LQG Benchmark Research Articles

ILC-based two-layer strategy for economic performance improvement in industrial MPC systems

The conventional LQG based economic performance design has found its difficulty in industrial application and so far, there is still no systematic and effective way to improve economic performance. As learned from the LQG benchmark performance assessment method, the economic performance improvement in MPC systems can be realized through adjusting controller parameters in addition to the well-known setpoints change approach. Therefore, we take advantage of LQG and iterative learning control (ILC) to propose a new two-layer periodical economic performance improvement strategy applicable in industrial MPC systems. By dividing the whole time into multiple intervals called periods and optimize the performance periodically, the economics finally reach its optimal. Promoted twice in a certain period, the performance acquires its first promotion through fixed variance obtained from the lower MPC layer, which transforms the nonlinear economic performance function (EPF) of LQG into a linear one. The ILC-based weight coefficients adjustment algorithm then provides the parameters to the MPC controller in the next period with the updating principle based on the idea of minimizing the tracking error between the current controller economic performance and an optimal one, which realizes the second performance improvement. Room for the second promotion is analyzed and convergence of the algorithm is proved. Finally, the effectiveness and applicability of the strategy are verified via a typical industrial separation process.

Understanding GANs in the LQG Setting: Formulation, Generalization and Stability

Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. In this paper, we provide an understanding of basic issues surrounding GANs including their formulation, generalization and stability on a simple LQG benchmark where the generator is Linear , the discriminator is Quadratic and the data has a high-dimensional Gaussian distribution. Even in this simple benchmark, the GAN problem has not been well-understood as we observe that existing state-of-the-art GAN architectures may fail to learn a proper generative distribution owing to (1) stability issues (i.e., convergence to bad local solutions or not converging at all), (2) approximation issues (i.e., having improper global GAN optimizers caused by inappropriate GAN’s loss functions), and (3) generalizability issues (i.e., requiring large number of samples for training). In this setup, we propose a GAN architecture which recovers the maximum-likelihood solution and demonstrates fast generalization. Moreover, we analyze global stability of different computational approaches for the proposed GAN and highlight their pros and cons. Finally, through experiments on MNIST and CIFAR-10 datasets, we outline extensions of our model-based approach to design GANs in more complex setups than the considered Gaussian benchmark.

Performance Assessment of FO-PID Temperature Control System Using a Fractional Order LQG Benchmark

In this paper, a fractional order LQG benchmark is proposed for the control performance assessment of fractional order control systems. Similar to the conventional LQG benchmark, the fractional order LQG performance benchmark curve is determined by the numerical calculation method, which avoids the calculation of the complex interaction matrix. The fractional order process model is discretized via fractional order calculus. Meanwhile, the fractional order integral is introduced into the conventional LQG cost function. Then solving the linear quadratic Gaussian problem under the fractional order model and fractional control, the optimal input and output variances are determined for different weighting factors and the performance curves can be achieved. The comparison between fractional order LQG and the conventional LQG shows the improvement of the proposed benchmark under the same condition. The proposed benchmark can provide a more direct and superior reference standard to evaluate the performance of fractional order control system. Finally, a case study of fractional order PID(FO-PID) controller in industrial heating furnace temperature control experiment with model matching and model mismatch conditions is used to verify the effectiveness of the proposed benchmark.

An improved LQG benchmark for MPC economic performance assessment and optimisation in process industry

AbstractPerformance assessment and optimisation for MPC have attracted much research interest. As a typical performance assessment benchmark, the LQG benchmark is regressed from asymmetrical points, leading to unnecessary computation and unsatisfactory regression results. To tackle this problem, an equigrid LQG benchmark was proposed for the two‐layer MPC assessment and optimisation, and the optimal setpoint for MPC was calculated to replace the experiential one. Then the LQG benchmark for sensitivity analysis was introduced. Economic performance assessment of the control system in a delayed coking furnace shows the effectiveness of the proposed approach. © 2012 Canadian Society for Chemical Engineering

Improved LQG benchmark for control performance assessment on ARMAX model process

Control performance assessment for MPC systems has attracted a lot of interest in recent years. Compared with the typical MVC benchmark, the LQG benchmark gives a pragmatic assessment result. Based on the traditional LQG benchmark, the equigrid approach can improve the regression performance. In addition to the numerical algorithm, the recursive algorithm and the analytical algorithm were introduced to analyze the essential relationship in the LQG benchmark, which can save the computing cost and improve the regression effect. Based on the ARMAX model, the detailed procedures for these algorithms were discussed. In the simulation to a SISO process and a MIMO process, the different types of LQG benchmarks were calculated.

Performance assessment of advanced supervisory–regulatory control systems with subspace LQG benchmark

In this paper, a subspace method for LQG design and performance assessment is proposed for control systems in which supervisory and regulatory controllers are employed in a cascade structure. Usually, this is the case when an advanced controller is used in a supervisory control layer on the top of the regulatory control system, resulting in a cascade control structure. The objective of this study is to provide the optimal LQG control design in the cascade control structure and also to propose a method for calculation of the LQG ‘trade-off’ curves for performance assessment. The trade-off curve provides the optimal performance limit in terms of the best achievable input and output variances. Three possible scenarios for LQG control design in this supervisory–regulatory structure are discussed in the paper. The problem formulations are presented in the subspace framework to directly derive the control law and LQG trade-off curve without need of the conventional parametric models. A simulation example is provided to demonstrate the proposed method.

Consistency of noise covariance estimation in joint input–output closed-loop subspace identification with application in LQG benchmarking

The LQG trade-off curve has been used as a benchmark for control loop performance assessment. The subspace approach to estimating the LQG benchmark has been proposed in the literature which requires certain intermediate matrices in subspace identification as well as the covariance matrix of the noise. It is shown in this paper that many existing closed-loop identification methods do not give a consistent estimate of the noise covariance matrix. As a result, we propose an alternative subspace formulation for the joint input–output closed-loop identification for which the consistency of the required subspace matrices and noise covariance is guaranteed. Simulation studies and experimental results are provided to demonstrate the utility of the proposed method.

Economic performance assessment of advanced process control with LQG benchmarking

Economic performance assessment of advanced process control is conducted to investigate performance potentials that can be obtained by control system improvement. An optimization-based approach for economic performance assessment of the constrained process control is integrated with the LQG benchmark in this paper. By explicitly incorporating uncertainty into the performance assessment problem, economic performance evaluation can be formulated as a stochastic optimization problem, which helps to identify the opportunity to improve profitability of the process by taking appropriate risk levels. Using the LQG benchmark to estimate achievable variability reduction through control system improvement, the proposed method provides an estimate of both the performance that can be expected from the improved control system and the operating condition that delivers the improved performance. The results obtained can serve as a tool for control engineers to make decisions on control system tuning and/or upgrading. The proposed algorithm is illustrated via simulation examples as well as an industrial example.