By Wasin Wongkum
Advisor: Assoc. Prof. Theeraphong Wongratanaphisan

Delta Robot

Delta Robot is a popular parallel robot which has 3 degree-of-freedom. It is used widely for packaging industry. The advantages of the Delta robot are high strength, high agility, low inertia and high precision making it suitable for high-speed & high-precision applications. Typically, parallel robot has complicated kinematic. However, the kinematic of Delta robot is quite simple.

Most Delta robots are symmetric in its structure i.e., each legs is installed on the base 120 degrees apart. For this the workspace of the robot is symmetric. However, in some applications, it may occur that the task space are not necessarily symmetric. This project focuses on synthesis of an asymmetric Delta robot.

Objective

• To study effects of the kinematics and workspace of the Delta robot which has different arm length and arm angles.
• To synthesize an asymmetric Delta robot optimized for a certain workspace.

by Prapon Ruttanatri, Ph.D. student

Advisor:  Assoc. Prof. Dr. Matthew O.T. Cole

Description of project

Active control of structural vibration in machining processes to prevent dynamic instabilities and chatter is the main issue for this project. A controller design is proposed based on a multi-mode description of flexible structure dynamics combined with cutting process equations that capture time-delayed feedback effects. A method for robust delayed-state feedback control synthesis is presented based on Lyapunov-Krasovskii functionals (LKFs).

Objective

To develop and compare controller design methodologies for active control of regenerative vibration in machining processes in order to improve/increase operating regions for stable cutting. The main focus is on the use of modern robust controller design methodologies and new techniques for controller design based on combined models of machine structure flexibility and cutting force generation mechanisms.

Hardware-in-the-loop evaluations overview:

The experimental system used for this study (Fig. 1) has been designed to exhibit two main structural resonances and is dynamically similar to an AMB-equipped milling spindle that exhibits significant cutting tool flexibility. The main structure is a flexure-pivoted beam connected to an end-mass through another flexure pivot. Two non- contact electromagnetic actuators are used to apply forces to the structure. Hardware-in-the loop simulation and controller testing for machining vibration can be undertaken based on the configuration shown in the block diagram Fig. 2. In this scheme, actuator 2 is an auxiliary actuator used to apply a simulated cutting force that is computed in real-time using a cutting force model implemented within the control hardware. This also requires real-time measurement of the “tool” displacement. Actuator 1 is the control actuator and is used to apply the stabilizing control forces. Note that, as the cutting force model is implemented digitally on the control hardware, the cutting model can be selected freely, subject to limits of actuator force capacity and bandwidth. Displacement of the structure can be measured by two non-contact sensors positioned close to the actuators. Additional vibration measurements are obtained by strain gauges at the flexure locations. Integration of strain sensing in spindle bearing guides has been considered for the purpose of tool deflection compensation. However, in the present case the signals provide dynamic state information related to tool deflection that can be used for feedback control of vibration. Displacement measured at the cutting location is used for calculation of the simulated cutting force but is not used for feedback. Full state information is obtained by combined use of the displacement and strain sensors located away from the “tool” end.

Publication:

• Prapon Ruttanatri, Matthew O.T. Cole and Radom Pongvuthithum, “Stabilizing Active Vibration Control of Machining Processes Based on Lyapunov-Krasovskii Functionals for Time-Delay Systems”, The 7th TSME International Conference on Mechanical Engineering, Chiang Mai, Thailand, page no. 152, December 13-16, 2016
• Prapon Ruttanatri, Matthew O.T. Cole and Radom Pongvuthithum, “Structural vibration control using delayed state feedback via LMI approach – with application to chatter stability problems” SAGE

Acknowledgement:

This work was partly supported by the RGJ-PhD scholarship program under the Thailand Research Fund (grant number PHD/0089/2553).

by Boonruk Suchaitanawanit, Ph.D. student

Advisor: Assoc. Prof. Matthew Cole

Time-Optimal Control

Nowadays many engineering operations require rapid movement with high precision. To acquire maximal speed of motion, an extreme value of actuation effort is employed which could lead to excitation of the flexible mode causing undesired vibration. The time interval can be minimized by a bang-bang control. However, with correct timing of switching action. vibration can be minimized. In this research, we focused on finding the correct timing for the switching action whist minimizing the interval of motion. Real world applications of time-optimal control includes motion of the flexible structures are such as hard-disk drive, crane and spacecraft structures.

 Structural Optimization

Conventionally, mechanical structure design and controller design are separate procedure. By combining two processes together, a better performance of the system could be achieved. A structure whose parameters are compatible with the tasks, might achieve better time performance the one that are not. The selected case study in this research involves tuning a stiffness of the flexible structure to match with the travelling distance associate with time-optimal motion.

Objective

The objective of the project is to develop a new mathematical strategy based on the convexity of the reachable set in order to solve time-optimal control problem. The proposed algorithm can guarantee the true optimality of the control solution since it solves directly for co-state variables which satisfy the necessary conditions rather than searching for switching time and later verify the optimality by using Pontryagin’s Minimum Principle. Figure 1 shows the example of the reachable set of 3 states linear model of the flexible structure.

The system along with time-optimal control solutions acquired by the proposed algorithm will be tuned to achieve even faster motion. The tuning algorithm uses iterative scheme to alter the structural parameters and control profile in order to reduce the motion interval. By exploiting the continuity of the reachable set the iterative tuning method based on the steepest descent gradient searching is able to move toward the local minimum.

The obtained solution was verified and applied on the experimental rig (fig. 2). Here linear translation of the crane-like structure with flexible armature is to provide vibration free rest-to-rest motion. Solution are shown in figure 3. The rig has tunable stiffness mechanism which allows natural frequency and damping ratio of the flexible link to be tuned for verifying the simulation results.

Publication

• B. Suchaitanwanit and M.O.T Cole, “An Algorithm to Obtain Control Solutions Achieving Minimum-Time State Transfer of Linear Dynamical System Based on Convexity of The Reachable Set”, In Proceeding of the 4^th International Conference on Intelligent Systems, Modeling and Simulation, Vol. 1, pp. 340-345, 2013.
• B. Suchaitanwanit and M.O.T Cole, “Fundamental Limit of Performance in Minimum-Time Motion Control due to Structural Flexibility”, In Memoirs of Muroran Institution of Technology, Vol. 6, pp. 7-12, 2013.