Optimal control of a wind energy conversion system and a wind turbine

Currently, a maximum power point tracking (MPPT) unit implemented in a wind energy conversion system (WECS) extracts the maximum mechanical power from the wind turbine used in the WECS. Therefore, the MPPT unit acts as a maximum mechanical power tracker (MMPT) that performs optimal control of the wind turbine to extract the maximum mechanical power from the wind turbine. In this paper, the basic concept of a maximum electrical power tracker (MEPT) is presented both theoretically and technically. It is demonstrated that an MEPT implemented in a WECS maximizes the output electrical power of the WECS. Thus, in contrast with an MMPT, the proposed MEPT optimally controls the whole of the WECS, rather than the wind turbine, to extract the maximum electrical power from the WECS. Since, in the WECS, the power efficiency of the whole of the WECS, not the wind turbine, should be maximized to extract the maximum output electrical power from the WECS, the conventional MPPT unit acting as an MMPT should be replaced with the proposed MEPT, and this is the superiority of the proposed MEPT to an MMPT or a conventional MPPT unit. To provide experimental verifications, 2 novel MEPT and MMPT with simple structures and better performance compared to the MPPT techniques commonly used in WECSs have been constructed, which are presented in detail.     

Wind time series modeling and stochastic optimal control for a grid‐connected permanent magnet wind turbine generator

In this paper, the control system of a permanent‐magnet synchronous machine wind turbine generator connected to the grid is studied. A set of wind speed time series is used to model the rapidly changing wind speed component as a stochastic process. Several control laws, including the nonlinear stochastic optimal controller, are developed, and their efficiency is examined comparatively and under various conditions. Also, the effect of parameter uncertainty to the system efficiency is shown through simulations. The results show that the system efficiency increase obtained by the use of sophisticated control techniques, although not dramatic, is not negligible. Copyright © 2015 John Wiley & Sons, Ltd.     

A new decentralized robust controller design for multi-area load–frequency control via incomplete state feedback

This paper deals with load–frequency control of a multi-area power installation. The robust control theory is utilized to decouple the areas for a decentralized robust load–frequency controller. The proposed controller ensures that the overall multi-area power system is asymptotically stable. A new technique is included to exclude feedback from any immeasurable state. The product comprises a set of local load–frequency controllers, one for each area. The design and operation of each local controller requires solely the corresponding area's parameters and state measurements. Measurements of the immeasurable states are unnecessary. System parameter uncertainties and generation rate constraints are included in the simulation study of a three-area power system. Good results are reported. Copyright © 1998 John Wiley & Sons, Ltd.     

Load frequency predictive control for power systems concerning wind turbine and communication delay

This article addresses a model predictive control (MPC) technique for load frequency control (LFC) system in the presence of wind power, communication delay, and denial-of-service (DoS) attack. In this article, communication delay is incorporated into a single area control error transmission for simplicity, wind power and load disturbance are regarded as Lipschitz nonlinear terms, as for the randomly occurring DoS attack, it is modeled as Bernoulli processes with known conditional probability. Thinking all these adverse factors to stability and the limitation of input constraint synthetically, the stability of LFC system can be guaranteed by delay-dependent Lyapunov function lemma and a state feedback MPC controller is designed to solve the LFC problems by minimizing the infinite-horizon objective function. Although some scholars have studied the performance degradation and instability of LFC system caused by cyber attack and/or communication delay and some very nice results have been addressed, limited works have considered the MPC approach to deal with both the problems of cyber attack and communication delay which explicitly considers the physical constraints. In addition, the delay-dependent Lyapunov function is adopted to deal with the problem of communication delay, which results in less conservatism of the presented method. Finally, the optimization problem with input constraint is solved and proven to be recursive feasibility, and the closed-loop system turns out to be stable. The reasonability and validity of the provided strategy is verified through several groups of simulation experiments. It illustrates that the proposed control method can keep the system frequency steady in the standard range in spite of various attack conditions.     

Semi‐decentralized approximation of optimal control of distributed systems based on a functional calculus

This paper discusses a new approximation method for operators that are solution to an operational Riccati equation. The latter is derived from the theory of optimal control of linear problems posed in Hilbert spaces. The approximation is based on the functional calculus of self‐adjoint operators and the Cauchy formula. Under a number of assumptions, the approximation is suitable for implementation on a semi‐decentralized computing architecture in view of real‐time control. Our method is particularly applicable to problems in optimal control of systems governed by partial differential equations with distributed observation and control. Some relatively academic applications are presented for illustration. More realistic examples relating to microsystem arrays have already been published. Copyright © 2014 John Wiley & Sons, Ltd.     

Hybridized gravitational search algorithm tuned sliding mode controller design for load frequency control system with doubly fed induction generator wind turbine

In this paper, the load frequency regulation problem of 2‐area interconnected power system is resolved using the sliding mode control (SMC) methodology. Interconnected 2‐area power systems with and without doubly fed induction generator wind turbines are considered for implementing the proposed optimal control methodology. Here, a heuristic gravitational search algorithm (GSA) and its variants such as opposition learning–based GSA (OGSA), disruption‐based GSA (DGSA), and disruption based oppositional GSA (DOGSA) are employed to optimize the switching vector and feedback gains of SMC. In order to overcome the inherent chattering problem in SMC, the control signals are considered in the objective function. The robustness of optimized SMC is analyzed by the inclusion of nonlinearities such as generation rate constraint (GRC), governor deadband, and time delay during the signal processing between the control areas, which are present in the real‐time power system. The insensitiveness of the optimal controller is shown by variation in system parameters like loading condition, speed governor constant, turbine constant, and tie‐line power coefficient. Further, the optimal SMC has been studied with significant load variations and wind power penetration levels in the control areas. The potential of proposed SMC design with chattering reduction feature is shown and validated by comparing the results obtained with the other reported methods in the literature.     

Robust decentralized design of power system stabilizers taking into consideration system uncertainties

In complex power systems, changes in network configurations, various loading conditions, etc., cause system uncertainties. Without considering such uncertainties in the design, the conventional power system stabilizers (PSSs) may deteriorate the system robust stability. To overcome this problem, the proposed design incorporates the uncertainty model in the system representation. Then, the PSSs in a multi‐machine power system are arranged as the decentralized controller in a multi‐input multi‐output (MIMO) system. The robust stability margin of the closed‐loop control system is guaranteed in terms of the MIMO gain margin and phase margin. Control parameters of PSSs are optimized by a tabu search. Non‐linear simulation studies confirm the robustness of the designed PSSs against various uncertainties. Copyright © 2005 John Wiley & Sons, Ltd.     

A decentralized receding horizon optimal approach to formation control of networked mobile robots

This paper presents a receding horizon optimal controller with guaranteed stability for multirobot formation, taking into account collision and obstacle avoidance. The proposed scheme is based on synchronous decentralized strategy wherein all the vehicles that are connected via a packed‐delaying network solve a finite horizon–constrained optimal control problem to obtain their own control action at each sampling instant. First, each robot is modeled by a single integrator dynamics; then, by defining a control law for each robot and considering the effect of communication delay, the closed‐loop dynamics is described as a delay differential equation with tunable parameters. Afterwards, a novel finite‐horizon optimal control setup is established to obtain these adjustable gains such that a desirable formation is achieved. The efficiency and applicability of the suggested scheme are demonstrated by simulation results.     

Optimal control of a production system with periodic maintenance

In this paper we consider a production system consisting of one machine for which maintenance is performed on a periodic basis. When the machine is undergoing maintenance, the system is shut down and cannot produce. One part-type is produced and the demand rate is assumed to be constant. In order to make on-time delivery, the objective is to produce following the demand as closely as possible. However, the maintenance disruptions make the production deviate from the demand. We formulate the production flow control problem as an optimal control model and use Pontryagin's minimum principle to solve the special case of one up-down cycle. We then solve the general N-cycle problem based on the one-cycle solution.     

Optimal control of a flexible manipulator and controller order reduction

Presented is a control system design study for a flexible manipulator. The device consists of a DC electric motor drive connected via two flexible links to an end effector for position control. The paper details in tutotrial fashion optimal control designs using both H₂ and H_∞ methods with dynamic weighting. The resulting controller is found to be fairly of high order for implementation and so controller order reduction is considered. It is observed that reduction of the controller order beyond a nominal amount cannot be done. A reason for this is postulated using novel perturbation models where it is found that the controller reduction problem is, in this case, a roadblock to practical implementation of the control. Copyright © 1998 John Wiley & Sons, Ltd.     

Optimal control of a parabolic distributed parameter system via orthogonal polynomials

A class of optimal control of systems with distributed parameters is considered. The process of the systems under consideration is governed by a linear parabolic partial differential equation. By use of the modal space technique, the optimal control of a distributed parameter system is simplified into the optimal control of a linear time-invariant lumped-parameter system. Next, a direct computational method for evaluating the modal optimal control and trajectory of the linear time-invariant lumped-parameter is suggested. The method is based on using finite interpolating orthogonal polynomials to approximate modal state variables. The formulation is straightforward and convenient for digital computation. An illustrative example is given to demonstrate the advantage of this method. © 1998 John Wiley & Sons, Ltd.     

Model predictive and linear quadratic Gaussian control of a wind turbine

Model Predictive and linear quadratic Gaussian controllers are designed for a 5MW variable‐speed pitch‐regulated wind turbine for three operating points – below rated wind speed, just above rated wind speed, and above rated wind speed. The controllers are designed based on two different linear dynamic models (at each operating point) of the same wind turbine to study the effect of utilising different control design models (i.e. the model used for designing a model‐based controller) on the control performance. The performance of the LQG controller is enhanced by improving the robustness, achieved by replacing the Kalman filter with a modified Luenberger observer, whose gain is obtained to minimise the effect of uncertainty and disturbance. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental results of a control time delay system using optimal control

The optimal control for a temperature system with time delay is considered. Experimental results of the control system are presented in this contribution. The integral term in the controller is approximated by a quadrature method. Experimental results obtained demonstrate the effectiveness of the approximation method. By a simple analysis in time domain, we demonstrate the robustness of the optimal controller. We compare the optimal control's performance with an industrial PID controller. This controller was robustly tuned. The experiments indicate the correct optimization of the plant when the optimal control was employed, despite limitations in the sensor, actuators, non‐modeled dynamics, and uncertain parameters of the process. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal control of harvesting in a stochastic metapopulation model

We consider a metapopulation model for a single species inhabiting two bounded contiguous regions where movement of the population across the shared boundary is allowed. The population in one of the bounded regions can be harvested. We introduce stochastic growth rates for the two populations in a system of ordinary differential equations that model the population dynamics in these two regions. We derive the resulting stochastic control problem with harvesting in the one region as the control. The existence of an optimal control is established by solving an associated quasi‐linear–quadratic optimal control problem. We present numerical simulations to illustrate several scenarios. Copyright © 2011 John Wiley & Sons, Ltd.     

Linear quadratic optimal model-following control of a helicopter in hover

Presented are results of a study of the application of linear quadratic optimal model-following control applied to a Bell 205 helicopter in hover. The primary objective of good in-flight stability robustness and performance was accomplished via singular value analysis using perturbed systems. Nominal aircraft models were compared with experimental data and discrepancies quantified in a robustness criterion. Current military handling quality requirements were specified as a target model to be followed. The linear quadratic optimal control and command feedforward was found suitable for these requirements. Design analyses enabled consideration of the tuning process, where effects of variations in selected tuning parameters demonstrated their sensitivity to the design.     

Optimal control analysis of a mathematical model for unemployment

Unemployment is continuously increasing worldwide because of enormous increase in population. This paper attempts to propose an optimal control policy for a deterministic unemployment model. The model considers three states, namely, unemployment, employment, and newly created vacancies. Factors like retirement and death of employed persons, termination from job, and so forth are also included in the model. The optimal control analysis for proposed unemployment model is performed using Pontryagin's maximum principle. The conditions for optimal control of the unemployment problem with effective use of implemented policies to provide employment to unemployed persons and to create new vacancies are derived and analyzed. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal control of a delayed breast cancer stem cells nonlinear model

In this article, we consider a nonlinear model, which is governed by an ordinary differential equations system with time delays in state and control. The model is used in order to describe the growth of breast cancer cells under therapy. We seek optimal therapies to minimize the number of cancer cells as well as the total quantity of drug used in the treatment. In this way, we formulate an optimal control problem. We prove the existence of an optimal therapy and use Pontryagin's maximum principle in order to find optimality conditions, which characterize such optimal therapy. At last, both numerical results and conclusion are presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal multi‐interval control of a cantilever beam by a recursive control algorithm

The optimal‐distributed control of a transversely vibrating cantilever beam is studied with the objective of minimizing the deflection and velocity in a given period of time with the minimum possible expenditure of force. The beam undergoes transient vibrations and is subject to given displacement and velocity initial conditions. The control is exercised by means of a transversely distributed force referred to as the control force. In the present study, a multi‐interval optimal control method is developed with the application of a maximum principle. The method consists of dividing the control duration into several intervals and using the maximum principle to obtain the optimality conditions at each interval. The explicit solutions for a cantilever beam are obtained by a recursive algorithm that takes the final conditions of the last interval as the initial conditions of the next interval. The formulation and the method of solution are suitable and convenient for digital computation. Numerical results are given, which compare the deflections, velocities and the control force under the optimal multi‐interval control with those under the optimal single‐interval control. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal control of electrical vehicle incorporated hybrid power system with second order fractional-active disturbance rejection controller

This article proposes a novel control methodology employing a fractional-active-disturbance-rejection-controller for the combined operation of load frequency control and automatic voltage regulator of a hybrid power system. A two area hybrid power system with diverse energy sources like solar-thermal, conventional-thermal and wind sources equipped with appropriate system nonlinearities is investigated. In order to ascertain the role of modern-day electric-vehicle (EV), the hybrid power system is incorporated with EVs in both the areas. To establish an effective frequency, voltage and tie line power control of the hybrid power system, a second order fractional-active-disturbance-rejection-controller with fractional-extended state observer is modeled as secondary controller. Magnetotactic-bacteria-optimization (MBO) technique is applied to obtain optimal values of the controller gains and the hybrid system parameters. The robustness of the controller gains is tested under different system parameter changes from their nominal values. In addition, the effect of incorporating a power system stabilizer on the hybrid power system is evaluated. Further, the impact of integrating renewable sources and EVs in the hybrid power system is explored. Moreover, the stability of the hybrid power system is monitored with the inclusion of FACTS device. The developed controller operates encouragingly with reference to system stability, rapidity and accuracy in comparison to testified control strategies available in the literature. The robustness test under load-perturbation, solar-insolation, wind input variations also proves the efficiency of MBO optimized second order fractional-active-disturbance-rejection-controller gains.