Real-Time Optimization for Estimation and Control: Application to Waste Heat Recovery for Heavy Duty Trucks

Abstract

This thesis aims at the investigation and development of the control of waste heat recovery systems (WHR) for heavy duty trucks based on the organic Rankine cycle. It is desired to control these systems in real time so that they recover as much energy as possible, but this is no trivial task since their highly nonlinear dynamics are strongly affected by external inputs (disturbances). Additionally, nonlinear operational constraints must be satisfied. To deal with this problem, in this thesis a dynamic model of a WHR that is based on first principles and empirical relationships from thermodynamics and heat transfer is formulated. This model corresponds to a DAE of index 1. In view of the requirements of the employed numerical methods, it includes a spline-based evaluation method for the thermophysical properties needed to evaluate the model. Therewith, the continuous differentiability of the state trajectories with respect to controls and states on its domain of evaluation is achieved. Next, an optimal control problem (OCP) for a fixed time horizon is formulated. From the OCP, a nonlinear model-predictive control (NMPC) scheme is formulated as well. Since NMPC corresponds to a state feedback strategy, a state estimator is also formulated in the form of a moving horizon estimation (MHE) scheme. In this thesis, we make use of efficient numerical methods based on the direct multiple shooting (DMS) method for optimal control, backward differentiation formulae for the solution of initial value problems for DAE, and the corresponding versions of the real-time iteration (RTI) scheme in order to approximately solve the OCP and implement the MHE and NMPC schemes. The simultaneous implementation of NMPC and MHE schemes based on RTI has been already proven to be stable in the control literature. Several numerical instances of the DMS method for the proposed OCP, NMPC and MHE schemes are tested assuming a given real-world operation scenario consisting of truck exhaust gas data recorded during a real trip. These data have been kindly provided by our industry cooperation partner Daimler AG. Additionally, the PI and LQGI control strategies, of wide-spread use in the literature of control of WHR, are also considered for comparison with the proposed scheme. An important result of this thesis is that, considering the highest energy recovery obtained from both strategies as a reference for the given operation scenario, the proposed NMPC scheme is able to reach an additional energy generation of around 3% when the full state vector is assumed to be known, and its computational speed allows it to update the control function in times shorter than the considered sampling time of 100 [ms], which makes it a suitable candidate for real-time implementation. In a more realistic scenario in which the state has to be estimated from noisy measurements, a combination of both aforementioned NMPC and MHE schemes yields an additional energy generation of around 2%. Concretely, this thesis presents novel results and advances in the following areas: • A first principles DAE model of the WHR is presented. The model is derived from the energy and mass conservation considerations and empirical heat transfer relationships; and features a tailored evaluation method of thermophysical properties with which it possesses the property of being at least continuously differentiable with respect to its controls and states on its whole domain of evaluation. • A new real-time optimization control strategy for the WHR is developed. It consists of an NMPC strategy based on efficient simulation, optimization and control tools developed in previous works. The scheme is able to explicitly handle nonlinear constraints on controls and states. In contrast to other NMPC instances for the WHR found in the literature, our scheme's efficient numerical treatment make it real-time feasible even if the full nonlinear WHR dynamics are considered. • To the author's knowledge, this is the first implementation that considers both the NMPC and the MHE approaches used simultaneously in the control of the WHR. The combination of NMPC and MHE produces a closed-loop, model-based implementation that can treat realistic measurements as inputs and calculates the corresponding control functions as outputs.