Optimal control of motion of the system based on mathematical pendulum with constant length

U radu se razmatra premeštanje matematičkog klatna (sa osvrtom na primenu pri modeliranju dizaličnih postrojenja) iz stanja kretanja tačke vešanja konstantnom brzinom u stanje mirovanja za unapred zadato vreme sa prigušivanjem oscilacija na kraju procesa. Rešenja se traže primenom Pontriagin-ovog principa maksimuma i adaptivnog odnosno digitalnog metoda prigušivanja oscilacija. Kao upravljačka veličina u oba slučaja koristi se ubrzanje tačke vešanja matematičkog klatna. Razmatran je slučaj sa konstantnom dužinom matematičkog klatna.The paper discusses the motion of the mathematical pendulum (with reference In the transportation machines modeling), from the stale o/ constant velocity motion of the suspension point to the stale of rest for the pre-assigned time with damping of oscillations at the end of the process. Solutions of the task were found by application of the Pontryagin's principle of maximum, and adaptive and digital methods of oscillations damping. Acceleration of the suspension point of the mathematical pendulum is used as the control value in all cases. The case of the constant length of the mathematical pendulum is discussed

Optimal control of motion of the system based on mathematical pendulum with constant length

U radu se razmatra premeštanje matematičkog klatna (sa osvrtom na primenu pri modeliranju dizaličnih postrojenja) iz stanja kretanja tačke vešanja konstantnom brzinom u stanje mirovanja za unapred zadato vreme sa prigušivanjem oscilacija na kraju procesa. Rešenja se traže primenom Pontriagin-ovog principa maksimuma i adaptivnog odnosno digitalnog metoda prigušivanja oscilacija. Kao upravljačka veličina u oba slučaja koristi se ubrzanje tačke vešanja matematičkog klatna. Razmatran je slučaj sa konstantnom dužinom matematičkog klatna.The paper discusses the motion of the mathematical pendulum (with reference In the transportation machines modeling), from the stale o/ constant velocity motion of the suspension point to the stale of rest for the pre-assigned time with damping of oscillations at the end of the process. Solutions of the task were found by application of the Pontryagin's principle of maximum, and adaptive and digital methods of oscillations damping. Acceleration of the suspension point of the mathematical pendulum is used as the control value in all cases. The case of the constant length of the mathematical pendulum is discussed

The application of input shaping to a system with varying parameters

The original input shaping technique developed by Singer and Seering is summarized and a different definition for residual vibration is proposed. The new definition gives better insight into the ability of input shaping method to reduce vibration. The extension of input shaping to a system with varying parameters, e.g. natural frequency, is discussed and the effect of these variations is shown to induce vibration. A modified command shaping technique is developed to eliminate this unwanted motion

Shaping Inputs to Reduce Vibration: A Vector Diagram Approach

This paper describes a method for limiting vibration in flexible systems by shaping the system inputs. Unlike most previous attempts at input shaping, this method does not require an extensive system model or lengthy numerical computation; only knowledge of the system natural frequency and damping ratio are required. The effectiveness of this method when there are errors in the system model is explored and quantified. An algorithm is presented which, given an upper bound on acceptable residual vibration amplitude, determines a shaping strategy that is insensitive to errors in the estimated natural frequency. A procedure for shaping inputs to systems with input constraints is outlined. The shaping method is evaluated by dynamic simulations and hardware experiments

Manipulation strategies for massive space payloads

The industrial and environmental applications for robots with a relatively large workspace has increased significantly in the last few years. To accommodate the demands, the manipulator is usually designed with long, lightweight links that are inherently flexible. Ongoing research at Georgia Tech into the behavior and design of these flexible links is discussed

Modeling and control of a two-arm elastic robot in gravity

This thesis develops and experimentally verifies a model of a two arm robot with highly elastic arms. The model is later used in this research to evaluate control algorithms. The model includes the effects of gravity. The dimensions of the arms are chosen to maximize the coupling between the flexible and large scale motion of the robot. The model is then linearized and a new analytical solution is presented for the natural frequencies and mode shapes of the robot at given equilibrium positions. This analytical solution is then compared to the assumed mode shape solutions to determine the accuracy relative to the number of assumed modes included in the model. An experimental test rig is built and tests are conducted to verify the model. A number of different amounts of end mass and torsional stiffness at the joints are used during the validation. For 12 cases tested, the measured first four natural frequencies are within ±7% of the frequencies predicted by the model with an average error of only 2.89%. Finally, the model is used to design a control algorithm for end effector control of the robot using a torque input at each of the two joints. An optimal control algorithm developed using LQR with the prescribed degree of stability method results in effective end effector control with short response time and little overshoot

Innovations in Rotary Drill Bit Design to Reduce Vibration and Improve Durability

Well drilling is an important process for extracting oil, natural gas, water, and mineral materials. Opening wells requires boring through earth formations, which can range from very soft to very hard. Penetrating into such formations requires specialized tools and operation procedures which should be employed based on the environment and application. Rotary drilling, in which a drill bit is used to crush the rock and penetrate into the formation, is one of the main methods of well drilling. Rotary cone bits are one of the main types of drill bits used for rotary drilling. There are two main problems encountered when drilling with rotary cone bits. Excessive vibration can cause damage to the entire system and can decrease efficiency of the drilling process. Failure of the bit’s bearings and seals can also result in damage to the bit and cessation of the drilling process. In recent years, a great deal of research has been undertaken to address these problems and find appropriate solutions to improve drilling efficiency and production rate while reducing the overall cost of drilling. In this thesis, a new design for rotary cone bits, with the objective of improving overall drilling performance, is presented. First, a new pattern for distribution of inserts over the cone is presented, which results in reduced vibration of the drillstring. Second a new design for the bit’s bearings is introduced that is capable of operating in harsh environments. Finally, an experimental set-up is introduced to evaluate the performance of the proposed designs

Dynamic modeling, property investigation, and adaptive controller design of serial robotic manipulators modeled with structural compliance

Research results on general serial robotic manipulators modeled with structural compliances are presented. Two compliant manipulator modeling approaches, distributed and lumped parameter models, are used in this study. System dynamic equations for both compliant models are derived by using the first and second order influence coefficients. Also, the properties of compliant manipulator system dynamics are investigated. One of the properties, which is defined as inaccessibility of vibratory modes, is shown to display a distinct character associated with compliant manipulators. This property indicates the impact of robot geometry on the control of structural oscillations. Example studies are provided to illustrate the physical interpretation of inaccessibility of vibratory modes. Two types of controllers are designed for compliant manipulators modeled by either lumped or distributed parameter techniques. In order to maintain the generality of the results, neither linearization is introduced. Example simulations are given to demonstrate the controller performance. The second type controller is also built for general serial robot arms and is adaptive in nature which can estimate uncertain payload parameters on-line and simultaneously maintain trajectory tracking properties. The relation between manipulator motion tracking capability and convergence of parameter estimation properties is discussed through example case studies. The effect of control input update delays on adaptive controller performance is also studied

Improved performance of hard disk drive servomechanism using digital multirate control

Ph.DDOCTOR OF PHILOSOPH