Optimal Control Structure Research Articles

An isogeometric approach to dynamic structures for integrating topology optimization and optimal control at macro and micro scales

In the context of active vibration suppression, an integrated topology optimization framework is proposed for the optimal control of dynamic structures. This article formulates a new composite objective function by considering the external harmonic excitations with different excitation frequencies and the complex-valued displacement field. Within the proposed optimal control performance function, the symmetric weighting matrix, the magnitudes of which are related to the importance of the control forces, is integrated into dynamic compliance to serve the state displacement. Utilizing the non-uniform rational B-splines (NURBS) basis functions, the material interpolation model defined at control points is described by the NURBS surface, which is incorporated into the optimization formulation for optimal structural and vibration control design. The sensitivity results are deduced in terms of the pseudo-densities and the corresponding weights at control points from both macro and micro perspectives of structural dynamics. To demonstrate the effectiveness of the integrated topology optimization of dynamic structures at macro and micro scales, several numerical examples, including the topology optimization of solid beams in plane stress and Mindlin plates with 3D microstructures, are provided and discussed in terms of structural shape and topology, frequency response curve, and modal displacement.

Reinforcement Learning for Jointly Optimal Coding and Control Policies for a Markovian System Controlled over a Communication Channel

This paper develops approximation and optimality results for the optimal control of a networked system. In this system, a Markovian process is managed over a finite-rate, noiseless communication channel. Solving this problem involves determining joint optimal coding and control policies that minimize cost over time. While theoretical results on optimal coding and control structures exist, practical implementation has remained largely infeasible for non-linear systems due to the computational complexities and uncountable state spaces. This research introduces an approach that combines structural results with reinforcement learning (RL) techniques. The method uses regularity properties of the system to approximate the uncountable state space with a countable one, which allows reinforcement learning algorithms to achieve near-optimal solutions. Specifically, we establish that finite model approximations (where infinite state spaces are quantized to finite ones) and sliding finite window approximations (where a finite memory "window" of past control actions is maintained at each time step) can be employed to develop near-optimality. These approximations allow the system to be reformulated as a Markov Decision Problem (MDP) with a finite state space, making RL algorithms implementable. The convergence of the reinforcement learning algorithm to a near-optimal policy (under both the previous approximations) is supported by theoretical analysis and performance simulations. We ensure that the solutions obtained are not only computationally feasible but also nearly optimal with respect to the original problem. The applications of this work extend to many networked control systems, especially those with zero-delay coding and partially observable Markov decision processes (POMDPs). By integrating structural results with learning algorithms, this paper provides a practical framework for implementing optimal control in finite-rate environments.

Control of extractive distillation processes with preconcentration for the separation of ternary azeotropic mixture ethyl acetate-ethanol–water in the face of multiple feed disturbances

The integration of preconcentration and solvent recovery functions is one of the effective ways to save energy consumption of extractive distillation processes for separating ternary azeotropic mixtures with a high content of one composition. However, the integration of various functions inevitably increases the difficulty of constructing robust control structures. In this paper, different proportion-integration (PI) control structures are investigated for the four-column extractive distillation with preconcentration process, while different PI and PI with model prediction controller (MPC) hybrid control structures are proposed for the three-column extractive distillation with integrated distillation column (TCED-IDC) process to deal with feed disturbances via taking the separation of ternary azeotropic mixture ethyl acetate-ethanol–water as a case study. The control structures are tested via introducing multiple feed disturbances including one feed flowrates disturbance and three feed compositions disturbances. The dynamic test comparison results show that the integration of preconcentration and solvent recovery functions causes a larger transient deviation in terms of dynamic responses of the individual optimal control structures. In addition, the integral of squared error of the TCED-IDC process are reduced by about 22 times after introducing the MPC in the face of feed disturbances.

A Review: Structural Shape and Stress Control Techniques and their Applications

AbstractThis review article presents prior studies on controlling shape and stress in flexible structures. The study offers a comprehensive survey of literature concerning the adjustment and regulation of shape, stress, or both in structures and emphasizes such control’s importance. The control of systems is classified into three primary classes: nodal movement control, axial force control, and controlling the two classes concurrently. Each class is thoroughly assessed, showcasing diverse methods anticipated by various scholars. Furthermore, the paper discusses methods to reduce the number of devices (actuators) to adjust and optimize actuators’ placement to achieve optimal structural control, considering the cost implications of numerous actuators. Additionally, various actuators are presented in detail, their advantages and disadvantages are also discussed. Moreover, the applications of the presented techniques are reviewed in detail, the essential recommendations for future work are also suggested.

Infinite-time robust optimal output tracking of continuous-time linear systems using undiscounted reinforcement learning

This research paper focuses on addressing the challenge of infinite-time linear quadratic tracking control (LQT) for linear systems with parametric uncertainty. Traditional solutions to the LQT problem often involve using a discount factor to prevent the cost function from growing unbounded over time. However, this approach can introduce instability in the closed-loop system. To overcome this issue, this paper proposes an alternative approach using an undiscounted cost function that ensures the asymptotic stability of the uncertain closed-loop system. To design a control scheme without requiring precise knowledge of the system dynamics, reinforcement learning (RL) algorithms are employed. However, for systems with uncertain parameters that may lead to instability, the convergence of RL algorithms to a stabilising solution is not guaranteed. To address this limitation, a robust optimal control structure is developed using on-policy and off-policy reinforcement learning algorithms, resulting in a model-free controller. The effectiveness of the proposed robust optimal controller is validated through comparative simulations on an uncertain model of a DC–DC buck converter connected to a constant power load. These simulations demonstrate the advantages and benefits of the robust optimal controller in handling parametric uncertainty and ensuring stability in the control system.

Multiscale stochastic optimal control of hysteretic structures based on wavelet transform and probability density evolution method

PurposeContemporary stochastic optimal control by synergy of the probability density evolution method (PDEM) and conventional optimal controller exhibits less capability to guarantee economical energy consumption versus control efficacy when non-stationary stochastic excitations drive hysteretic structures. In this regard, a novel multiscale stochastic optimal controller is invented based on the wavelet transform and the PDEM.Design/methodology/approachFor a representative point, a conventional control law is decomposed into sub-control laws by deploying the multiresolution analysis. Then, the sub-control laws are classified into two generic control laws using resonant and non-resonant bands. Both frequency bands are established by employing actual natural frequency(ies) of structure, making computed efforts depend on actual structural properties and time-frequency effect of non-stationary stochastic excitations. Gain matrices in both bands are then acquired by a probabilistic criterion pertaining to system second-order statistics assessment. A multi-degree-of-freedom hysteretic structure driven by non-stationary and non-Gaussian stochastic ground accelerations is numerically studied, in which three distortion scenarios describing uncertainties in structural properties are considered.FindingsTime-frequency-dependent gain matrices sophisticatedly address non-stationary stochastic excitations, providing efficient ways to independently suppress vibrations between resonant and non-resonant bands. Wavelet level, natural frequency(ies), and ratio of control forces in both bands influence the scheme’s outcomes. Presented approach outperforms existing approach in ensuring trade-off under uncertainty and randomness in system and excitations.Originality/valuePresented control law generates control efforts relying upon resonant and non-resonant bands, and deploys actual structural properties. Cost-function weights and probabilistic criterion are promisingly developed, achieving cost-effectiveness of energy demand versus controlled structural performance.

STEWART PLATFORM DYNAMICS MODEL IDENTIFICATION

Context. At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion.
 Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification.
 Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals.
 Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models.
 Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences.

Wave Energy Optimal Control Structure With Second-Order Sliding Mode Tracking: Hardware-in-the-Loop Assessment

Wave Energy Optimal Control Structure With Second-Order Sliding Mode Tracking: Hardware-in-the-Loop Assessment

A bilevel programming model for cross-regional energy coordination mechanism to relieve China’s atmospheric pollution

The research motivation comes from the fact that the vigorously promoted ‘coal to gas’policy under the pressure of China’s Ministry of Environmental Protection(MEP) has led to severe gas shortage in many regions. This study explores a cross-regional energy coordination scheme, in which China’s MEP sets pollution transfer prices and pollution standards for each region, while each region determines its energy inputs and pollutant removal amounts. It is first formulated as a bilevel programming called PTEC and then it is transformed and a corresponding algorithm is proposed. To verify the effectiveness of the proposed model, the SO2 control in Beijing-Tianjin-Hebei Delta is finally selected. Results display that to meet the national pollution standards, the PTEC mode just need to reduce SO2 by 1.5434 million tons, which is 5.02% and 4.97% lower than the current command mode and the ‘coal to gas’ mode, respectively. Furthermore, the PTEC increases the industrial net output of Beijing, Tianjin, and Hebei by 21.9037%, 43.4486%, and 11.0651% compared with the other two modes. Our study can provide certain reference significance for pollution control and energy structure optimization.

Optimal control of high-rise building structures against earthquake excitations using independent stories as TMD

In this paper, in order to control the behavior of tall building structures against vibrations caused by earthquakes, the parameters of a new passive control system named “independent story” are optimized. This control system is installed like a large tuned mass damper in the main story of the building. Moreover, in order to improve the performance of this control system, six liquid viscous dampers connected from the roof of an independent story to the main story of the building, have also been used to increase damping of the system. The main goal of the present research is to optimize the parameters of this system, including selecting the optimal story/stories of the building to install the independent story/stories, such that the maximum reduction in the mean values of the maximum displacement and maximum acceleration responses of different stories of the building can be obtained, simultaneously. To evaluate the performance of the proposed control system, as a numerical example, a 3-D model of a twelve-story steel building structure is selected for which three degrees of freedom in each story have been considered. Then, a deep search is conducted to find the story/stories of the building at which the independent story control system along with the related supplemental liquid viscous dampers can be constructed/installed such that the best performance of this control system in response reduction of the building can be obtained. Finally, the optimal values of the mass and damping of the supplemental dampers of this system are found to be about 6% of the total mass of the building, and 13 kN-sec/mm, respectively; and the eighth and twelfth stories of the building are the best places for implementation of the proposed control system. By applying the optimal values of all the design parameters of the IS control system, the mean values of the building roof story response reductions were obtained to be about: 28.60% and 26.67% reduction on maximum displacement responses in x and y directions, respectively; and those of the maximum acceleration responses as 43% and 48.89%.

A scenario-based economic-stochastic model predictive control for the management of microgrids

The world’s electricity generation is heavily dependent on the consumption of fossil fuels. Electric generation from renewable resources is necessary due to the imperative need to reduce greenhouse gases to avoid a climate crisis. These resources exhibit random and intermittent behaviour. Therefore, there is a need to develop new management and control tools for these insertions into the current electricity system. Microgrids have become an effective tool to solve this problem, where these control systems play a principal role. For this reason, an optimal control structure consisting of two Model Predictive Control strategies is proposed for a microgrid Energy Management System. The first controller aims to optimise the microgrid’s economic performance under an established criterion, using nominal forecasts of the disturbances on the system, such as the energy generated by renewable resources. The second is a stochastic approach using scenario-based methods to consider forecast errors in the nominal predictions used for the disturbances. The simulations were carried out on a microgrid model corresponding to the National Technological University, Reconquista Regional Faculty, highlighting that actual samples of energy consumption are available. It is worth noting that with the proposed structure, optimal solutions are obtained considering the random behaviour of the disturbances, without making assumptions about the distribution functions of the random variables. Moreover, it applies to different scales of microgrids.

Full cycle on-line autonomous reconfiguration of MIMO control system based on REGA pairing principle for heat exchanger networks

This study presents a novel autonomous reconfiguration strategy to achieve full cycle optimal control of the heat exchanger networks. The proposed method aims to select the optimal control structure online to solve the problem of slow time-varying process transition caused by the inevitable fouling accumulation. An auxiliary variable is introduced to increase the degree of control freedom, and a flexible control structure is studied to provide appropriate pairings dynamically between variables. Subsequently, the nonparametric Relative Energy Gain Array (REGA) is considered to form the switching mechanism that determines the switching instants and variable pairing modes between control loops. Furthermore, the online optimization of switching regions ensures the optimal control performance. Finally, one typical experiment for the heat exchanger network in crude distillation unit was conducted and the results illustrated the effectiveness of the proposed control method. Compared with the conventional control system, the available service time is extended by nearly 18 months, and there is still room for further adjustment.

Optimal rule based fuzzy-PI controller for core power control of nuclear reactor

In this paper, an optimal rule based fuzzy proportional integral controller is proposed to control the core power of the molten salt breeder reactor (MSBR) model. Firstly, a nonlinear MSBR model is considered. It is then linearized using the perturbation linearizing approach, and the transfer function of the linearized MSBR system is established. Secondly, an optimal Fuzzy-PI control structure is formulated where a PI controller is set as the principal controller for the MSBR model and a fuzzy control system is used to adjust the PI controller parameters during any disturbance in the MSBR. The rule base system of the fuzzy controller is optimized with a reshaped class topper optimization algorithm. Finally, the optimized Fuzzy-PI controller tests under a variety of conditions. Furthermore, the Nyquist stability approach is used to analyze the stability of the closed loop MSBR model.

Optimal Active Vibration Control of Tensegrity Structures Using Fast Model Predictive Control Strategy

Active vibration control of tensegrity structures is often challenging due to the geometrical nonlinearity, assemblage uncertainties of connections, and actuator saturation of controllers. To tackle these technical difficulties, a fast model predictive control (FMPC) strategy is herein implemented to effectively mitigate the structural vibration. Specifically, based on the explicit expression form of the Newmark- β method, the computation of the matrix exponential is avoided and replaced by one online and two offline transient analyses at each sampling instant on the structure, and the optimal control input is attainted from the second-order dynamic equation without forming an expanded state-space equation. Meanwhile, the artificial fish swarm algorithm (AFSA) is embedded to automatically derive optimal arrangement of actuators with the selection of a reasonable objective function. Two illustrative examples, including two standard and clustered tensegrity beams and a clustered tensegrity tower, have been fully investigated. The outcomes from illustrative examples prove the effectiveness and feasibility of the proposed method in optimal active vibration control of tensegrity structures, implying a promising prospect of the investigated approach in analyzing and solving relevant engineering problems.

A robust optimal distributed control design for simultaneous voltage regulation and current sharing in DC microgrid

AbstractIn this article, a robust optimal distributed controller is designed for achieving average voltage regulation and current sharing in a DC microgrid. Each distributed generation unit (DGU) consists of a DC‐DC buck converter that supplies a local constant current load. The proposed controller only utilises output currents of converters and the possible maximum error values in estimation of series resistance in the RLC filter used in each DGU. The proposed controller is formed such that the possible estimation error is considered as an uncertain parameter. In addition to obtaining two main objectives, average voltage regulation, and current sharing, a robust control problem is solved through an optimal control technique to calculate controller parameters such that the stability of the grid is guaranteed. The stability of the closed loop system with parametric uncertainty is proved through Lyapunov analysis. The closed loop system with the suggested controller is tested by simulations and through different scenarios to reveal the reliable and satisfactory performance of the proposed robust optimal control structure.

Stability of systems governed by elliptic partial differential equations

In this paper, we are concerned with global stability and optimal control analysis of systems governed by elliptic PDEs. We first investigate the eigenvalues distribution and the corresponding eigenfunctions of this system by Galerkin approximation method. Then, we show that this method allows us to obtain a new criterion for the global stability for this type of system. Afterward, we describe the structure of optimal controllers. Finally, as applications, we not only obtain the completeness of this system but also prove the existence and exponential stability of the closed-loop system governed by elliptic PDEs.

Adaptive linear quadratic regulator for optimal structural control based on wavelet transform and genetic algorithm

PurposeIn real life, excitations are highly non-stationary in frequency and amplitude, which easily induces resonant vibration to structural responses. Conventional control algorithms in this case cannot guarantee cost-effective control effort and efficient structural response alleviation. To this end, this paper proposes a novel adaptive linear quadratic regulator (LQR) by integrating wavelet transform and genetic algorithm (GA).Design/methodology/approachIn each time interval, multiresolution analysis of real-time structural responses returns filtered time signals dominated by different frequency bands. Minimization of cost function in each frequency band obtains control law and gain matrix that depend on temporal-frequency band, so suppressing resonance-induced filtered response signal can be directly achieved by regulating gain matrix in the temporal-frequency band, leading to emphasizing cost-function weights on control and state. To efficiently subdivide gain matrices in resonant and normal frequency bands, the cost-function weights are optimized by a developed procedure associated to genetic algorithm. Single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) structures subjected to near- and far-fault ground motions are studied.FindingsResonant band requires a larger control force than non-resonant band to decay resonance-induced peak responses. The time-varying cost-function weights generate control force more cost-effective than time-invariant ones. The scheme outperforms existing control algorithms and attains the trade-off between response suppression and control force under non-stationary excitations.Originality/valueProposed control law allocates control force amounts depending upon resonant or non-resonant band in each time interval. Cost-function weights and wavelet decomposition level are formulated in an elegant manner. Genetic algorithm-based optimization cost-efficiently results in minimizing structural responses.

Undiscounted reinforcement learning for infinite-time optimal output tracking and disturbance rejection of discrete-time LTI systems with unknown dynamics

This paper proposes a novel control structure to solve the infinite-time linear quadratic tracking (LQT) problem. The major challenge in the LQT problem is the boundedness issue of the cost function in an infinite time framework. In many studies, a discount factor is utilised to overcome the challenge. However, it can affect the stability of the closed-loop system and the steady-state error. This paper proposes an optimal control structure that guarantees zero steady-state error with bounded cost function without utilising the discount factor. The optimal gains of the proposed control structure are computed via model-based and model-free reinforcement learning (RL) algorithms. As a novelty in model-based RL algorithms, a model predictive RL algorithm is proposed to reduce the number of iterations in the learning phase. A model-free reinforcement learning algorithm is utilised to obtain optimal control for tracking the reference online and without any knowledge of system dynamics. Finally, the simulation results verify the advantages of the proposed optimal control structure.

Research for Optimal Programs for Controlling the Relative Motion of a Spacecraft with Limited Thrust

The problem of optimal control of the relative motion of a spacecraft with a finite thrust engine in arbitrary circumcircular orbits using the Pontryagin’s maximum principle is considered. Motion is studied in an orbital cylindrical coordinate system, using variables written in the form of secular and periodic components of relative motion in the orbital plane. The main attention is paid to the analysis of the optimal control structure with a free and transversal orientation of the thrust vector in the presence of passive areas on the trajectory. As a criterion for choosing the optimal control, the motor operating time of the corrective motors was considered. Characteristic control structures for various areas of initial driving conditions have been determined, and estimates of the marginal costs of motor time have been obtained.

Modeling and Optimal Control of a Two-Species Bioproducing Microbial Consortium

Motivated by recent laboratory experiments, we study microbial populations with light-inducible genetic differentiation that generates a two-species microbial consortium relevant for bioproduction. First, we derive a hierarchy of models describing the evolution of the microbial populations, each with decreasing complexity. This sequential order reduction reveals the connections between several popular classes of models used in this context. Second, we demonstrate the analytical insight the order reduction provides by studying the optimal control of such a reduced-order system of nonlinear ordinary differential equations. Appealing to Pontryagin’s maximum principle, we find different optimal control structures within different regions of the parameter space. Explicit solutions are obtained in a subset of parameter space, while, for the remainder of parameter space, closed-form solutions are obtained that depend on a scalar value that solves a particular transcendental equation. We show that a unique solution of the scalar equation exists and lies in a known compact interval, making its numerical approximation particularly easy. The analytical results are verified against direct numerical calculations.