Optimal Control System Research Articles

Intelligent Optimal Control System With Flexible Objective Functions and Its Applications in Wastewater Treatment Process

Optimal control system has been considered as a valuable technique to enhance the reliability and security of wastewater treatment process (WWTP). However, due to the complex environments, it is difficult to realize the optimal control with changeable operational conditions in WWTP. To overcome this problem, an intelligent optimal control system with flexible objective functions (IOCS-FOF) was proposed in this paper. The main merits of this proposed IOCS-FOF were shown as follows. First, an optimal control system scheme was developed, where different time-scale operational objectives were detailed to describe the operational features. Second, a flexible objective strategy was designed to determine suitable objective functions, which could adapt to complex environments of WWTP. Third, a novel dynamic multiobjective optimization algorithm for flexible objectives (FO-DMOA) was developed to obtain the optimal solutions of IOCS-FOF. Finally, the proposed IOCS-FOF was applied in the benchmark simulation model No. 1 (BSM1) to confirm its technique capability. The results demonstrate that this proposed method can improve the operation performance of WWTP.

Hardware in the Loop Simulation of Control Optimal of DC Motor Base on Modified Quantum-Behaved Particle Swarm Optimization

Proportional, Integral, Dervative (PID) controller is a simple and very reliable controller, but to determine the optimal control system parameters on the PID controller (Kp, Ki, and Kd) is not easy. This paper aims to determine the optimal parameters of the PID controller using Modified Quantum Behave Particle Swarm Optimization (MQPSO) to regulate the speed control of a DC motor. MQPSO is a method that has particle search behavior that is more detailed than its predecessor methods, namely Particle Swarm Optimization (PSO) and Quantum-Behaved Particle Swarm Optimization (QPSO). The test is done through Software In the Loop Simulation (SILS) by representing a DC motor in the transfer function, after the optimal control parameters are obtained then applied to the Hardware In the Loop Simulation (HILS) test using the actual DC motor. The test results show that the PID controller that has been optimized using MQPSO results in achieving DC motor response under steady conditions and is faster than the PID controller that is optimized using Ziegler-Nichols (ZN), PSO and QPSO. The completion time obtained by MQPSO is 41.0201 ms, which is also faster than using QPSO 42.8276 ms, PSO 43.7008 ms and ZN 61.8571ms.

Dual-Plate Injector for Throttling of Hydrogen Peroxide Monopropellant Thruster

This study provides an experimental analysis of the throttling methods implemented using a throttleable injector that generates a thrust in the range 24–64% on a 50 N monopropellant thruster using 90 wt.% hydrogen peroxide and . The injector proposed in this study is a dual-plate injector. It is capable of controlling the mass flow rate using radial slotted and showerhead-type plates. The slotted plate was rotated and pressed against the showerhead-type plate by intersecting a number of injection ports to control the mass flow rate. Firing tests were conducted over the throttling range to verify the feasibility of the concept of the dual-plate injector. The experimental data of the injectant flow rate and chamber pressure were analyzed parametrically. It was observed that the dual-plate injector had a characteristic velocity in the range 81–97% depending on the range of thrust. In addition, a correlation was observed between the characteristic velocity efficiency and response time of the injector under varying injection conditions; that is, the characteristic velocity tends to increase with a decrease in the response time. The result can be applied to optimal control systems, and also be used to execute advanced missions accurately using a monopropellant thruster.

Second Chebyshev wavelets (SCWs) method for solving finite-time fractional linear quadratic optimal control problems

In this paper, we present an indirect computational procedure based on the truncated second kind Chebyshev wavelets for finding the solutions of Caputo fractional time-invariant linear optimal control systems which the functional cost consists of the finite-time quadratic cost function. Utilizing the operational matrices of second Chebyshev wavelets (SCWs) of the Riemann–Liouville fractional integral, the corresponding linear two-point boundary value problem (TPBVP), obtained from the fractional Euler–Lagrange equations, is reduced to a coupled Sylvester-type matrix equation. An equivalent linear matrix form using the Kronecker product is constructed. The upper bound of the error of the SCWs approximation and the convergence of the proposed method are investigated. Low computational complexity and flexible accuracy are two important superiorities of this approach. Numerical experiments provide satisfactory results compared to the exiting techniques.

Applying Semiconductor Frequency Converters to Optimize Control Systems Operating at Nonferrous Metallurgy Production Facilities

Applying Semiconductor Frequency Converters to Optimize Control Systems Operating at Nonferrous Metallurgy Production Facilities

Wireless Networked Optimal Controllers for Multiple Plants

The wireless communication technologies nowadays are the most common ubiquitous innovations used in our life. It is much easier to run than wired one, and its applications are increasing steadily. It is now extensively utilized in wireless equipment controlling during the continuous development. That is, from a reasonable distance, we can monitor and control our electronics and electrical equipment. It can be said that tools can only be managed with a controller in hand from a distance without being close to the controller. One of the popular technology requirements in the present time is wireless technology. In this article, the proposed multi plant multi controller (MPMC) system is based on wireless sensor networks (WSNs). The aims are to design and implement of wireless closed-loop optimal control system for multiple plants. The system consists of two main parts: the station part and the sensing part. The station part is designed for the purpose to control the system through the graphical user interface (GUI) designed in the LabVIEW program that gives signals to the sensing part wirelessly through the ZigBee nodes. The sensing part receives a signal from the station part wirelessly through the ZigBee node and used a wireless speed sensor to calculate the speed of connecting DC motors. Then, the sensing part returns the measure reading to the station side through another ZigBee node, to show the result in the GUI controlling the operations of the two plants. The work proves the feasibility of implementing the optimal MPMC systems through wireless networks using ZigBee technology.

Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case

<p style='text-indent:20px;'>In the real world, the demand cannot be depicted exactly because of customer behavior cannot be forecasted without error. In this paper, we study the effect of the error of the estimated price-demand parameters by analyzing the sensitivity of the optimal joint pricing and ordering policy on the price-demand parameters based on a periodic-review, multi-period and lost sale inventory model for perishable products with constant quantity decay rate and price-sensitive demand. Firstly, we formulate the joint pricing and inventory control problem and find the optimal ordering quantity and the optimal price for deterministic price-demand function. The optimal solutions show that the retailer tends to set a lower price in early periods of each ordering cycle in order to reduce the inventory holding costs. Furthermore, the sensitivity of the optimal joint pricing and inventory control system with respect to the price-demand parameters is examined analytically and evaluated numerically. The sensitivity analysis reveals that compared to the optimal ordering quantity, the optimal prices are less sensitive in the demand-price parameters. Finally, according to the findings of the sensitivity analysis, a heuristic method of regulating the estimated demand-price parameters is employed to improve the average profit. <b>185</b> words.</p>

Optimal control of Chlamydia model with vaccination

In this work, a vaccination model for Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease free equilibrium of model is shown to be locally asymptotically stable when the reproduction number is less than unity. The disease-free equilibrium of the model was proven not to be globally asymptotically stable. The model is also shown to undergo the phenomenon of backward bifurcation when the associated reproduction number is less than unity. The necessary conditions for the existence of optimal control and the optimality system for the model are established using the Pontryagin’s Maximum Principle. Global Sensitivity analysis is also carried out to determine parameters which most affect the dynamics of the disease, when the reproduction number, exposed, infectious and treated populations are used as response functions. The parameters that strongly drive the dynamics of the disease when the infectious class is used as the response function are the natural death rate \(\mu \), the treatment failure rate \(\varphi \), and the fraction of people that failed treatment p. Simulations of the optimal control system reveal that the strategy that combines Chlamydia trachomatis prevention and treatment is the most cost-effective strategy in the fight against the disease.

Model mikroturbiny wiatrowej o regulowanym kącie ustawienia łopat

The article presents the results of research into the operation of a model of a wind micropower plant with a variable blade angle. The research was carried out on a miniature model of a measuring stand built for the purpose of carrying out work on pre-developed projects of wind micro power plants. The stand allows to carry out measurements related to the selection of the optimal propeller geometry, as well as the development and testing of algorithms for optimal control of the micropower plant. The physical basics of wind turbine operation and the methods of its optimal control are presented. The results of the performed measurements for the selected propeller blade geometry with the possibility of changing its setting angle are presented. A DC generator with a load with a non-linear characteristic in the form of a Li-Po battery cell was used. The results of operation of a simple MPPT control algorithm are presented. The lack of optimal control systems for the operation of micropower plants is dictated by the general belief that the costs of its production are high in relation to the possible improvement of the efficiency of micropower plants. Moreover, the practical methods of controlling larger wind turbines are not optimal for small and very small turbines. The conducted research focused on determining the possibility of using turbines with variable blade angles depending on its rotational speed. In larger wind farms, changing the blade angle is mainly used to limit the power of the turbine at high wind speeds. In micro wind power plants such solutions are not used for economic reasons. However, the use of a simple mechanism for changing the angle of the blades depending on the rotational speed of the propeller can increase the efficiency of the turbine in a wider range of wind speeds. The small dimensions of the research model allow for quick and cheap development of preliminary prototypes of turbine blades thanks to the possibility of using 3D printing technology.

Chen-Chao Koo and the Early Numerical Weather Prediction Experiments in China

Although the first successful numerical weather prediction (NWP) project led by Charney and von Neumann is widely known, little is known by the international community about the development of NWP during the 1950s in China. Here, a detailed historical perspective on the early NWP experiments in China is provided. The leadership in NWP of the late Professor Chen-Chao Koo, a protégé of C. G. Rossby at the University of Stockholm during the late 1940s and a key leader of modern meteorology (particularly of atmospheric dynamics and physics) in China during the 1950s–70s, is highlighted. The unique contributions to NWP by Koo and his students, such as the ideas of formulating NWP as an “evolution” problem, in which the past data over multiple time steps are utilized, rather than an initial-value problem, and on the cybernetic aspects of atmospheric processes, i.e., regarding the motion of the atmosphere at various time scales as an optimal control system, are also emphasized.

Penalty Electricity Price-Based Optimal Control for Distribution Networks

With the integration of large-scale renewable energy and the implementation of demand response, the complexity and volatility of distribution network operations are increasing. This has led to the inconsistency between the actual net power consumption of power users and their optimal dispatching orders. As a result, the distribution networks cannot operate according to their optimization strategy. The study proposed a penalty electricity price mechanism and the optimal control method based on this electricity price mechanism for distribution networks. First, we established the structure of the distribution network optimal control system. Second, aiming at the actual net power consumption (including power generation and consumption) of power users tracking their dispatching orders, we established a penalty electricity price mechanism. Third, we designed an optimal control strategy and process of distribution networks based on the penalty electricity price. Finally, we verified the proposed method by taking the IEEE-33 node system as an example. The verification results showed that the penalty electricity price could effectively limit the net power consumption fluctuations of power users to achieve optimal control of distribution networks.

Optimal feedback control of stock prices under credit risk dynamics

In this paper we provide a stock price model that explicitly incorporates credit risk, under a stochastic optimal control system. The stock price model also incorporates the managerial control of credit risk through a control policy in the stochastic system. We provide explicit conditions on the existence of optimal feedback controls for the stock price model with credit risk. We prove the continuity of the value function, and then prove the dynamic programming principle for our system. Finally, we prove the Viscosity Solution of the Hamilton–Jacobi–Bellman equation. This paper is particularly relevant to industry, as the impact of credit risk upon stock prices has been prominent since the commencement of the Global Financial Crisis.

Inverse optimal control from incomplete trajectory observations

This article develops a methodology that enables learning an objective function of an optimal control system from incomplete trajectory observations. The objective function is assumed to be a weighted sum of features (or basis functions) with unknown weights, and the observed data is a segment of a trajectory of system states and inputs. The proposed technique introduces the concept of the recovery matrix to establish the relationship between any available segment of the trajectory and the weights of given candidate features. The rank of the recovery matrix indicates whether a subset of relevant features can be found among the candidate features and the corresponding weights can be learned from the segment data. The recovery matrix can be obtained iteratively and its rank non-decreasing property shows that additional observations may contribute to the objective learning. Based on the recovery matrix, a method for using incomplete trajectory observations to learn the weights of selected features is established, and an incremental inverse optimal control algorithm is developed by automatically finding the minimal required observation. The effectiveness of the proposed method is demonstrated on a linear quadratic regulator system and a simulated robot manipulator.

OPTIMAL CONTROL OF AN ACTUATOR OF A ROBOTIC GEARBOX

Problem. Despite the vigorous development of electric vehicles, the task of facilitating the driver to handle with elements of mechanical transmission remains relevant. For this purpose, the automation of mechanical transmission units is performed. For instance, so-called robotic gearboxes are widespread. The principle of operation of such gearboxes is similar to mechanical ones, but special separate actuators carry out the selection and shifting into the desired gear. The design of a robotic gearbox was proposed at the Automobile Department of Kharkiv National Automobile and Highway University. At this gearbox, two DC motors are used as actuators. The efficiency of this gearbox largely depends on the efficiency of the DC motors control system, which should provide smooth but at the same time fast and accurate positioning of their shafts. In previous works, PID controllers were used to controlling the actuator of the gearbox. However, although the PID controller provides satisfactory quality of the control system, it is not an optimal controller. Goal. The goal of this paper is to develop an optimal controller for the actuators of the robotic gearbox mentioned above. Methodology. To meet this goal, it was proposed to use a linear-quadratic controller (LQR). The analysis of the impact on transient processes in the control system of the values of the weighting factors in the quadratic performance criterion is performed. Results. The LQR synthesized provides high speed of response (within of 0.5 s) at the desired gear selecting and more than two times less overshoot compared to the PID regulator. Originality. The regularities in the gearbox drive performance when changing the values of the weighting factors in the performance criterion have been established. An optimal control system for the robotic gearbox actuator has been developed. Practical value. The implementation of the designed controller will increase the efficiency of the gearbox under consideration.

Adaptive optimal control of stencil printing process using reinforcement learning

The stencil printing process (SPP) is a critical operation in surface mount technology (SMT) because it contributes to 60% of soldering defects. The complex relationships between solder paste volume transfer efficiency (TE) and the SPP variables make the control of the solder paste volume TE during production a challenging problem. This research aims to optimize the stencil printing parameters in real time to control the solder paste volume TE and increase the first-pass yields of printed circuit boards (PCBs). A Reinforcement learning (RL) approach, specifically Q-learning, is used to control and maintain the volume TE within the spec limits in an optimal adaptive control system. RL deals with the problem of building a control system or an autonomous agent that can learn how to take the proper actions to reach its objectives through interaction with its environment. The application of RL in SPP is not yet fully explored; therefore, this study investigates the impacts of applying Q-learning to control the volume TE in real time. The proposed control systems capture the induced variations in the SPP for two printing directions and consequently adjust the significant and easy-to-change printing parameters in real time. Two types of Q-learning are explored: Q-table that uses a tabular format to store the Q-values and Q-network that uses an artificial neural network (ANN) to approximate the Q-value function. Moreover, a new heterogeneous reward function-based clustering is proposed, which is integrated into the Q-network to enhance its performance. The results show that the developed control systems can learn the optimal policy and take the proper actions to transit from initial states to terminal states. The proposed control systems using Q-network with a function approximator and heterogeneous reward function converge fully much faster than Q-table using continuous state space. Moreover, Q-network control systems are capable to transit more states to terminal states with a lower number of actions when compared to Q-table control systems.

Modelling and pH Control in Raceway and Thin-Layer Photobioreactors for Wastewater Treatment

One of the most critical variables in microalgae-related processes is the pH; it directly determines the overall performance of the production system especially when coupling with wastewater treatment. In microalgae-related wastewater treatment processes, the adequacy of pH has a large impact on the microalgae/bacteria consortium already developing on these systems. For cost-saving reasons, the pH is usually controlled by classical On/Off control algorithms during the daytime period, typically with the dynamics of the system and disturbances not being considered in the design of the control system. This paper presents the modelling and pH control in open photobioreactors, both raceway and thin-layer, using advanced controllers. In both types of photobioreactors, a classic control was implemented and compared with a Proportional–Integral (PI) control, also the operation during only the daylight period and complete daily time was evaluated. Thus, three major variables already studied include (i) the type of reactors (thin-layers and raceways), (ii) the type of control algorithm (On/Off and PI), and (iii) the control period (during the daytime and throughout the daytime and nighttime). Results show that the pH was adequately controlled in both photobioreactors, although each type requires different control algorithms, the pH control being largely improved when using PI controllers, with the controllers allowing us to reduce the total costs of the process with the reduction of CO2 injections. Moreover, the control during the complete daily cycle (including night) not only not increases the amount of CO2 to be injected, otherwise reducing it, but also improves the overall performance of the production process. Optimal pH control systems here developed are highly useful to develop robust large-scale microalgae-related wastewater treatment processes.

An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model.

This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20–43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919–2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity.

Optimal Sliding Mode Control of Permanent Magnet Direct Drive Linear Generator for Grid-Connected Wave Energy Conversion

the key goal of this article is on the design and optimum sliding mode control for Grid-Connected direct drive extraction method of ocean wave energy by Multi-Objective Particle Swarm Optimization (MOPSO). A Linear Permanent Magnet Generator simulates the ocean wave energy extraction system, driven by an Archimedes Wave Swing. Uncontrolled three-phase rectifiers, a three-level buck-boost converter and 3 level neutral point clamped inverter are planned grid integration of Wave Energy Conversion device. The technique monitors the three-level buck-boost converter service cycle linked to the PMLG output terminals and decides the optimum switching sequence of 3 level neutral point clamped inverter to enable the grid relation. Simulations using Matlab/Simulink were carried out to test working of the wave energy converter after the suggested optimal control method was applied under various operating settings. Various simulation test results indicate that the proposed optimum control system is tested in both normal and irregular ocean waves. And it has been shown that the control method of the MOPSO sliding mode is ideal for maximizing energy transfer efficiency. Better voltage management at the DC-link and for achieving greater controllability spectrum was accomplished by the proposed Duty-ratio optimal control system.

Optimal Sliding Mode Control of Permanent Magnet Direct Drive Linear Generator for Grid-Connected Wave Energy Conversion

the key goal of this article is on the design and optimum sliding mode control for Grid-Connected direct drive extraction method of ocean wave energy by Multi-Objective Particle Swarm Optimization (MOPSO). A Linear Permanent Magnet Generator simulates the ocean wave energy extraction system, driven by an Archimedes Wave Swing. Uncontrolled three-phase rectifiers, a three-level buck-boost converter and 3 level neutral point clamped inverter are planned grid integration of Wave Energy Conversion device. The technique monitors the three-level buck-boost converter service cycle linked to the PMLG output terminals and decides the optimum switching sequence of 3 level neutral point clamped inverter to enable the grid relation. Simulations using Matlab/Simulink were carried out to test working of the wave energy converter after the suggested optimal control method was applied under various operating settings. Various simulation test results indicate that the proposed optimum control system is tested in both normal and irregular ocean waves. And it has been shown that the control method of the MOPSO sliding mode is ideal for maximizing energy transfer efficiency. Better voltage management at the DC-link and for achieving greater controllability spectrum was accomplished by the proposed Duty-ratio optimal control system.

An Optimal Control Perspective on Weather and Climate Modification

Intentionally altering natural atmospheric processes using various techniques and technologies for changing weather patterns is one of the appropriate human responses to climate change and can be considered a rather drastic adaptation measure. A fundamental understanding of the human ability to modify weather conditions requires collaborative research in various scientific fields, including, but not limited to, atmospheric sciences and different branches of mathematics. This article being theoretical and methodological in nature, generalizes and, to some extent, summarizes our previous and current research in the field of climate and weather modification and control. By analyzing the deliberate change in weather and climate from an optimal control and dynamical systems perspective, we get the ability to consider the modification of natural atmospheric processes as a dynamic optimization problem with an emphasis on the optimal control problem. Within this conceptual and unified theoretical framework for developing and synthesizing an optimal control for natural weather phenomena, the atmospheric process in question represents a closed-loop dynamical system described by an appropriate mathematical model or, in other words, by a set of differential equations. In this context, the human control actions can be described by variations of the model parameters selected on the basis of sensitivity analysis as control variables. Application of the proposed approach to the problem of weather and climate modification is illustrated using a low-order conceptual model of the Earth’s climate system. For the sake of convenient interpretation, we provide some weather and climate basics, as well as we give a brief glance at control theory and sensitivity analysis of dynamical systems.