Improving the grid frequency by optimal design of model predictive control with energy storage devices

This paper proposes the optimal design of model predictive control (MPC) with energy storage devices by the bat‐inspired algorithm (BIA) as a new artificial intelligence technique. Bat‐inspired algorithm‐based coordinated design of MPCs with superconducting magnetic energy storage (SMES) and capacitive energy storage (CES) is proposed for load frequency control. Three‐area hydrothermal interconnected power system installed with MPC and SMES is considered to carry out this study. The proposed design procedure can account for generation rate constraints and governor dead bands. Transport time delays imposed by governors, thermodynamic processes, and communication telemetry can be captured as well. In recent papers, the parameters of MPC with SMES and CES units are typically set by trial and error or by the designer's expertise. This problem is solved here by applying BIA to tune the parameters of MPC with SMES and CES units simultaneously to minimize the deviations of frequency and tie line powers against load perturbations. Simulation results are carried out to emphasize the superiority of the proposed coordinated design as compared with conventional proportional‐integral controller and with BIA‐based MPC without SMES and CES units.     

Minimizing control energy in a class of bounded‐control linear‐quadratic regulator problems

Minimal‐control‐energy strategies are substantiated and illustrated for linear‐quadratic problems with penalized endpoints and no state‐trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite‐dimensional set of admissible control trajectories to the finite‐dimensional Euclidean space of initial conditions. An efficient real‐time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure‐upper‐bounded brake, flexible‐endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd.     

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

In this paper, learning control is integrated with non‐linear optimal control to enhance control performance of a class of non‐linear systems with time‐varying parametric uncertainties. A suboptimal control strategy based on a control Lyapunov function (CLF) and Sontag's formula provides suboptimal performance as well as stability along the time horizon for the nominal part of the non‐linear dynamic system. The proposed learning mechanism learns the unknown time‐varying parametric uncertainties so as to eliminate uncertain effects. System information both in time horizon and learning repetition horizon are incorporated in a composite energy function (CEF). The proposed control scheme achieves asymptotic convergence along the learning repetition horizon and boundedness and pointwise convergence of the tracking error (perfect tracking performance) along the time horizon. Copyright © 2001 John Wiley & Sons, Ltd.     

Energy‐optimal control of a particle in a dielectrophoretic system

Dielectrophoresis is an electrokinetics‐based phenomenon that involves the motion of a particle due to interaction between its dipole moment and an applied nonuniform electric field. This technique is very effective in particle manipulation and separation. In this paper, we consider an energy optimal transfer of a particle in a dielectrophoretic system from one specified location to another desired location. The system is described by a set of ordinary differential equations with a quadratic term in the control variable (the control being the applied voltage on the electrodes which induces the electric field), making the system nonaffine. Copyright © 2011 John Wiley & Sons, Ltd.     

Joint control for flexible‐joint robot with input‐estimation approach and LQG method

In this work, the input‐estimation (IE) algorithm and the linear quadratic Gaussian (LQG) controller are adopted to design a control system. The combined method can maintain higher control performance even when the system variation is unknown and under the influence of disturbance input. The IE algorithm is an on‐line inverse estimation method involving the Kalman filter (KF) and the least‐square method, which can estimate the system input without additional torque sensor, while the LQG control theory has the characteristic of low sensitivity of disturbance. The design and analysis processes of the controller will also be discussed in this paper. The joint control of the flexible‐joint robot system is utilized to test and verify the effectiveness of the control performance. According to the simulation results, the IE algorithm is an effective observer for estimating the disturbance torque input, and the LQG controller can effectively cope with the situation that the disturbance exists. Finally, higher control performance of the combined method for joint control of the robotic system can be further verified. Copyright © 2007 John Wiley & Sons, Ltd.     

A robust control system scheme based on model predictive controller (MPC) for continuous‐time systems

In this paper, an LMI framework based on model predictive strategy is addressed to design a robust dynamical control law in a typical control system. In the proposed method, instead of traditional static controller, a dynamic control law is used. With a suitable matrix transformation, the controller parameters selection are translated into an optimization problem with some LMI constraints. The plant input and output constraints are also handled with another LMIs. The controller is represented in state space form, and its parameters are computed in real‐time operation. For achieving this goal, by solving an optimization problem, a dynamic controller is designed, which meets the required plant performances. These results are used in 2 numerical examples to demonstrate the effectiveness of the proposed approach.     

An approximate dynamic programming method for multi‐input multi‐output nonlinear system

Approximate dynamic programming is a useful tool in solving multi‐stage decision optimal control problems. In this work, we first promote the action‐dependent heuristic dynamic programming method to multi‐input multi‐output control system by extending its action network to multi‐output form. The detailed derivation is also given. We then apply this method to the fluctuation control of a spark engine idle speed. An engine idling model is set up to verify the control effect of this method. Results here show that this method requires several iterations to suppress unbalanced combustion by manipulating spark ignition timing. This method provides an alternative for a simpler multi‐input multi‐output approximate dynamic programming scheme. Moreover, it has a faster iteration convergence effect. The derivation of this method also has a rigorous mathematical basis. Although illustrated for engines, this control system framework should also be applicable to general multi‐input multi‐output nonlinear system. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal control for discrete‐time singular stochastic systems with input delay

The finite‐horizon linear quadratic regulation problem is considered in this paper for the discrete‐time singular systems with multiplicative noises and time delay in the input. Firstly, the extremum principle is discussed, and a stationary condition is derived for the singular stochastic system. Then, based on the relationships established between the state and the costate variables, the stationary condition is also shown to be a sufficient criterion assuring the existence of the solution for the stochastic control problem. The optimal controller is designed as a linear function of the current state and the past inputs information, which can be recursively calculated by effective algorithms. With the designed optimal controllers, the explicit expression is also derived for the minimal value of the performance index. One numerical example is provided in the end of the paper to illustrate the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ control for linear switched systems with time‐varying delay and dead‐zone inputs via an adaptive memory controller

This paper deals with the problem of robust H_∞ control for linear switched systems with time‐varying delay and dead‐zone inputs. First, a new state‐dependent switching law is proposed for the switched system with stable and unstable subsystems. Based on the proposed switching law and using the scaled small gain theorem, a more general stability criterion for the switched delay systems is established. Second, an adaptive memory controller is proposed for the switched system with dead‐zone inputs. With the help of a two‐term approximation of the time‐varying delay, the proposed memory controller only depends on the bounds of the time‐varying delay. Sufficient conditions on the existence of the desired controller are formulated in terms of linear matrix inequalities. Three examples are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal trajectory control for a two‐link rigid‐flexible manipulator with ODE‐PDE model

In this paper, the optimal trajectory control problem for a two‐link rigid‐flexible manipulator is considered. Since the two‐link rigid‐flexible system is a distributed system, an ordinary differential equation and partial differential equation (ODE‐PDE) dynamic model of the manipulator is established by Hamilton's principle. Based on the ODE‐PDE model, an optimal trajectory controller is proposed in this paper, which includes 2 stages. In the first stage, the optimal trajectory is created by using the differential evolution algorithm. Energy consumption and deflection of the flexible link are chosen as performance indexes. Cubic spline interpolation is applied to obtain the continuous trajectory. In the second stage, the aim is to regulate 2 joints to follow the optimal trajectory and simultaneously suppress vibration of the flexible link. To achieve it, boundary control laws are designed and the stability analysis is given. In simulations, the effectiveness of the optimal controller is verified by MATLAB.     

High‐order observers‐based LQ control scheme for wind speed and uncertainties estimation in WECSs

Tip speed ratio control is a popular method in wind energy conversion systems in order to capture the maximum power. This method, however, requires wind speed information, which is difficult in practice to accurately measure it. Therefore, estimation methods are usually applied, where a high‐precision estimate leads to a high‐efficient system. Based on the fact that the wind speed varies in a random way, this paper proposes a generalized high‐order observer to estimate the aerodynamic torque and the wind speed accordingly. This observer algorithm releases the assumption that the wind speed should be slowly varying, which is required in previous observer designs. Moreover, two other generalized high‐order observers are also applied to estimate the uncertainties, which depend on state variables and cannot be considered as slow‐varying disturbances. Using the outputs of these observers, a robust high‐performance optimal control system is developed for the rotor speed to keep the optimal tip speed ratio. The stability analysis of the designed control system is fully presented. The effectiveness of the proposed technique is validated via simulation studies.     

Inverse optimal controller based on extended Kalman filter for discrete‐time nonlinear systems

In this study, we present an inverse optimal control approach based on extended Kalman filter (EKF) algorithm to solve the optimal control problem of discrete‐time affine nonlinear systems. The main aim of inverse optimal control is to circumvent the tedious task of solving the Hamilton‐Jacobi‐Bellman equation that results from the classical solution of a nonlinear optimal control problem. Here, the inverse optimal controller is based on defining an appropriate quadratic control Lyapunov function (CLF) where the parameters of this candidate CLF were estimated by adopting the EKF equations. The root mean square error of the system states is used as the observed error in the case of classical EKF algorithm application, whereas, here, the EKF tries to eliminate the same root mean square error defined over the parameters by generating a CLF matrix with appropriate elements. The performance and the applicability of the proposed scheme is illustrated through both simulations performed on a nonlinear system model and a real‐time laboratory experiment. Simulation study demonstrate the effectiveness of the proposed method in comparison with 2 other inverse control approaches. Finally, the proposed controller is implemented on a professional control board to stabilize a DC‐DC boost converter and minimize a meaningful cost function. The experimental results show the applicability and effectiveness of the proposed EKF‐based inverse optimal control even in real‐time control systems with a very short time constant.     

Delay‐dependent robust passive control for a class of nonlinear systems with time‐varying delays

In this paper, the problem of robust passive control for a class of nonlinear systems with time‐varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov–Krasovskii functionals approach, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of time delay. We also design a state feedback controller that guarantees a robust asymptotically stable and strictly passive closed‐loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques. Copyright © 2007 John Wiley & Sons, Ltd.     

Quantitating the effect of prosthesis design on femoral remodeling using high‐resolution region‐free densitometric analysis (DXA‐RFA)

Dual energy X‐ray absorptiometry (DXA) is the reference standard method used to study bone mineral density (BMD) after total hip arthroplasty (THA). However, the subtle, spatially complex changes in bone mass due to strain‐adaptive bone remodeling relevant to different prosthesis designs are not readily resolved using conventional DXA analysis. DXA region free analysis (DXA RFA) is a novel computational image analysis technique that provides a high‐resolution quantitation of periprosthetic BMD. Here, we applied the technique to quantitate the magnitude and areal size of periprosthetic BMD changes using scans acquired during two previous randomized clinical trials (2004 to 2009); one comparing three cemented prosthesis design geometries, and the other comparing a hip resurfacing versus a conventional cementless prosthesis. DXA RFA resolved subtle differences in magnitude and area of bone remodeling between prosthesis designs not previously identified in conventional DXA analyses. A mean bone loss of 10.3%, 12.1%, and 11.1% occurred for the three cemented prostheses within a bone area fraction of 14.8%, 14.4%, and 6.2%, mostly within the lesser trochanter (p < 0.001). For the cementless prosthesis, a diffuse pattern of bone loss (−14.3%) was observed at the shaft of femur in a small area fraction of 0.6% versus no significant bone loss for the hip resurfacing prosthesis (p < 0.001). BMD increases were observed consistently at the greater trochanter for all prostheses except the hip‐resurfacing prosthesis, where BMD increase was widespread across the metaphysis (p < 0.001). DXA RFA provides high‐resolution insights into the effect of prosthesis design on the local strain environment in bone. © 2017 The Authors Journal of Orthopaedic Research published by Wiley Periodicals, Inc. on behalf of Orthopaedic Research Society. J Orthop Res 35:2203–2210, 2017.

     

A new optimal linear quadratic observer‐based tracker under input constraint for the unknown system with a direct feed‐through term

This paper develops a new optimal linear quadratic observer‐based tracker with input constraint for the linear unknown system with a direct transmission term from input to measured output. The off‐line observer/Kalman filter identification method is used to determine the linear sampled‐data model with a direct feed‐through term. On the basis of this model, a high‐gain optimal linear quadratic analog observer‐based tracker is proposed, so that it can effectively induce a high quality performance on the state estimation and the trajectory tracking design. Besides, the prediction‐based digital redesign method is utilized to obtain a relatively low‐gain and implementable observer and digital tracker from the theoretically well‐designed high‐gain analog observer and tracker for the linear system with a direct transmission term from input to output. To reduce the magnitude of control input, which is caused by the high‐gain property to fit the requirement of the input constraint, the modified linear quadratic analog tracker is proposed. Thus, the control input can be compressed effectively without losing the original high performance of tracking much. Copyright © 2014 John Wiley & Sons, Ltd.     

Quantized feedback fault‐tolerant H ∞ controller design for linear systems with adaptive mechanism

This paper addresses the design problem of fault‐tolerant H _∞ controller for linear systems with state quantization. By combining linear matrix inequality technique and indirect adaptive method, a new method is proposed to design a fault‐tolerant controller against actuator faults via quantized state feedback. The controller gains are updating according to the online estimation of eventual faults, which are dependent on the quantized state signals. Meanwhile, the proposed designs conditions with variable gains can be proved to be less conservative than those of the traditional controller with fixed gains. A numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

A time‐varying coefficient‐based manipulability‐maximizing scheme for motion control of redundant robots subject to varying joint‐velocity limits

A time‐varying coefficient‐based manipulability‐maximizing (TVCMM) scheme subject to varying joint‐velocity limits (VJVL) is proposed and investigated in this paper for the optimal motion control of redundant robot manipulators (where a planar robot manipulator is specifically considered). In order to improve the manipulability during the end‐effector task execution, a manipulability‐maximizing index is considered into the scheme formulation. Besides, for the remedy of the nonzero initial/final joint‐velocity problem, a time‐varying coefficient is introduced and incorporated in the scheme, which is further reformulated as a quadratic program (QP) subject to equality and bound constraints. For guaranteeing the physical realizability of such a scheme, an efficient linear variational inequality‐based (LVI‐based) numerical algorithm is employed to solve such a QP, and an experiment based on a 6‐DOF manipulator is presented, of which the redundancy is on the horizontal plane. Simulative and experimental results validate the physical realization, effectiveness, and accuracy of the proposed QP‐based manipulability‐maximizing scheme. Copyright © 2012 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.     

Robust internal model‐based LQG design for active noise control of a one‐dimensional acoustic duct system

A control design method is proposed to design controllers to achieve global sound pressure attenuation for noise of narrow‐band frequencies in a one‐dimensional acoustic duct system. This method combines a linear‐quadratic‐gaussian (LQG) theory with an internal model principle to design internal model‐based active noise controllers so that noise of a specific (target) frequency in a duct can be reduced. The designed controller is, nevertheless, hyper sensitive to the perturbation of the target noise frequency. A reduced parameter sensitivity technique is further incorporated to improve robustness such that noise of narrow‐band frequencies can be attenuated. Computer simulation shows the effectiveness of robustness improvement for the proposed design method. In addition, global sound pressure attenuation along the duct is achieved. Experimental results also demonstrate frequency robustness improvement and global sound pressure attenuation despite the fact that the dynamic effects of the actuator are not considered in the control design. Both simulation and experimental results support the feasibility of the proposed design method. Copyright © 1999 John Wiley & Sons, Ltd.