by Kanya Rattanamongkhonkun, Ph.D. Student
Advisor: Assoc. Prof. Dr. Radom Pongvuthithum
Research Overview
Control designs for nonlinear systems have been studied for a few decades. More and more researchers are interesting in nonlinear control systems. This is because nonlinearities naturally arise in many physical systems such as robotic systems, physical systems with friction, chemical processes and economics model with chaotic behavior.
Even though, there are many techniques that allow linear control design to be applied to nonlinear system, they often involve some forms of approximation such as linearization and treating the nonlinear terms as disturbances or assume that the nonlinear terms is precisely known so that feedback linearlizable is applicable. Therefore, unless the parameters or the structures of the nonlinear system are precisely known, global stability usually cannot be proved. Moreover, there are several types of systems that cannot be stabilized by linear control law. A well-known example is a class of chain of power integrators, a lower triangular system which the power of states in the chain of integrators are not equal to one. This class of system cannot be stabilized by any linear controller even locally since the linearized system might have unstable and uncontrollable modes. In addition, employing nonlinear control design can achieved a different type of stability such as finite-time stability. This type of stability cannot happen in a linear system since the system trajectories will be equal to zero in finite time. This implies that the solution of the system is not unique.
Practically, it is very difficult to obtain an exact model of a real system. This may be due to the lack of actual information of the real system, changing of parameters values due to different environment operation, or even deterioration of the system over time, etc. Thus, system models usually contain errors or uncertainties.
Another interesting topic in control is time-delay nonlinear uncertainties. This phenomenal can be found in chemical process where a system of chemical reactor can be modeled as a nonlinear system with time-delay uncertainty. Also, the time-delay can be found in machining processes such as milling process and turning. Although, in machining processes, the time-delay can be measured from the spindle speed, cutting speed can be varied greatly.
In this work, we focus on designing a control law which can deal with both nonlinearly unknown parameters and time-delay uncertainties in the same time. Moreover, our control design is not only able to handle the time-delay uncertainties but is independent of time-delay information which is more robust and flexible in the implementation.
Objective
To construct a time-delay free controller for a class of time-delay triangular systems with nonlinearly unknown parameters which can guarantee the boundedness of all closed-loop trajectories and convergence of the system states.
Publications
- Pongvuthithum, K. Rattanamongkhonkun and W. Lin. “Asymptotic regulation of time-delay nonlinear systems with unknown control directions.” IEEE Transaction on Automatic Control, vol. 63(5), pp. 1495-1502, 2018. doi:10.1109/TAC.2017.2748898.
- Rattanamongkhonkun, R. Pongvuthithum and W. Lin. “Nonsmooth feedback stabilization of a class of nonlinear systems with unknown control direction and time-delay.” International Journal of Robust and Nonlinear Control, (Accepted), 2018. doi:10.1002/rnc.4317
- Wei Lin, K. Rattanamongkhonkun and Radom Pongvuthithum. “LgV-type adaptive controllers for non-affine systems with parametric uncertainty.” IEEE Transaction on Automatic Control, (Accepted)
- Rattanamongkhonkun, R. Pongvuthithum, W. Lin and G. Tao. “Feedback stabilization of nonlinear systems with unknown control directions and time-delay.” Asian Control Conference (ASCC 2017), pp. 138-143 2018. doi:10.1109/ASCC.2017.8287156. Gold Coast Convention and Exhibition CentreGold Coast, Australia, December 17-20, 2017.
- Rattanamongkhonkun, R. Pongvuthithum and W. Lin. “global stabilization of a class of time-delay nonlinear systems with unknown control directions by nonsmooth feedback.” IFAC-PapersOnLine, vol. 51(14), pp. 78-83, 2018. doi:https://doi.org/10.1016/j.ifacol.2018.07.202. 14th IFAC Workshop on Time Delay Systems (IFAC TDS 2018), Budapest, Hungary, June 28-30, 2018.
- Wei Lin, K. Rattanamongkhonkun and Radom Pongvuthithum. “Adaptive stailization of cncertain non-affine systems with nonlinear parameterization.” 18th IFAC Symposium on System Identification (SYSID 2018), Stockholm, Sweden, July 9-11, 2018.
Acknowledgement
This work is supported by The Royal Golden Jubilee Ph.D. Program (RJG).