Design of multivariable identification signals for constrained systems.

摘要

System identification plays an important role in model predictive control (MPC) and other applications where mathematical models of processes are involved, and the input signal design is the first and crucial step towards a successful identification practise. This thesis is focused on developing the general methodology that can be used in designing the input signals for the identification of linear systems. The methodology tries to maximize the hypervolume of the input space so that the signal-to-noise ratio is optimized. Thus, the generated model is supposed to be more accurate than others.; In order to shorten identification experiment time and describe the interactions among the inputs and outputs precisely, the multi-input multi-output (MIMO) framework is adopted in the design. Because normal operation conditions and product qualities need to be ensured during experiments, constraints on both inputs and outputs are incorporated. Most of the previous design methods are based on the steady state gain matrix, whereas the actual responses of dynamic systems under perturbations are usually different from their steady state values. As a result, these steady state designs are either too conservative or cause violations to the constraints. This problem is solved in this thesis by the proposed dynamic design method. In this method, the dynamic signatures are calculated based on the system dynamics described by the a-priori system models, and used in the design. Then the amplitude matrix is optimized to achieve the maximal signal-to-noise ratio. Since a-priori dynamic models of the systems are usually not accurate, they should be updated along with the experiments, and new input signals should be designed with updated models. The key problem of this iterative design and identification process is judging the convergence of the models, which is solved in this thesis by the proposed standard of magnitude matrix norm error.; The decentralized design for the identification of high dimensional systems is also addressed in this thesis by introducing the mixed integer programming framework to model the problem. In this framework, the grouping of input variables is represented with discrete decision variables and the optimal combination can thus be found.