Optimal Controller Gain Selection Using the Power Flow Information of Bond Graph Modeling

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Abstract

In the design of a controller, the selection of controller gains is the most time consuming and ad hoc of tasks. The difficulty lies in the fact that optimization tools cannot always find global optima, thus the solution found is more than likely sub-optimal. However, trying to find a more optimal solution quickly becomes cost ineffective. The controller gain selection process lacks a method for measuring the balance between 'good' and 'good enough'. The question of whether the controller gains need to be optimized further, or re-optimized in the instance of an existing design, often goes unanswered.

This paper is a companion paper to System Efficiency Measurement through Bond Graph Modeling. In the companion paper, a method was shown, through the use of bond graphs, to evaluate the efficiency of a control scheme. This paper uses a similar method for evaluating the efficiency of controller gains for a given control system. The efficiency is used to define the optimal performance of the system. If the current set of controller gains is able to make use of the system’s available energy, and these gains satisfy classical control criteria, then this set of gains is as close to the optimal solution as it needs to be. Further optimization would then be a waste of time and money, since the system performance cannot be improved. On the other hand, if the current set of gains does not make good use of the system’s available energy, then the gains need to be optimized further.

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Last modified: July 12, 2005 -- © François Cellier