajectory is periodic. A continuous nonlinear integral feedback component is utilized in the design of both controllers and Lyapunov-based techniques are used to guarantee that the tracking error is asymptotically driven to zero. Numerical simulation results are presented for both controllers. In Chapter 4, a new dynamic model for continuum robot manipulators is derived. The dynamic model is developed based on the geometric model of extensible continuum robot manipulators with no torsional effects. The development presented in this chapter is an extension of the dynamic model proposed in [2] (by Mochiyama and Suzuki) to include a class of extensible continuum robot manipulators. First, the kinetic energy of a slice of the continuum robot is evaluated. Next, the total kinetic energy of the manipulator is obtained by utilizing a limit operation (i.e., sum of the kinetic energy of all the slices). Then, the gravitational potential energy of the manipulator is derived. Next, the elastic potential energy of the manipulator is derived for both bending and extension. Finally, the dynamic model of a planar 3-section extensible continuum robot manipulator is derived by utilizing the Lagrange representation. Numerical simulation results are presented for a planar 3-section extensible continuum robot manipulator

Online Time Delay Estimation in Delay Differential Equation Based Chaotic Systems

<span style="font-size: 13px; font-family: Helvetica, Arial, sans-serif;">Bu çalismada, gecikmeli fark denklemleri tabanli kaotik sistemlerde zaman gecikmesi kestirimi ele alinmistir. Zaman gecikmesi, sistemin dogrusalligini bozan bir parametre olarak düsünülmüstür. Bu düsünce dogrultusunda, dogrusal olmayan bir kestirim yönteminden faydalanilmistir. Bu yöntem, Lyapunov kararlilik analizlerine dayanmaktadir ve tüm sinyallerin küresel olarak sinirli kalmasini ve kestirim hatasinin sifira yakin bir noktaya yakinsamasini garanti etmektedir. Zaman gecikmesi kestirimi yönteminin etkinligini göstermek için, birbirinden farkli, gecikmeli fark denklemleri tabanli kaotik sistem modelleri kullanilarak birden fazla sayisal benzetim çalismalari yapilmistir. Sayisal benzetim çalismalari sonucunda, yöntemin etkili bir sekilde çalistigi görülmüstür.</span><span style="font-size: 13px; font-family: Helvetica, Arial, sans-serif;">In this work, time delay estimation in delay differential equation based chaotic systems is handled. The time delay is handled as a parameter which effects the system nonlinearly. Under the light of this consideration, a nonlinear parameter estimator is utilized. The aforementioned method is based on Lyapunov stability analysis and assures global boundedness of all the signals and the convergence of the estimation error to the vicinity of zero. Several simulations are given to demonstrate the efficiency of the proposed time delay estimator for various delay differential equation based chaotic systems. From the numerical simulation studies, it is observed that the method works efficiently.</span

A Passivity-based Decomposing Method for Operational Space Control of Kinematical Redundant Tele-operation Systems

In the passivity-based decomposing method, a bilateral tele-operation system is virtually decomposed into 2 sub-systems (shape/locked) to ensure coordination between the master and slave robots and to provide a general referenced motion of the closed-loop bilateral tele-operation along with the passivity of the master and slave robots. So far, the passivity-based decomposing methods in the literature have been studied only for the joint-space control of tele-operation systems with kinematical similar master and slave robots. in this study, a passivity-based decomposing method is proposed for operational space control of bilateral tele-operation systems with kinematic redundancy in the slave robot. The main objectives of the proposed method are to ensure operational space coordination between the robots' end-effector trajectories and to achieve a referenced general movement of the closed-loop tele-operation system. in addition, the kinematic redundancy of the slave robot, which usually complicates the control problem, is turned into an advantage, and secondary tasks are designed for the slave robot. Moreover, experiments are carried out to validate the achievement of the proposed method using a kinematical redundant tele-operation setup.TUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [113-E-147]This work was supported by TUBITAK project no. 113-E-147

Experimental Verification of Lead-Lag Compensators on a Twin Rotor System

Twin rotor system is a laboratory setup resembling a simplified helicopter model that moves along both horizontal and vertical axes. The literature on control of twin rotor systems reflects a good amount of research on designing PID controllers and their extensions considering several aspects, as well as onsome nonlinear controllers. However, there is almost no previous work on design of lag-lead type compensators for twin rotor systems. In this study, by considering this open research problem, lag and lead type compensators are designed and then experimentally verified on the twin rotor system. Specifically, first, lag and lag-lag compensators are designed to obtain a reduced steady state error as compared with proportional controllers. Secondly, lead compensation is discussed to obtain a reduced overshoot. Finally, lag-lead compensators are designed to make use of their favorable properties. All compensators are applied to the twin rotor system in our laboratory. From experimental studies, it was observed that steady state error was reduced when a lag compensator was used in conjunction with a lead compensator

Experimental Verification of Lead-Lag Compensators on a Twin Rotor System

WOS: 000461056600010Twin rotor system is a laboratory setup resembling a simplified helicopter model that moves along both horizontal and vertical axes. The literature on control of twin rotor systems reflects a good amount of research on designing PM controllers and their extensions considering several aspects, as well as onsome nonlinear controllers. However, there is almost no previous work on design of lag-lead type compensators for twin rotor systems. In this study, by considering this open research problem, lag and lead type compensators are designed and then experimentally verified on the twin rotor system. Specifically, first, lag and lag-lag compensators are designed to obtain a reduced steady state error as compared with proportional controllers. Secondly, lead compensation is discussed to obtain a reduced overshoot. Finally, lag-lead compensators are designed to make use of their favorable properties. All compensators are applied to the twin rotor system in our laboratory. From experimental studies, it was observed that steady state error was reduced when a lag compensator was used in conjunction with a lead compensator