Optimal decentralized control of a wind turbine and diesel generator system

This article presents a decentralized optimal controller design technique for the frequency and power control of a coupled wind turbine and diesel generator. The decentralized controller consists of two proportional-integral (PI)-lead controllers which are designed and optimized simultaneously using a quasi-Newton based optimization technique, namely, Davidon–Fletcher–Powell algorithm. The optimal PI-lead controllers are designed in such a way that there are no communication links between them. Simulation results show the superior performance of the proposed controller with a lower order structure compared to the benchmark decentralized linear-quadratic Gaussian integral controllers of orders 4 and 11. It is also shown that the proposed controller demonstrates an effective performance in damping the disturbances from load and wind power, as well as a robust performance against the parameter changes of the power system.     

Stabilizing a multimachine system via non-linear voltage controller with the use of a local control strategy

A new local control strategy with non-linear optimal controllers for a multimachine system is presented. Non-linear Field Voltage Controllers (NFVC) are designed with the use of the feedback linearization approach to adjust generator state variables to external reference signals resulting from optimal power flow calculation [P_i, Q_i, V_ti] in the stabilized power system. A non-linear control law has been derived for the three-dimensional [δ, ω, E′_q] one-axis model of a generator. The local control strategy has been verified for the New England 39 bus system. An extensive simulation study shows robustness of the non-linear controllers and better performance than PSS-based classical controllers. © 1997 John Wiley & Sons, Ltd.     

Digital redesign of analog controllers based on minimizing integral of squared errors

Digital redesign is to replace an existing well‐designed analog feedback controller by a digital one along with a sampler and a hold. In this paper, we present a digital redesign technique which takes into account both closed‐loop and intersample behaviour. More precisely, we give a numerical procedure to optimally discretize an analog controller such that the integral of the squared error between the closed‐loop step responses of the analog and digital controlled systems is minimized. A parametric expression is derived for evaluating the integral performance index. With this expression, the optimal digital redesign problem becomes an optimal parameter selection problem which can be solved using existing optimal parameter search algorithms. Moreover, it allows one to obtain optimal reduced‐order digital controllers for sampled‐data control systems over a range of sampling periods. Copyright © 2003 John Wiley & Sons, Ltd.     

Minimum effort dead‐beat control of linear servomechanisms with ripple‐free response

A new and systematic approach to the problem of minimum effort ripple‐free dead‐beat (EFRFDB) control of the step response of a linear servomechanism is presented. There is specified a set of admissible discrete error feedback controllers, complying with general conditions for the design of ripple‐free dead‐beat (RFDB) controllers, regardless of the introduced degree of freedom, defined as the number of steps exceeding their minimum number. The solution is unique for the minimum number of steps, while their increase enables one to make an optimal choice from a competitive set of controllers via their parametrization in a finite‐dimensional space. As an objective function, Chebyshev's norm of an arbitrarily chosen linear projection of the control variable was chosen. There has been elaborated a new, efficient algorithm for all stable systems of the given class with an arbitrary degree of freedom. A parametrized solution in a finite space of polynomials is obtained through the solution of a standard problem of mathematical programming which simultaneously yields the solution of a total position change maximization of servomechanism provided that a required number of steps and control effort limitation are given. A problem formulated in this way is consecutively used in solving the time‐optimal (minimum‐step) control of a servomechanism to a given steady‐state position with a specified limitation on control effort. The effect of EFRFDB control on the example of a linear servomechanism with torsion spring shaft, with the criterions of control effort and control difference effort, is illustrated and analysed. Copyright © 2001 John Wiley & Sons, Ltd.     

Delay‐dependent feedforward control of time‐delay systems with parametric uncertainties via dynamic IQCs

This paper studies the design problem of a robust delay‐dependent H _∞ feedforward controller design for a class of linear uncertain time‐delay system having state and control delays when the system is subject to ‐type disturbances. The proposed controller scheme involves two main controllers, which are static state‐feedback and dynamic feedforward controllers. The state‐feedback controller is used for stabilizing the delay and uncertainty‐free system, whereas the feedforward controller performs disturbance attenuation. Dynamic type integral quadratic constraints (IQCs), which consist of frequency‐dependent multipliers, have been introduced to represent the delays and parametric uncertainties in the system where the degree of the multiplier used in IQC representation is in an adjustable nature. This scheme allows the designer to obtain less conservative controllers with increasing precision. Sufficient delay‐dependent criteria in terms of linear matrix inequalities are obtained such that the uncertain linear time‐delay system is guaranteed to be globally, uniformly, asymptotically stable with a minimum disturbance attenuation level. Several numerical examples together with the simulation studies provided at the end illustrate the usefulness of the proposed design. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

Comparative performance analysis of 2DOF state feedback controller for automatic generation control using whale optimization algorithm

This paper presents the design of two‐degree‐of‐freedom state feedback controller (2DOFSFC) for automatic generation control problem. A recently developed new metaheuristic algorithm called whale optimization algorithm is employed to optimize the parameters of 2DOFSFC. The proposed 2DOFSFC is analyzed for a two‐area interconnected thermal power system including governor dead band nonlinearity and further extended to multiunit hydrothermal power system. The supremacy of the 2DOFSFC is established comparing with proportional‐integral, proportional‐integral‐derivative (PID), and 2DOFPID controllers optimized with different competitive algorithms for the concerned system. The sensitivity analysis of the optimal 2DOFSFC is performed with uncertainty condition made by varying bias coefficient B and regulation R parameters. Furthermore, the proposed controller is also verified against random load variations and step load perturbation at different locations of the system.     

Robust stabilization of switched positive discrete‐time systems with asynchronous switching and input saturation

This paper investigates the stabilization problems of switched positive discrete‐time systems with asynchronous switching and input saturation jointly. The asynchronous switching means that state feedback controllers lag behind the subsystems for a period. Next, the input saturation comes from the saturation effect of state feedback controllers. In this paper, the exponential stability condition is firstly obtained based on mode‐dependent average dwell time method. Then, under zero initial condition, we analyze the boundedness and l₁ ‐gain performance of the system with disturbance. Finally, considering that state feedback controllers for some subsystems cannot be designed, we study the exponential stability condition of the system with unstable subsystems. Moreover, optimization methods are given to get the optimal solution to the nonlinear inequality constraints.     

AGC of a two‐area multi‐source power system interconnected via AC/DC parallel links under restructured power environment

In this paper, automatic generation control (AGC) of a two‐area multi‐source power system interconnected via alternating current/direct current (AC/DC) parallel links under restructured power environment is proposed. Each area is equipped with multipower generating sources such as thermal and hydro/gas. To execute the different market contracts in restructured power system, the optimal regulators are designed and implemented using optimal control theory. It is observed that the system dynamic results effectively satisfy the AGC requirements in restructured power system, as well as the system dynamic performance is improved by using AC/DC parallel links in comparison with that obtained with AC link as an area interconnection between the control areas. Furthermore, the eigenvalue study is performed to examine the system stability with and without AC/DC parallel links. Finally, the effectiveness of the optimal regulators is checked for the system under study with physical constraints like time delay, boiler dynamics, generation rate constraints, and governor dead band nonlinearity and variations in system parameters from the nominal values. It is shown that the optimal regulators optimized for linear system are robust enough and work well in the proposed realistic AGC system incorporating physical constraints and wide variations in parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Implementation lessons and pitfalls for real‐time optimal control with stochastic systems

Modern computational power and efficient direct collocation techniques are decreasing the solution time required for the optimal control problem, making real‐time optimal control (RTOC) feasible for modern systems. Current trends in the literature indicate that many authors are applying RTOC with a recursive open‐loop structure, relying on a high recursion rate for implicit state feedback to counter disturbances and other unmodeled effects without explicit closed‐loop control. The limitations of using rapid, instantaneous optimal solutions are demonstrated analytically and through application to a surface‐to‐air missile avoidance control system. Two methods are proposed for control structure implementation when using RTOC to take advantage of error integration through either classical feedback or disturbance estimation. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

Restricted structure control of multiple model systems with Series 2 DOF tracking and feedforward action

The solution of a scalar optimal control problem is discussed where the feedback, series tracking and feedforward controllers are chosen to have a very simple. Each controller term may be chosen to be of reduced order, lead/lag, or PID forms, and the controller is required to minimize an LQG cost‐index. The optimization is based upon a cost‐function which also allows separate costing of the terms due to the feedback, tracking and feedforward controllers. The system model can be uncertain and can be represented by a set of models over which the optimization is performed. This provides a form of robust optimal control that might even be applied to non‐linear systems that can be approximated by a set of linearized models. The theoretical problem considered is to obtain the causal, stabilizing, feedback, series‐tracking and feedforward controllers, of a prespecified form, that minimize an LQG criterion over the set of possible linear plant models. The underlying practical problem of importance is to obtain a simple method of tuning low‐order controllers, given only an approximate model of the process. The results are illustrated in a power generation control problem for a system represented by 12 different linearized plant models. The single feedback controller that is obtained has a simple form and stabilizes the full set of models. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust continuous‐time controller design via structural Youla–Kučera parameterization with application to predictive control

This paper addresses the continuous‐time control of uncertain linear SISO plants and its nominal and robust stability and nominal and robust performance objectives. A specific application of the Youla–Ku?era (Q) parameterization concept leads to a new development of observer‐like controller structures. This method is combined with a nominal design of continuous‐time generalized predictive control suitable for both minimum‐phase and non‐minimum‐phase plants. The subsequent design procedure consists of two steps. Firstly, the nominal stability and nominal performance of the control system are established by using an analytical design methodology, based on a collection of closed‐loop prototype characteristics with definite time‐domain specifications. And secondly, a generic structure of the controller is enhanced by suitable Q‐parameters guaranteeing that the control system has the required robustness properties. The proposed structural (reduced‐order) Q‐parameterization relies on an observer structure of controllers, which can be easily enhanced with certain filters necessary for control robustification. To reduce the complexity of the resulting robust controllers, we suggest using a structural factorization, which allows for simple forms of robustifying (phase‐lag) correctors of low order, easy for implementation, and convenient for optimization and tuning. Two numerical examples are given to illustrate the composed technique and its practical consequences. Copyright © 2004 John Wiley & Sons, Ltd.     

Design and performance analysis of elephant herding optimization based controller for load frequency control in thermal interconnected power system

In this present contribution, an attempt has been taken to design and analyze the performance of elephant herding optimization (EHO) based controller for load frequency control (LFC) applications of interconnected power system. The studied system is a two‐area nonreheat thermal interconnected system which is widely used in literature. A proportional‐integral‐differential controller is utilized for LFC of the studied system. EHO technique is applied to obtain the tuned set of controller parameters. The objectives considered for design of the controller are the minimization of settling times and integral‐time‐multiplied‐absolute‐error of frequency deviations (FDs) and tie‐line power deviation (TPD). The design objectives are integrated together to form a function with single objective by assigning equal weights after normalization. Several test cases of diverse set of disturbances are taken into account to test the performance of the proposed controller and the obtained results are compared with other controllers designed with differential evolution, gray wolf optimization, particle swarm optimization, teacher‐learner‐based optimization, and whale optimization algorithm. Furthermore, the time‐domain simulations of FDs and TPD are illustrated to support the tabulated results. In addition, comparative statistical analysis is presented to validate the robust behavior of the proposed controller.     

Euler‐Lagrange equation: Case of energy‐optimal approach for induction machine

The optimal control problem that hinges on the Euler‐Lagrange equation can be applied to electric‐machine drives and the necessary and sufficient optimality conditions around the system control and the control variables can be designed in a congruent way. In this paper, a variational problem is proposed to minimize energy consumption by an Induction Motor (IM) under a Rotor Field–Oriented Vector Drive (RFOVD) during torque and speed transients. The optimal stimulus is to take into account real applications, like perturbed load torques, and an abrupt speed input. The approach consists of an off‐line algorithm that minimizes a cost functional or integral of the weighted sum of IM energy/power under the dynamic stress of the rotor flux and of rotation speed. The variational problem leads to a nonlinear differential equation known as the Euler‐Lagrange equation. A new method is suggested to run out an analytical solution and results in a time‐varying rotor flux considered as the optimal state variable of the dynamic IM model that saves energy of the IM drive under RFOVD. This solution provides loss‐minimization in steady‐state operations at an infinite horizon and performs adaptive suboptimal minimum‐energy consumption for torque transients. Simulation and experimental results are fully performed on 1.5‐kW laboratory IM, and prove the validity of the proposed method for both steady‐state and transient‐IM drive operations.     

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

By integrating the robust stabilizability condition, the orthogonal‐function approach (OFA) and the Taguchi‐sliding‐based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust‐optimal fuzzy parallel‐distributed‐compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi–Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite‐horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI‐based robust stabilizability condition, the robust‐optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrained‐optimization problem represented by the algebraic equations with constraint of LMI‐based robust stabilizability condition; thus, greatly simplifying the robust‐optimal PDC control design problem. Then, for the static constrained‐optimization problem, the TSBDEA has been employed to find the robust‐optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal control of non‐linear chemical reactors via an initial‐value Hamiltonian problem

The problem of designing strategies for optimal feedback control of non‐linear processes, specially for regulation and set‐point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations associated to a bilinear approximation of the dynamics and a quadratic cost is presented. The usual boundary‐value situation for the coupled state–costate system is transformed into an initial‐value problem through the solution of a generalized algebraic Riccati equation. This allows to integrate the Hamiltonian equations on‐line, and to construct the feedback law by using the costate solution trajectory. Results are shown applied to a classical non‐linear chemical reactor model, and compared against suboptimal bilinear‐quadratic strategies based on power series expansions. Since state variables calculated from Hamiltonian equations may differ from the values of physical states, the proposed control strategy is suboptimal with respect to the original plant. Copyright © 2005 John Wiley & Sons, Ltd.     

Reference output tracking control for a flexible air‐breathing hypersonic vehicle via output feedback

This paper addresses the problem of reference output tracking control for the longitudinal model of a flexible air‐breathing hypersonic vehicle (FAHV) by utilizing the output feedback control approach. The dynamic characteristics of the FAHV along with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover, there exist some intricate couplings between the engine and flight dynamics as well as complex interaction between rigid and flexible modes in the longitudinal model. These couplings bring difficulty to the flight control design for the intractable hypersonic vehicle systems. This paper deals with the problem of reference output tracking control for the longitudinal model of the FAHV. By utilizing the trim condition information including the state of altitude, velocity, angle of attack, pitch angle, pitch rate and so on, the linearized model is established for the control design objective. Then, the reference output velocity and altitude tracking control design problem is proposed for the linearized model. The flexible models of the FAHV system are hardly measured because of the complex dynamics and the strong couplings of the FAHV. Thus, by using only limited flexible model information, the reference output tracking performance analysis criteria are obtained via Lyapunov stability theory. Then, based on linear matrix inequality optimization algorithm, the static output feedback controller is designed to stabilize the closed‐loop systems, guarantee a certain bound for the closed‐loop value of the cost function, and can make the control output achieve the reference velocity and altitude tracking performance. Subsequently, the condition of dynamic output feedback controller synthesis is given in terms of linear matrix inequalities and a numerical algorithm is developed to search for a desired dynamic output feedback controller which minimizes the cost bound and obtains the excellent reference altitude and velocity tracking performance simultaneously. The effectiveness of the proposed reference output tracking control method is demonstrated in simulation part. Furthermore, the superior reference velocity and altitude performance commands could be achieved via using static and dynamic output feedback controllers under lacking some unmeasured flexible states information in the measurement output vector. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal trajectory generation and robust flatness–based tracking control of quadrotors

This work proposes an optimal trajectory generation and a robust flatness–based tracking controller design to create a new performance guidance module for the quadrotor in dense indoor environments. The properties of the differential flatness, the B‐spline, and the direct collocation method are exploited to convert the constrained optimization problem into a nonlinear programming one, which can be easily resolved by a classic solver. After that, the obtained optimal reference trajectory is applied to the dynamic quadrotor model and two different flatness‐based controllers, namely, one based on feedback linearization and one based on feedforward linearization, are developed and compared to ensure the trajectory tracking despite the existence of disturbances and parametric uncertainties. Numerical simulation is executed to evaluate the proposed optimal trajectory generation approach and the robust tracking strategies. It turns out that the controller based on feedforward linearization outperforms the feedback linearization one in robustness and permits obtaining a performance guidance law for an uncertain quadrotor system.     

Optimal dropout policies for networked control systems

By realizing the feedback paths over communication networks, we get a class of networked control systems (NCSs), where the network's quality‐of‐service (QoS) is commonly characterized by the average dropout rate of feedback data packets. The control performance of an NCS however, is determined not only by the average dropout rate but also by the dropout pattern of feedback data packets. This paper provides a systematic way to determine the optimal dropout pattern (policy) under a given average dropout rate, where the performance is measured by the output signal power under an exogenous white noise. By modeling the finite‐memory dropout policies with the general Markov chain, this paper formulates the optimal dropout policy design into the optimization of parameters of a dropout Markov chain. That optimization is first solved by an augmented Lagrangian gradient method, which may be stuck at local optima because of the problem's non‐convexity. To compensate this weakness, we apply the branch‐and‐bound method to the optimization whose constraints are bilinear. The branch‐and‐bound method can approach the global optimal solution with any desired tolerance in finite steps. The obtained optimal dropout policy may be interpreted as a network's QoS constraint whose enforcement provides a hard guarantee on the control system's performance. An example is used to illustrate the effectiveness of the achieved results. Copyright © 2012 John Wiley & Sons, Ltd.