A method for designing small scale control laws for large scale thermal systems is proposed. For high order models, traditional control theory produces high order control laws, which are impractical to implement. Here, Balanced Truncation is used to reduce the order of the model, while preserving as much as possible the dynamical properties that are important for controller design. Then, a low order controller is designed by applying a standard linear quadratic optimal control design procedure on the reduced model. The small scale controller performance is tested by incorporating it in a simulation with the full scale model. A geometric approach is used, in order to propose that the norms that are defined on the input and output spaces of the system should be the same in the model reduction phase and in the optimal controller design phase. This way, the cost function of the optimal controller is taken into account during the model reduction phase. A reduced order observer which allows real time estimation of process values that cannot be directly measured can be easily designed. The input signals that are computed during closed loop simulation can be also used in real time open loop operation. Hence, the work has a pure computational aspect: calculate the heat fluxes that are required in order to track a temperature profile that is given for a set of output points. Integrating standard computational methods with standard control theory via the Balanced Truncation algorithm is proved to be a powerful tool.
A new method for the model reduction technique via a limited frequency interval impulse response Gramian
