Performance Assessment with LQG-benchmark from Closed-loop Data

The MVC-benchmark discussed in Chapter 10 may not be directly applicable to assessing the performance of those control systems whose objective is not just minimizing process output variance but also keeping the input variability (for example, valve movement) within some specified range to reduce upset to other processes, conserve energy and lessen the equipment wear. The objective of such controllers may be expressed as minimizing a linear quadratic function of input and output variances. The LQG-benchmark is a more appropriate benchmark for assessing the performance of such controllers. However, calculation of the LQG-benchmark requires a complete process model [155, 22], which is a demanding requirement or simply not possible in practice. An open-loop test for obtaining the process model may not always be feasible. A frequency domain approach is proposed by Kammer ([156, 157, 158]) for testing the LQ optimality for performance assessment of a controller using closed-loop data with setpoint excitations. However this approach does not give quantitative values for the controller performance in terms of process input and output variances. In other words, it does not separate the non-optimality/optimality with respect to process response (output) variance and process input variance. The idea of using a subspace-matrices based approach to obtain the LQG-benchmark variances of the process input and output for controller performance assessment has been explored in [159]. The required subspace matrices, corresponding to the deterministic and stochastic inputs respectively, are estimated from closed-loop data with setpoint excitation. This method is applicable to both univariate and multivariate systems.