Model Predictive Control of Dissipative Distributed Parameter Systems

• Author / Creator

  Liu, Liu

• Distributed parameter systems (DPSs) are distinguished by the fact that the states, controls, and outputs may depend on spatial position. The certain class of dissipative DPSs includes many underlying chemical and mechanical spatiotemporal phenomena such as chemical reactions, convection and diffusion, flexible structures and certain wave propagation problems, all of which can be described by partial differential equations (PDEs). In the past decade, considerable work has concentrated on the construction of a general framework of reduced-order control synthesis for PDEs systems arising from the modeling of DPSs on the basis of low-order ODEs models which are derived by spectral decomposition schemes. Among those control synthesis, model predictive control (MPC) is a popular and widely used method because of its ability to account for input and state constraints. However, these works did not address completely the problem of state constraints in the predictive controller design for either the PDE systems with non-self-adjoint operators or the PDE system describing flexible structures. Furthermore, almost all the existing MPC designs for DPSs are developed in an implicit form and implemented in an on-line way, which leads to the numerically-determined control actions and relatively large computational effort.

  This thesis presents a MPC scheme for the parabolic PDE system where a convective term is included in the operator to describe the convective heat and mass transfer which makes the operator non-self-adjoint as well as a MPC scheme for the flexible structural system described by a fourth-order PDE, and an explicit/multi-parametric MPC scheme for dissipative PDE systems. First, a MPC scheme which accounts for the input and state constraints is proposed for the parabolic PDEs system describing the axial dispersion chemical reactor. Subsequently, an approach is proposed to approximate the infinite-dimensional representation of Euler-Bernoulli beam system by a reduced-order finite-dimensional model, and the proposed MPC scheme is implemented on the reduced-order beam system. Following this, an explicit MPC scheme, which is solved off-line, is proposed to stabilize the certain class of dissipative PDE systems as well as guarantee the input and state constraints.

• Subjects / Keywords

  • Distributed parameter systems
  • Model Predictive Control
  • Input/state constraints

• Graduation date

  Spring 2015

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3VT0W

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.