Convergence of Laguerre Impulse Response Approximation for Noninteger Order Systems

One of the most important issues in application of noninteger order systems concerns their implementation. One of the possible approaches is the approximation of convolution operation with the impulse response of noninteger system. In this paper, new results on the Laguerre Impulse Response Approximation method are presented. Among the others, a new proof of convergence of approximation is given, allowing less strict assumptions. Additionally, more general results are given including one regarding functions that are in the joint part of and spaces. The method was also illustrated with examples of use: analysis of “fractional order lag” system, application to noninteger order filters design, and parametric optimization of fractional controllers

Influence of compressor degradation on optimal operation of a compressor station

Normal practice in a compressor station with compressors in parallel is to allocate the mass flows equally. However, this strategy is not optimal if the compressors are not identical. A common reason why compressors become non-identical is because their performance degrades over time. Degradation increases the power necessary to run the compressor station and changes the optimal allocation of mass flows. This paper presents a framework for optimal operation in a compressor station with degrading compressors. The optimisation framework proposed in this work explicitly includes a model of degradation in the optimisation problem and analyses how the optimal load-sharing changes when the compressors are degrading. The optimisation framework was applied in an industrial case study of a compressor station in which three parallel compressors are subject to degradation. The case study confirms that it is possible to minimise the extra power consumption due to degradation by adjusting the operating conditions of the compressor station. The analysis also gives insights into the impact of degradation on the optimal solution when compressors work at their limits

Automatic Scenario Generation for Robust Optimal Control Problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 2 14+3×192 boundary scenarios are considered. A validation with randomly-drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used

Automatic scenario generation for efficient solution of robust optimal control problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴⁺³×¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive

Automatic scenario generation for efficient solution of robust optimal control problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴+³ₓ¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive

Data-Driven Predictive Control With Improved Performance Using Segmented Trajectories

A class of data-driven control methods has recently emerged based on Willems’ fundamental lemma. Such methods can ease the modeling burden in control design but can be sensitive to disturbances acting on the system under control. In this article, we propose a restructuring of the problem to incorporate segmented prediction trajectories. The proposed segmentation leads to reduced tracking error for longer prediction horizons in the presence of unmeasured disturbance and noise when compared with an unsegmented formulation. The performance characteristics are illustrated in a set-point tracking case study in which the segmented formulation enables more consistent performance over a wide range of prediction horizons. The method is then applied to a building energy management problem using a detailed simulation environment. The case studies show that good tracking performance is achieved for a range of horizon choices, whereas performance degrades with longer horizons without segmentation

Application of gaussian processes to online approximation of compressor maps for load-sharing in a compressor station

Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the characteristics that can be used in optimization of the operating strategy. This paper proposes a new algorithm for online learning of the characteristics of the compressors using Gaussian Processes. The performance of the new approximation is shown in a case study with three compressors. The case study shows that Gaussian Processes accurately capture the characteristics of compressors even if no knowledge about the characteristics is initially available. The results show that the flexible nature of Gaussian Processes allows them to adapt to the data online making them amenable for use in real-time optimization problems

Discrete-time feedback stabilization

This paper presents an algorithm for designing dynamic compensator for infinitedimensional systems with bounded input and bounded output operators using finite dimensional approximation. The proposed method was then implemented in order to find the control function for thin rod heating process. The optimal sampling time was found depending on discrete output measurements

Predictive control co-design for enhancing flexibility in residential housing with battery degradation

Buildings are responsible for about a quarter of global energy-related CO2 emissions. Consequently, the decarbonisation of the housing stock is essential in achieving net-zero carbon emissions. Global decarbonisation targets can be achieved through increased efficiency in using energy generated by intermittent resources. The paper presents a co-design framework for simultaneous optimal design and operation of residential buildings using Model Predictive Control (MPC). The framework is capable of explicitly taking into account operational constraints and pushing the system to its efficiency and performance limits in an integrated fashion. The optimality criterion minimises system cost considering time-varying electricity prices and battery degradation. A case study illustrates the potential of co-design in enhancing flexibility and self-sufficiency of a system operating under different conditions. Specifically, numerical results from a low-fidelity model show substantial carbon emission reduction and bill savings compared to an a-priori sizing approach

Fast and accurate method for computing non-smooth solutions to constrained control problems

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve time