Controller performance analysis with LQG benchmark obtained under closed loop conditions

This paper proposes a new method for obtaining a linear quadratic Gaussian (LQG) benchmark in terms of the variances of process input and output from closed-loop data, for assessing the controller performance. LQG benchmark has been proposed in the literature to assess controller performance since the LQG tradeoff curve represents the limit of performance in terms of input and output variances. However, an explicit parametric model is required to calculate the LQG benchmark. In this work, we propose a data driven subspace approach to calculate the LQG benchmark under closed-loop conditions with certain external excitations. The optimal LQG-benchmark variances are obtained directly from the subspace matrices corresponding to the deterministic inputs and the stochastic inputs, which are identified using closed-loop data with setpoint excitation. These variances are used for assessing the controller performance. The method proposed in this paper is applicable to both univariate and multivariate systems. Profit analysis for the implementation of feedforward control to the existing feedback-only control system is also analyzed under the optimal LQG performance framework. The proposed method is illustrated through a simulation example and an application on a pilot scale process.