Modern Optimal Control Theory Research Articles

Optimal vibration control of moving-mass beam systems with uncertainty

A linear optimal regulator for uncertain system is designed through the application of the probability density evolution method to linear quadratic regulator controller. One important background of this work is bridge-vehicle/gun-projectile system. This type of optimal problem is currently transformed into a moving load problem. The developed optimal regulator can provide the law of probability densities of outputs varying with time. In order to make the advocated method reach an optimal performance, the beneficial weighting matrix pair (Q, R) is selected using a trade-off sense. The designed regulator is then applied to a coupled simply supported beam-moving mass system, choosing the mid-span deflection as an output response and considering stochastic system parameters. The numerical example shows that the robustness of the proposed optimal regulator cannot be overestimated in comparison with a deterministic linear quadratic regulator controller. Further, the proposed method can produce an efficient solution channel for modern optimal control theory, especially, when compared with different uncertain optimal control techniques.

Optimization of Induction Heating Regarding Typical Quality Criteria: Problem Solution Based on 2D FEM Analysis

One of the most widespread methods of heating is induction mass heating because it offers certain advantages over similar technologies, including convectional and electrical heating. A significant economical effect can be achieved through optimization of heating modes and design parameters of induction heaters on the basis of modern optimal control theory for distributed parameters systems. The paper is devoted to the numerical simulation and optimal with respect to typical quality criteria control of thermal modes for metals induction heating before hot forming operations. Two-dimensional non-linear time-optimal control problem, problem of maximum heating accuracy and problem of minimum energy consumption are formulated and reduced to the mathematical programming problems. Optimization procedures are based on the developed at SamSTU alternance method of optimal control theory for distributed parameters systems. 2D FLUX code provides FEM analysis of interrelated electromagnetic and temperature fields during induction heating of a cylindrical billet before its hot forming. The model integrated into optimization procedures provides options for variation of the heating system parameters or billet geometry, and for evaluating the process optimization abilities. Computational results for optimal heating of aluminum cylindrical billets are shown and analyzed.

Maximum principle for optimal distributed control of viscous weakly dispersive Degasperis–Procesi equation

This paper is concerned with the optimal distributed control of the viscous weakly dispersive Degasperis–Procesi equation in nonlinear shallow water dynamics. It is well known that the Pontryagin maximum principle, which unifies calculus of variations and control theory of ordinary differential equations, sets up the theoretical basis of the modern optimal control theory along with the Bellman dynamic programming principle. In this paper, we commit ourselves to infinite dimensional generalizations of the maximum principle and aim at the optimal control theory of partial differential equations. In contrast to the finite dimensional setting, the maximum principle for the infinite dimensional system does not generally hold as a necessary condition for optimal control. By the Dubovitskii and Milyutin functional analytical approach, we prove the Pontryagin maximum principle of the controlled viscous weakly dispersive Degasperis–Procesi equation. The necessary optimality condition is established for the problem in fixed final horizon case. Finally, a remark on how to utilize the obtained results is also made. Copyright © 2015 John Wiley & Sons, Ltd.

Problem Oriented Simulation of Heating Stage in Technological Chain for Metal Hot Forming

Most high duty parts used in various fields of productions are forged parts made of steel. The conventional forging process chains include an induction heating systems and hot forming equipment. The large amount of consumed energy and an excess of material (flash) are the main factors motivating necessity to optimize the industrial technologies of metal hot forming. A significant economical effect can be achieved through optimization of heating modes and design parameters of induction heaters on the basis of modern optimal control theory for distributed parameters systems. The aim of the presented research is a problem-oriented simulation of induction heating stage in the forging chain. 2D ANSYS model provides FEM analysis of interrelated electromagnetic, temperature and thermal stress fields during induction heating of a steel cylindrical billet before its hot forming. The model has interface adapted to optimization procedures; it provides more options for variation of the heating system parameters or billet geometry and material properties, and for evaluating the process optimization abilities.

A study on vertical motions of high-speed planing boats with automatically controlled stern interceptors in calm water and head waves

The controllable flaps and interceptors in planing crafts not only may reduce the resistance, but also could be designed to make a boat run at or near optimum attitude in various environments, which results in a reduction in both resistance and vertical motion in waves. Planing vessels suffer from porpoising instability and violent vertical motion at high forward speeds. The controllable flaps and interceptors can be used to control and reduce the vertical motion of planing crafts. In the present study, the impact of controlled interceptors on a planing craft seakeeping quality is investigated through application of experimental and theoretical methods. In the experimental part of the study, a scaled-down model of a high-speed planing catamaran is tested with and without controllable stern interceptors in calm water and regular head waves, to investigate the effect of automatically controlled interceptors on vertical motion reduction of the model. Through application of modern optimal control theory and Savitsky's method, a control-oriented model of the vertical motion of the planing boat with interceptors in calm water and waves is developed. A simulation environment has been developed in MATLAB and SIMULINK. MATLAB has been used to formulate the model and to provide a suitable environment for control studies. The results obtained, the model, shows good agreement between the experimental and simulated data. Both the experimental and simulated results show that controllable aft interceptors can be used not only for minimising resistance, but also for reducing the vertical motions, especially at or near the resonant frequency. The results also proved that in automatic control system for controlling stern interceptors, a feedback of pitch angle and pitch velocity to the interceptors are effective for vertical motion damping of planing boat in calm water and head waves.

Multi-model Description of Monitoring and Control Systems of Natural and Technological Objects

The paper discusses theoretical foundations of a formal description of monitoring and control systems (MTSs) that are used for the monitoring and control of various natural and technological systems (NTSs). The performed state-of-theart analysis has demonstrated that the theory, methods and techniques related to the application of various types of models, such as mathematical, logical-algebraic, logical-linguistic, simulation and combined ones, for describing NTO MCS are widely used. On that basis, a conceptual description of NTO monitoring and control systems is proposed. It is based on a concept of NTO MCS multi-model description. The proposed general model includes particular dynamic models that describe motion control, channel control, operation control, flow control, resource control, operation parameter control, structure dynamic control, and auxiliary operation control of the considered monitoring and control system. The proposed interpretation of NTO MCS structure dynamics control processes provides advantages of applying the modern optimal control theory to NTO MCS analysis and synthesis.

Integrated supply chain planning based on a combined application of operations research and optimal control

In operations research (OR), remarkable advancements have been achieved in the domain of supply chain (SC) planning for the last two decades. In recent years, the works on SCs have been broadened to integrate production and transportation planning along with covering the SC dynamics and execution control. Based on a combination of fundamental results of the modern optimal program control (OPC) theory with the optimization methods of OR, an original integrated model of production and transportation planning in the SC is developed. It is shown explicitly how to distribute static and dynamics variables and constraints among the OR and OPC models and interconnect static elements in optimization linear programming model with corresponding dynamic elements in OPC model. This makes it possible to integrate SC production and transportation planning and execution taking into account process non-stationarity caused by structure dynamics. In doing so, the developed framework contributes to the advancing decision-making support for supply chain management (SCM). Conventionally isolated SCM problems may be considered from a different viewpoint and new integrated problems may be revealed, stated and solved due to the mutual enriching of OR and OPC techniques.

Dynamic supply chain scheduling

Based on a combination of fundamental results of modern optimal program control theory and operations research, an original approach to supply chain scheduling is developed in order to answer the challenges of dynamics, uncertainty, and adaptivity. Both supply chain schedule generation and execution control are represented as an optimal program control problem in combination with mathematical programming and interpreted as a dynamic process of operations control within an adaptive framework. Hence, the problems and models of planning, scheduling, and adaptation can be consistently integrated on a unified mathematical axiomatic of modern control theory. In addition, operations control and flow control models are integrated and applicable for both discrete and continuous processes. The application of optimal control for supply chain scheduling becomes possible by formulating the scheduling model as a linear non-stationary finite-dimensional controlled differential system with the convex area of admissible control and a reconfigurable structure. For this model class, theorems of optimal control existence can be used regarding supply chain scheduling. The essential structural property of this model are the linear right parts of differential equations. This allows applying methods of discrete optimization for optimal control calculation. The calculation procedure is based on applying Pontryagin's maximum principle and the resulting essential reduction of problem dimensionality that is under solution at each instant of time. The gained insights contribute to supply chain scheduling theory, providing advanced insights into dynamics of the whole supply chains (and not any dyadic relations in them) and transition from a partial one-way schedule optimization to the feedback loop-based dynamic and adaptive supply chain planning and scheduling.

Drag-free control system for frame dragging measurements based on cold atom interferometry

This paper describes the design and analysis of the drag-free and attitude control system (DFACS) for frame dragging measurements using a cold atom interferometer. The general architecture of the DFACS is derived and important aspects of the control system are discussed. This includes requirements and constraints, design and equipment issues. The actual control algorithms derived in this paper are designed as decoupled SISO controllers using modern optimal control theory (LQG, H ∞ ). The performance of the control system is analyzed in a comprehensive simulation campaign. From the results it can be concluded that the proposed system can meet the requirements for frame dragging measurements, with very little additional technology adaptation for the drag-free sensor and micro-propulsion system.

A method for the optimal control of forging process variables using the finite element method and control theory

In this paper, a new method is advanced for optimal control of the thermomechanical parameters during hot plastic-working processes of advanced materials, based on the finite element method and modern optimal control theory. The proposed method can be described as follows. First, the optimal trajectories of the thermomechanical parameters were defined from a grain size evolution model and the stable regions of the thermomechanical parameters. The stable regions were determined by combining artificial neural networks (ANN) with the dissipative structure theory. Second, the finite element models were transferred to suitable state–space models. Third, the optimal profile for the process parameters was fixed based on the state–space models and linear quadratic regulator (LQR) theory in order that the thermomechanical parameters of selected locations within the forging conform to the optimal trajectories and physical constraints. Applying the proposed method to an upsetting process of IN718 alloy, the ram velocity profile was determined to obtain high quality forgings. The proposed method lays the theoretical foundation for the open-loop control of forging processes for difficult-to-deform materials.

Infinite dimensional optimal control theory

One of the milestones in modern optimal control theory is the, Pontryagin Maximum Principle, which was firstly established by Pontryagin and his colleagues in later 50s for finite dimensional optimal control problems. In this survey paper, we revisit some extensions of the maximum principle in infinite dimensional spaces, developed via the infinite dimensional spike variation technique

Synergistic aircraft design using CFD air loads

A novel approach to the art of optimal design of modem flying vehicles including the application of multiple objective functions and constraints is presented. The method employs a two stage optimization procedure so that local minima and global minima of multiple objective functions can be determined synergistically. The concept of system identification is also used to characterize a nonlinear system in terms of generalized state space coordinates. Next, the modern optimal control theory is applied to design concurrently the multidisciplinary functional elements of an advanced aircraft system. Hence, the procedure proposed here should hopefully advance the art of modern aircraft design and reduce the period of design cycle and cost by an order of magnitude.

Passive and Semi-Active Airspring Suspensions for Rail Passenger Vehicles—Theory and Practice

The performance of passive and semi-active secondary airspring suspension systems on rail passenger vehicles has been studied theoretically and experimentally. Classical and modern optimal control theory was utilized in the studies. The concept of the semi-active damper was realized in a laboratory test by a butterfly valve, for which a practical position control logic was developed. The quarter vehicle test rig results have shown that by making the orifice damper variable, a 29 per cent ride improvement has been achieved. For the full vehicle computer simulation, a ride improvement of 20 per cent has been achieved. In addition, for both cases, the dynamic suspension working space has been reduced by 10 per cent.

Non-linear multidisciplinary design optimization using system identification and optimal control theory

A novel approach to the art of optimal design of modern flying vehicles including the application of multiple objective functions and constraints is presented and should hopefully advance the art of modern aircraft design. First, the concept of system identification is used to characterize non-linear systems in terms of generalized state space coordinates. Next, modern optimal control theory is applied to design concurrently, the functional elements of an aircraft system. Furthermore, modal coordinates are used to formulate the equations of motion of the total system so that the computational effort is minimized. The proposed analytical concept is validated using simple test cases.

Optimal control of the activated sludge process

This paper describes an application of modern optimal control theory techniques in the regulation of the activated sludge process. The process is simulated using multicomponent biological reactor and dynamical thickening models. The control problem is formulated with recycle and wastage rates as control variables and is characterized by high dimensionality and system model nonlinearity. The solution is obtained by a Newton-type successive approximations control method. In the case study, this approach is compared with (1) the commonly proposed recycle ratio control strategy and (2) a constant recycle and wastage rate stategy. Wastage regulation is shown to be a much more effective control input than recycle for reducing effluent organic variability. The control framework proposed can be extended to include other regulation schemes and account for process and input uncertainties.

Horizontal Plasma Position Control System for a Tokamak Using Modern Optimal Control Theory

A feedback system based on the modern optimal control theory for the horizontal position control of a tokamak plasma device is constructed with an analog sample and hold technique. The efficacy of this system is studied experimentally. High-speed control is realized by analog circuits. The sample and hold method is suitable for separating first-order values from zeroth-order ones, and hence it is useful for the linearization of the non-linear system for a tokamak circuit. These techniques give the guidance for the optimal regulator to control the plasma position.

Optimal Control for Xenon Spatial Oscillations in Load Follow of a Nuclear Reactor

A simple core control model is developed for the control of xenon spatial oscillations in load following operations of a current-design nuclear pressurized water reactor. The model is formulated as a linear-quadratic tracking problem in the context of modern optimal control theory, and the resulting two-point boundary problem is solved directly by the techniques of initial value methods. The system of state equations is composed of the one-group diffusion equation with temperature and xenon feedbacks, the iodine-xenon dynamics equations, and an energy balance relation for the core. Control is via full-length and part-length control rod banks, boron, and coolant inlet temperature. The system equations are linearized around an equilibrium state, which is an eigensolution of the nonlinear static equations with feedback. The nonlinear eigenvalue problem is shown to have a unique positive solution under certain conditions by using the bifurcation theory, the solution being obtained by an iteration based on the use of monotone operators. A modal expansion reduces the linearized equations to a lumped parameter system.

Analysis of Modern Optimal Control Theory Applied to Plasma Position and Current Control in TFTR

The strong compression TFTR discharge has been segmented into regions where linear dynamics can approximate the plasma's interaction with the OH and EF power supply systems. The dynamic equations for these regions are utilized within the linear optimal control theory framework to provide active feedback gains to control the plasma position and current. Methods are developed to analyze and quantitatively evaluate the quality of control in a nonlinear, more realistic simulation. Tests are made of optimal control theory's assumptions and requirements, and the feasibility of this method for TFTR is assessed.

状態遷移行列による多層平面壁体伝熱系の解析 : その 1 近似伝達関数モデルの作成とその精度

The objective of this study is to analyze the dynamic behaviour of room air and surface temperatures when (a) the system parameters are time dependent, (b) the radiant heat exchange between interior surfaces or the multi-space heat transfer has to be considered and (c) the modern optimal control theory is applied to these control systems. State variable vector is applicable to solve these problems. In this paper, the mathematical modeling of the multi-layer heat transfer system is described and the accuracy of its approximate transfer functions is discussed in detail by using vector locus of the frequency response. The summaries are as follows : 1) Various aspects to analyze the multi-layer heat transfer system are investigated. They are; (a) basic equation describing the system, (b) analytical domain and (c) state space concept. 2) Sensitivities of the heat flux response at the surface of a concrete wall against the air temperature exitation are examined to the parameter variation. Heat flux at the surface is very sensitive to the variation of the exited-side film conductance. 3) The frequency responses of several transfer functions models are compared with the exact one by using vector locus. An approximate transfer functions model is proposed to describe the heat flux response at the surface of multi-layer slabs against the surface temperature exitation. This model is based on the approximate 2-P chain matrix of each layer. 4) This model is applied to various kinds of multi-layer walls and roofs. Sufficient results can be obtained.

Optimal control in some cancer chemotherapy problems

This paper deals with a number of ideas which may be applicable when investigating the use of modern optimal control theory to certain cancer chemotherapy problems. A new mathematical model is developed and incorporates the growth kinetics of the tumour together with a cell loss term involving the therapeutic agent. Then several new models with different performance criteria are discussed for populations of normal and tumour cells. The final section deals with a new control problem for a model having two compartments and a cell-cycle-specific chemotherapeutic agent.