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A comparative study of linear and nonlinear optimal control of a three-tank system

ISA TRANSACTIONS 2023年 132卷 419-427页

作者： Emebu, Samuel Kubalcik, Marek Backi, Christoph Josef Janacova, Dagmar Tomas Bata Univ Zlfn Fac Appl Informat Dept Automat & Control Engn Stranemi 4511 Zlfn 76005 Czech Republic Tomas Bata Univ Zlfn Fac Appl Informat Dept Proc Control Stranemi 4511 Zlfn 76005 Czech Republic Norwegian Univ Sci & Technol Fac Nat Sci Dept Chem Engn Hgsk Ringen 1 N-7491 Trondheim Norway Univ Benin Fac Engn Dept Chem Engn POB 1154 Benin Nigeria

In this work, a laboratory scaled industrial interconnected nonlinear Multi-Input|Multi-Output (MIMO) three-tank system, was modelled to control the liquid levels. Ensuing the tradition in the process industry to apply linear controller to most control processes, a linear control scheme was developed for this system. However, since linear schemes are proximate to actual process models, they may not be adequate, especially for highly nonlinear systems. Therefore, a nonlinear control scheme was also developed and compared with the linear scheme. Specifically, optimal linear and nonlinear controllers were designed. In summary, the results of the two control schemes showed adequate performance. However, the linear controller had more robust control and required lesser computational demand compared to the nonlinear scheme. To enhance the computational demand of the nonlinear scheme, a third-party MATLAB toolbox, Automatic control and Dynamic Optimization (ACADO) toolbox, that interfaces MATLAB with C++ to speed up computations was also utilised, and its results compared, and tentatively validate the earlier solved nonlinear control scheme.(c) 2022 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： linear optimal control Nonlinear optimal control Hamilton -Jacobi equation ACADO Three-tank-system

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On linear quadratic optimal control of discrete-time complex-valued linear systems

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optimal control APPLICATIONS & METHODS 2020年第2期41卷 499-520页

作者： Zhou, Bin Harbin Inst Technol Ctr Control Theory Guidance Technol Harbin Peoples R China Harbin Inst Technol Ctr Control Theory Bin Zhou Guidance Technol Harbin Peoples R China

We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete-time complex-valued linear systems, which have several potential applications in control theory. Firstly, an iterative algorithm was proposed to solve the discrete-time bimatrix Riccati equation associated with the LQR problem. It is shown that the proposed algorithm converges to the unique positive definite solution (bimatrix) to the bimatrix Riccati equation with appropriate initial conditions. With the help of this iterative algorithm, the LQR problem for the antilinear system, which is a special case of complex-valued linear system, was carefully examined and three different Riccati equations-based approaches were provided, namely, bimatrix Riccati equation, anti-Riccati equation, and normal Riccati equation. The established approach is then used to solve the LQR problem for a discrete-time time-delay system with one-step state delay, and a numerical example was used to illustrate the effectiveness of the proposed methods.

关键词： bimatrix complex-valued linear systems linear optimal control Riccati equations time-delay systems

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Robust and LPV Economic linear optimal control

Robust and LPV Economic Linear Optimal Control

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American control Conference

作者： Jin Zhang Donald J. Chmielewski Illinois Institute of Technology Chicago IL 60616

ISBN: (纸本)9781538679012;9781538679265

This work investigates how to address box-type uncertainties in economic linear optimal control (ELOC). We consider two methods, a robust formulation for when the uncertainty is completely unknown and a linear Parameter Varying formulation for when uncertainty can be measured in real time. In both cases, the infinite number of conditions that need to be satisfied are reduced to a finite set of constraints. The resulting problem formulations have similar structure to the ELOC and can be solved globally by employing the generalized Benders decomposition.

关键词： linear optimal control Problem Formulation Benders decomposition Robustness Uncertainty

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Excitation Regulation Capability Analysis of CSP Generator Based on linear optimal control 30

Excitation Regulation Capability Analysis of CSP Generator B...

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30th Chinese control and Decision Conference (CCDC)

作者： Zhang Ruiping Gu Yaoqin Wang Ningbo Ma Ming Lanzhou Jiaotong Univ Sch Automat & Elect Engn Lanzhou 730070 Peoples R China Gansu Elect Power Co Wind Power Technol Ctr Lanzhou 730070 Peoples R China

ISBN: (纸本)9781538612446

Aiming at the problem of grid-connected stability of CSP and improving the excitation regulation ability of CSP turbogenerator, a new excitation controller based on the linear optimal control theory is designed. Considering the difference with the traditional thermal power turbogenerator, the controller is obtained by describing the state space matrix of the excitation system, and then the obtained basis of controllability is substitutied into Riccati equation to calculate the optimal feedback matrix of the excitation system. On the basis, the linear optimal excitation control system of CSP turbogenerator is established and the ability of excitation system to regulate reactive power and AVC control in power system is verified though the three-phase short circuit fault. The analysis results show that the excitation system based on the linear optimal control is more regulation than the traditional PID and AVR + PSS control, and can effectively regulate the excitation, improve the grid adaptability of CSP and provide the possibility of further exploring the potential of large-scale CSP.

关键词： CSP Turbogenerator Excitation controller Regulation linear optimal control

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Testing of linear models for optimal control of second-order dynamical system based on model-reality differences

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RESULTS IN control AND OPTIMIZATION 2021年 4卷

作者： Kek, Sie Long Sim, Sy Yi Chen, Chuei Yee Univ Tun Hussein Onn Malaysia Dept Math & Stat Pagoh Campus Pagoh 84600 Johor Malaysia Univ Tun Hussein Onn Malaysia Dept Elect Engn Technol Pagoh Campus Pagoh 84600 Johor Malaysia Univ Putra Malaysia Dept Math & Stat Seri Kembangan 43400 Selangor Malaysia

In this paper, the testing of linear models with different parameter values is conducted for solving the optimal control problem of a second -order dynamical system. The purpose of this testing is to provide the solution with the same structure but different parameter values in the model used. For doing so, the adjusted parameters are added to each model in order to measure the differences between the model used and the plant dynamics. On this basis, an expanded optimal control problem, which combines system optimization and parameter estimation, is introduced. Then, the Hamiltonian function is defined and a set of the necessary conditions is derived. Consequently, a modified model -based optimal control problem has resulted. Follow from this, an equivalent optimization problem without constraints is formulated. During the calculation procedure, the conjugate gradient algorithm is employed to solve the optimization problem, in turn, to update the adjusted parameters repeatedly for obtaining the optimal solution of the model used. Within a given tolerance, the iterative solution of the model used approximates the correct optimal solution of the original linear optimal control problem despite model-reality differences. The results obtained show the applicability of models with the same structures and different parameter values for solving the original linear optimal control problem. In conclusion, the efficiency of the approach proposed is highly verified.

关键词： Conjugate gradient linear optimal control Iterative solution Adjusted parameters Model-reality differences

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Excitation Regulation Capability Analysis of CSP Generator Based on linear optimal control

Excitation Regulation Capability Analysis of CSP Generator B...

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第30届中国控制与决策会议

作者： ZHANG Ruiping GU Yaoqin WANG Ningbo MA Ming School of Automation and Electrical Engineering Lanzhou Jiaotong University Wind Power Technology Center of Gansu Electric Power Company

关键词： CSP Turbogenerator Excitation controller Regulation linear optimal control

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optimal control for Thermal Management of a Proton Exchange Membrane Fuel Cell Stack With Koopman-Based Modeling

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JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND control-TRANSACTIONS OF THE ASME 2025年第2期147卷 021003页

作者： Huo, Da Hall, Carrie M. IIT Dept Mech Mat & Aerosp Engn 10 West 35th St Chicago IL 60616 USA

This study presents a novel approach to optimal control utilizing a Koopman operator integrated with a linear quadratic regulator (LQR) to enhance the thermal management and power output efficiency of an open-cathode proton exchange membrane fuel cell (PEMFC) stack. First, a linear time-invariant dynamic model was derived through Koopman operator to forecast the behavior of the PEMFC stack. Second, this Koopman-based model was directly integrated with LQR for optimizing temperature, temperature variations, and output power efficiency of the PEMFC stack by regulating fan speed, with a physics-based model serving as the plant model. Finally, the performance of the Koopman-based LQRs (KLQR) was compared to a baseline proportional-integral (PI) controller across various ambient temperatures and operating conditions, focusing on temperature, temperature variations, and net power output. The results demonstrate the proposed Koopman-based approach can be seamless integration with linear optimal control algorithms, effectively minimizing temperature, temperature variations across the PEMFC stack, and the net power outputs under different ambient temperature and operating conditions.

关键词： proton exchange membrane fuel cell (PEMFC) data-driven modeling Koopman operator linear optimal control linear quadratic regulator physics-based modeling

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Improving power system low-frequency oscillations damping based on multiple-model optimal control strategy using polynomial combination algorithm

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ENERGY REPORTS 2023年 10卷 1228-1237页

作者： Pagard, Elahe Shojaeian, Shahrokh Rezaei, Mohammad Mahdi Islamic Azad Univ Elect Engn Dept Khomeinishahr Branch POB 84175-119 Esfahan Iran

In this paper, the damping of low-frequency oscillations (LFOs) in a power system containing Static VAR Compensator (SVC) is investigated based on Multiple-Model linear optimal control (MMLOC) Strategy. The performance of MMLOC is enhanced using Polynomial Combination Algorithm (PCA). A linear optimal controller (LOC) generates the optimal control signal with linearization the nonlinear state equations of the system and solving the Riccati equation. One LOC generates synchronized control signals for the synchronous generator excitation system as well as SVC. The LOC is assigned to generate each model's control signal. The final control signal is made by interpolating the LOC output signals obtained from each model using PCA. Considering a three-phase symmetrical fault on a near bus to the generator, the proposed control strategy is evaluated. This strategy not only maintains stability but also reduces LFO effectively. Furthermore, steady state error of rotor speed and rotor angle tend to zero favorably. Simulations are done for single- and multi-machine power systems via a MATLAB m-code. & COPY;2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Power system stability Low frequency oscillation linear optimal control Multi -model control Polynomial combination algorithm

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optimal co-designs of communication and control in bandwidth-constrained cyber-physical systems

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AUTOMATICA 2022年 142卷

作者： Negi, Nandini Chakrabortty, Aranya North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA

We address the problem of sparsity-promoting optimal control of cyber-physical systems (CPSs) in the presence of communication delays. The delays are categorized into two types - namely, an inter-layer delay for passing state and control information between the physical layer and the cyber layer, and an intra-layer delay that operates between the computing agents, referred to here as control nodes (CNs), within the cyber-layer. Our objective is to minimize the closed-loop H-2-norm of the physical system by co-designing an optimal combination of these two delays and a sparse state-feedback controller while respecting a given bandwidth cost constraint. We propose a two-loop optimization algorithm for this. Based on the alternating directions method of multipliers (ADMM), the inner loop handles the conflicting directions between the decreasing H-2-norm and the increasing sparsity level of the controller. The outer loop comprises a semidefinite program (SDP)-based relaxation of non-convex inequalities necessary for closed-loop stability. Moreover, for CPSs where the state and control information assigned to the CNs are not private, we derive an additional algorithm that further sparsifies the communication topology by modifying the row and column structures of the obtained controller, resulting in a reassignment of the communication map between the cyber and physical layers, and determining which physical agent should send its state information to which CN. Proofs for closed-loop stability and optimality are provided for both algorithms, followed by numerical simulations. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： linear optimal control Structural optimization Time-delay systems Delay analysis Bandwidth allocation

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Sparsity-promoting optimal control of cyber-physical systems over shared communication networks

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AUTOMATICA 2020年 122卷 109217-109217页

作者： Negi, Nandini Chakrabortty, Aranya North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA

Recent years have seen several new directions in the design of sparse control of cyber-physical systems (CPSs) driven by the objective of reducing communication costs. One common assumption made in these designs is that the communication happens over a dedicated network. For many practical applications, however, communication must occur over shared networks, leading to two critical design challenges, namely - time-delays in the feedback and fair sharing of bandwidth among users. In this paper, we present a set of sparse H-2 control designs under these two design constraints. An essential aspect of our design is that the delay itself can be a function of sparsity, which leads to an interesting pattern of trade-offs in the H-2 performance. We present three distinct algorithms. The first algorithm preconditions the assignable bandwidth to the network and produces an initial guess for a stabilizing controller. This is followed by our second algorithm, which sparsifies this controller while simultaneously adapting the feedback delay and optimizing the H-2 performance using alternating directions method of multipliers (ADMM). The third algorithm extends this approach to a multiple user scenario where an optimal number of communication links, whose total sum is fixed, is distributed fairly among users by minimizing the variance of their H-2 performances. The problem is cast as a difference-of-convex (DC) program with mixed-integer linear program (MILP) constraints. We provide theorems to prove the convergence of these algorithms, followed by validation through numerical simulations. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： linear optimal control Structural optimization Time-delay systems Delay analysis Bandwidth allocation

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