Observation and control of a ball on a tilting
The ball and plate system is a nonlinear MIMO system that has interesting characteristics which are also present in aerospace and industrial systems, such as: instability, subactuation, nonlinearities such as friction, backlash, and delays in the measurements. In this work, the modeling of the sy...
| Autor Principal: | Contreras Martinez, Dimel Arturo |
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| Formato: | Tesis de Maestría |
| Idioma: | Inglés |
| Publicado: |
Pontificia Universidad Católica del Perú
2017
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| Materias: | |
| Acceso en línea: |
http://tesis.pucp.edu.pe/repositorio/handle/123456789/9641 |
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| Sumario: |
The ball and plate system is a nonlinear MIMO system that has interesting characteristics
which are also present in aerospace and industrial systems, such as: instability, subactuation,
nonlinearities such as friction, backlash, and delays in the measurements.
In this work, the modeling of the system is based on the Lagrange approach. Then it is
represented in the state-space form with plate accelerations as inputs to the system. These
have a similar effect as applying torques. In addition, the use of an internal loop of the servo
system is considered. From the obtained model, we proceed to carry out the analysis of
controllability and observability resulting in that the system is globally weak observable and
locally controllable in the operating range. Then, the Jacobi linearization is performed to use
the linearized model in the design of linear controllers for stabilization.
On the other hand, analyzing the internal dynamics of the ball and plate system turns out
to be a non-minimum phase system, which makes it difficult to design the tracking control
using the exact model. This is the reason why we proceed to make approximations. Using the
approximate model, nonlinear controllers are designed for tracking using different approaches
as: feedback linearization for tracking with and without integral action, backstepping and
sliding mode. In addition, linear and nonlinear observers are designed to provide full state
information to the controller.
Simulation tests are performed comparing the different control and observation approaches.
Moreover, the effect of the delay in the measurement is analyzed, where it is seen that the
greater the frequency of the reference signal the more the error is increased. Then, adding the
Smith predictor compensates the delay and reduces the tracking error.
Finally, tests performed with the real system. The system was successfully controlled for
stabilization and tracking using the designed controllers. However, it is noticed that the effect
of the friction, the spring oscillation and other non-modeled characteristics significantly affect
the performance of the control. |
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