Flatness-based MPC and observer design for PDE systems

• Applicant: Professor Dr.-Ing. Thomas Meurer
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 274852737

The building sector is considered as one of the largest energy consumers with more that 80% of the provided energy spent for building operation during the building life cycle. In view of this, automation, control and optimization can be identified as key ingredients to achieve energy efficient building operation. Since buildings inherently evolve along multiple time and spatial scales, mathematical modeling typically leads to a system representation in terms of partial differential equations (PDEs). Based on this distributed-parameter system description, this project aims at the development of flatness-based optimal and model predictive control (MPC) design methods for PDEs. This includes the design of state observers to enable the realization of the MPC schemes as well as the efficient numerical implementation using appropriate reduced-order models. Here, the flatness property of the distributed-parameter system is exploited to deduce methods for optimal control by reducing the dynamic optimal control problem with PDE, state and input constraints to a constrained static optimal control problem in the flat output trajectory and its derivatives. With this, it on the one hand desired to address optimal trajectory planning and feedforward control for PDE systems. On the other hand, this parametrized static optimization problem constitutes the basis to develop stabilizing MPC schemes for PDE systems. In addition to the combination of the determined optimal feedforward control with suitable feedback control strategies to stabilize the distributed-parameter error system, the degrees-of-freedom introduced in the flat output trajectory can be determined consecutively by introducing an appropriate optimization horizon. This leads to a flatness-based receding horizon algorithm, whose closed-loop stability properties will be addressed using Lyapunov techniques. These analytic design techniques are merged with methods of approximation and model order reduction, which leads to computationally efficient semi-numeric design approaches. Here, special emphasis will be given to schemes that preserve the flatness property from the PDE system to the ODE representation. Observer design is based on the extension of backstepping-based approaches and moving horizon estimation to semilinear PDEs with higher-dimensional spatial domain. This will include a rigorous functional analytic formulation and the incorporation of approximation methods to address real-time capabilities. The developed methods will be evaluated for the example of energy efficient building operation. For this, models of different complexity will be considered in simulation scenarios starting from the representation of a single room influenced by thermal control (vents) to interconnected rooms with convective exchange of mass and thermal energy.

• DFG Programme: Research Grants
• Cooperation Partners: Professor Dr. Lars Grüne; Professor Dr. Stefan Volkwein