Combined plant and control optimization: Theory, strategies and applications

In designing “smart” artifacts the coupling between the plant (i.e., controlled system) and controller design optimization problems requires special care: while these problems are typically solved sequentially, often by separate experts in each domain, such a strategy does not guarantee system optimality. Such coupling has not been rigorously explored, and while several optimization strategies have been used successfully to achieve system optimality, their ability to do so generally remains unproven. In addition, most combined plant/controller optimization studies assume availability of precise measurements of all plant states, which is not always possible.; This dissertation explores rigorously the coupling between plant and controller optimization using set theory and necessary optimality conditions. Comparing system optimality conditions to individual plant and controller ones reveals a coupling term that quantifies the coupling between the two design problems. Using this coupling term, special scenarios under which the plant and controller optimization problems decouple are classified.; Two nested optimization strategies, direct nested optimization (DNO) and projected nested optimization (PNO), are introduced and shown to guarantee system optimality. The passive and active subsystems of a car suspension are optimized using PNO, yielding a system-optimal suspension that surpasses its purely passive, purely active and sequentially optimized passive/active counterparts in both the time and frequency domains.; These results are extended to incorporate not only plant and controller design, but also the design of a state estimator. A derivation of necessary conditions for combined plant/observer/regulator optimality shows that PNO guarantees system optimality and is an extension of the orthogonal projection lemma. Comparing the system optimality conditions to individual plant, observer and regulator optimality conditions furnishes a coupling term quantifying the plant/observer/regulator coupling. Applying these results to the car suspension case study produces system-optimal suspension designs under limited and noisy measurement conditions. The dissertation concludes by applying PNO to the optimization of gain-scheduled adaptive systems, using the optimization of an elevator's plant and gain-scheduled linear quadratic Gaussian (LQG) control as an example.