How good is quantized model predictive control with horizon one?

Model Predictive Control is increasingly being used in areas where decision variables are constrained to finite or countably infinite sets. Well known fields include Power Electronics, Signal Processing, and Telecommunications. Typically, the applications utilize high speed sampling and, thus, there is an incentive to reduce computational burden. One way of achieving this is to use small optimization horizons. This raises the question as to the optimality and performance of control laws with short horizons. In this paper, we give necessary and sufficient conditions for horizon one quantized model predictive control to be equivalent to the use of larger horizons. We also explore situations where horizon one is near optimal

Control of Lithium-Ion Battery Warm-up from Sub-zero Temperatures

The archetype of rechargeable technology, Li-ion batteries have over the last decade benefited from improvements in material science through increased energy and power density. Although widely adopted, these batteries suffer from significant performance degradation at low temperatures, posing a challenge for automotive applications, especially during vehicle start-up. This begs the question: if one was to seek an energy optimal warm-up strategy, how would it look? Moreover, if as much as 22% of reduction in range of electric vehicles is attributable to onboard battery heating systems, would an optimal heating strategy alleviate this energy drain and at what drawback? This thesis addresses these questions. To that end, we pose and solve two energy-optimal warm-up strategies in addition to developing tools that will enable one to make prudent decisions on whether warm-up is feasible if the battery energy state falls too low. In this dissertation, we address the four main aspects of control design modeling, control, verification and adaptation. There are two primary control strategies that are designed in this dissertation and tools to analyze them are developed. The first warm-up scenario involves a receding horizon optimal control problem whose objective trades-offs increase in battery's temperature by self-heating against energy expended. The shape of battery current is restricted to be bi-directional pulses that charge and discharge the cell at relatively high frequencies via an external capacitor. The optimal control problem solves for the amplitude of the pulse train and the results clarify issues associated with capacitor size, time and lost energy stored. The second control policy is deduced by solving an optimal discharge control problem for the trajectory of power that could self-heat the cell and at the same time feed an external heater whilst minimizing the loss in state of charge. Batteries inevitably age as they are used and consequently their dynamics also change. Since both proposed methods are model based, the last of part of this dissertation proposes a novel augmented-state-space partitioning technique which can be used to design cascaded nonlinear estimators. Using this partitioning technique, the relative average estimability of the different states of the electrical and thermal model is studied and Dual Extended Kalman Filters are built and validated in simulations. All the methods developed are demonstrated via a combination of simulation and experiments on Iron Phosphate or Nickel Manganese Cobalt Li-ion battery cell which have high power capability and could be used in replacement of 12V starter batteries or 48V start-stop applications.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/136964/1/elemsn_1.pd