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Controlling the Secondary Mirror of a Reflective Telescope Using a Controlled Stewart Platform

Mahdieh, Jalal | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: English
  3. Document No: 49605 (58)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Salarieh, Hassan; Khayyat, Ali Akbar
  7. Abstract:
  8. Reflective telescopes are devices which commonly use two mirrors, to gather and reflect light rays. In these types of telescopes, the main responsibility of the secondary mirror is to lead the reflected light from primary to detection place. The purpose of this project is to adjust the secondary mirror’s position to reduce the optical errors. So, we are going to study the M2 unit of the telescope. The M2 unit consists of a Hexapod made with six linear actuators in the conventional 3-3 arrangement, and its function is the accurate positioning of the secondary mirror. The main performance required for the M2 unit is the active mirror position adjustment in 5 axes to compensate the existing aberration at the entering wavefront of light rays to the telescope. Then, we are going to discuss the optical aspects of this problem. So that, we will describe the nature and the way of the emitting of the wavefront. The purpose of an optical imaging system is to gather light rays from a point source and redirect them in such a way that the rays converge to a point called an image. Then we will refer to the Zernike polynomials. The Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. They play an important role in optical sensors. The wavefront sensor can calculate the coefficients of the Zernike expansion. Therefore, the sensor can announce the amount of each kind of aberrations. Our main purpose is to omit the aberrations Tip/Tilt, Defocus, and Coma which are the main kinds of aberrations which can be controlled by the M2 unit. For controlling the system, we are going to discuss the inverse kinematics and the dynamics of the Stewart platform. This discussion has an important role on the platform moving control. By using the inverse kinematics and having the position of the moving plate, we can gain the length of each limb that is the desired purpose in this project, because the position of the platform is determined using the optical parameters. In this project a linear PID control and a nonlinear sliding mode control are designed for controlling the hexapod of the M2 unit. PID controller is a linear controller, but Sliding mode controller is a non-linear one that can show robustness against the uncertainty of dynamical systems. The significant achievement of this project is to achieve the permissive tracking error for optical system performance in removing the aberration which is about 1µm
  9. Keywords:
  10. Stewart Platform ; Aberration Coefficient ; Telescope Mirror ; Locomotion Control ; Secondary Mirror ; Vista Telescopes

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