Towards the performance monitoring of constrained control systems
This thesis contains contributions in the areas of the performance moni toring of SISO and MIMO control systems and the performance monitoring and analysis of MPC control systems. Knowledge of the time delay allows for the com putation of a minimum variance benchmark. A novel time delay estimation method which requires temporarily changing the tuning of the PID controller of a SISO process is introduced. Another time delay estimation method for SISO control loop monitoring is introduced which requires a process regulated by a PID controller during routine operation to be temporarily switched to relay control. For MIMO control systems, it is necessary to obtain an estimate of the interactor matrix to ob tain a minimum variance benchmark. The identiﬁcation of the ﬁrst few Markov parameters, which is necessary for identiﬁcation of the interactor, is investigated the open-loop and closed-loop for FIR, ARX, and ARMarkov models. One contri bution in this area is an analysis of the bias due to structural differences between the process and model. It is found that the Markov parameters for the FIR and AR Markov models can be estimated without bias in the presence of non-white noise in the open-loop. An analysis of the covariance of the ﬁrst few Markov parameters shows that the ﬁrst few Markov parameters can be estimated with greater conﬁ dence with an ARMarkov model than with an FIR model. Another contribution is the use of the Generalized Binary Signal (GBN) signal for Markov parameter identiﬁcation. The GBN signal allows for uncorrelated excitation signals to be gen erated, which makes it possible to excite multiple inputs at one time. A method is introduced for diagnosing whether suboptimal MPC performance is due to mis match between the process model and the actual process or a poor estimate of the noise characteristics used to design the Kalman ﬁlter. Next, the performance of a minimum variance MPC with input constraints is analyzed for various horizons by obtaining the linear, piecewise control laws. Lastly, the performance of an MPC with input constraints and a ﬁxed horizon is analyzed for different penalty ratios of the output to the input.