The autocovariance least-squares method for estimating covariances: application to model-based control of chemical reactors

Abstract

Abstract-This paper demonstrates the autocovariance least-squares (ALS) technique on two chemical reactor control problems. The method uses closed-loop process data to recover the covariances of the disturbances entering the process, which are required for state estimation. The data used for this purpose may be collected with or without the controllers running. We do not assume that the plant is at steady state nor that only nonzero disturbances are affecting the plant at the time of data collection. The ALS method also accounts for integrated white noise disturbances, which are required for offset-free control. Two examples are provided in this paper: a carefully controlled laboratory reactor and an industrial reactor controlled by a state-of-the-art advanced model predictive control (MPC) system. A variety of control scenarios are tested and the results demonstrate that the ALS method has the potential to improve the best industrial practice of process control by a factor of three to five.

A Prediction-Error Covariance Estimator for Adaptive Kalman Filtering in Step-Varying Processes: Application to Power-System State Estimation

“…Regarding the Myers method, the reason lies in more significant numerical stability problems. Instead, the worsening of the PECE method's accuracy as N decreases is due to the increasing effect of the measurement noise on the sample covariance matrix (16). Indeed, we have observed that the small peak of the errors of the PECE method close to the step-variation has the same amplitude irrespectively of the value of N, whereas the errors after the step are highly affected by the measurement noise.…”

“…The only parameter that has to be set in the PECE method is N, specifically the number of previous innovations used to calculate the sample innovation-covariance matrix in (16). In this section, we present the influence of N on the SE accuracy considering both the base case and the base case plus steps in which q/r < 1.…”

Application of an Autocovariance Least - Squares Method for Model Predictive Control of Hybrid Ventilation in Livestock Stables

“…A new Autocovariance Least-Squares (ALS) method for estimating noise covariances using routine operating data is employed to recover the covariances and adaptively determine an optimal filter gain. Odelson, Lutz, Rawlings [6] and Odelson, Rajamani, Rawlings [7] have researched and proved the superior advantages of ALS method convincingly through comparing with previous work.…”

“…The covariance can be found uniquely when the matrix A has full column rank. However, in the augmented system as (9d), the dimension of the driving noise is w ∈ ℜ 11 , according to [6] and [7], it is unlikely to find unique estimates of the covariance (Q w , R v ), and the solution may not be positive semi-definite. In order to avoid leading to any meaningless solution, adding the semi-definite constraint directly to the estimation problem to maintain a convex program as (35) will ensure uniqueness of the covariance estimation.…”

An improved real-time adaptive Kalman filter with recursive noise covariance updating rules

“…In the correlation techniques, the covariance matrices are estimated based on the sample autocorrelations between the innovations by exploiting the relations between the estimation error covariance and the innovation covariance [11][12][13][14]. The drawbacks of this method are that it does not guarantee the positive definiteness of the matrices, the estimated covariances are biased [15], and the above techniques require a large window of data, which makes them impractical. Maximum likelihood methods estimate the covariances by maximizing the likelihood function of the innovations [16], but these methods need heavy computations and they can be implemented offline.…”