Optimal and suboptimal control policies for a solar collector system

An optimal control problem to maximize the net energy gathered by a flat-plate solar collector system by controlling the collector fluid flow rate is investigated. The problem is formulated in terms of a distributed parameter system and solved using the method of characteristics. It is shown that if the pump of the collector loop is such that its pumping power is greater than a linear function of the fluid velocity, then the optimal control policy is one in which the fluid flow is instantly switched between zero and maximum rates. Necessary conditions that determine the optimal switching times are derived. Because the resultant switching function of the optimal policy is shown to be decomposable into two parts, one that depends on the state of the system and another that requires a priori knowledge of the solar intensity over the entire period of operation, a suboptimal control policy that can be implemented by an on/off feedback controller with hysteresis is proposed. When this suboptimal policy is compared with the optimal policy, it is shown that on a clear day with sufficient solar insolation to dictate a two-switch optimal policy, the two policies are identical. Under other weather conditions, the feedback suboptimal controller will keep the pump off for a slightly shorter period of time than the time dictated by the optimal control.     

Reduced complexity adaptive nonlinear control of a distributed collector solar field

An approach to the control of a distributed collector solar field relying on feedback linearization, Lyapunov based adaptation and a simplified plant model is presented. The control objective consists of manipulating the oil flow so that the outlet oil temperature is regulated around a given setpoint. For dealing with plant nonlinearities and external disturbances, a nonlinear transformation is performed on the accessible variables such that the transformed system behaves as an integrator, to which linear control techniques are then applied. Since the transformation depends on an unknown parameter, an adaptation law is designed so as to minimize a Lyapunov function for the whole system's state. For the sake of control synthesis a simplified plant model which retains the bilinear nonlinearity is employed. The resulting control law has the same control structure of the one yielding exact input-output linearization but assumes a different placement of a temperature sensor. In order to justify this procedure, plant internal dynamics is studied. Experimental results obtained in the actual field are presented.     

双线性时滞系统的最优控制及其在精馏塔的应用

本文利用块脉冲函数(BPFs)和参数优化方法,提出了解决具有任意状态时滞、控制时滞及其任意初始条件的多变量双线性系统最优控制问题的具体算法,该算法被成功地用于一类可用双线性时滞模型描述的精馏塔的温度最优控制,同时,通过其它例子仿真,也表明这个算法是令人满意的。     

Optimal control of distributed bilinear systems

The optimal control problem for a bilinear distributed parameter system subject to a quadratic cost functional is solved. It is shown that the optimal control is given by a convergent power series in the state with tensor coefficients.     

Dynamic ordering and pricing for a perishable goods supply chain

The paper studies the combined problem of pricing and ordering for a perishable product supply chain with one supplier and one retailer in a finite horizon. The lifetime of the product is two periods and demand in each period is random and price-sensitive. In each period, the supplier determines first a wholesale price and then the retailer decides an order quantity and retail prices. We show that the optimal pricing strategy for the non-fresh product depends only on its inventory, and the optimal pricing strategy and the optimal order quantity for the fresh product depend only on the wholesale price and they have a constant relation. Moreover, the game between the retailer and the supplier for finite horizon is equivalent to a one period game with only one order. Thus, the optimal policies are identical at each period. For the additive and multiplicative demands, we further obtain equations to compute the optimal strategies. All of above results are extended into the infinite horizon case and longer lifetime products. Finally, a numerical analysis is given.     

Regional optimal control of a bilinear wave equation

We study a regional optimal control problem of a bilinear wave equation evolving on a spatial domain Ω with a distributed controls. We search a distributed control which aims to minimise a given functional cost that contains the gap between a desired state and the reached one. This latter is defined only on a subregion ω of Ω. Therefore, we prove existence and we give characterisation of an optimal control. The obtained results lead to an algorithm that we illustrate by simulations.     

基于双线性模型的连续时间非线性最优控制的DISOPE 算法

对连续时间非线性最优控制问题出了基于双线性二次型问题的ＤＩＳＯＰＥ算法,在模型与实际存在差异的情况下,通过求解修正的基于双线性模型的优化总理２和参数估计问题,给出了实际问题的最优解,提出了求解非齐次双线性二次型问题的迭代算法,分析了该算法的收敛性,仿真结果表明该算法比现有算法有更好的收敛特性。     

Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction

We present a framework to solve a finite-time optimal control problem for parabolic partial differential equations (PDEs) with diffusivity-interior actuators, which is motivated by the control of the current density profile in tokamak plasmas. The proposed approach is based on reduced order modeling (ROM) and successive optimal control computation. First we either simulate the parabolic PDE system or carry out experiments to generate data ensembles, from which we then extract the most energetic modes to obtain a reduced order model based on the proper orthogonal decomposition (POD) method and Galerkin projection. The obtained reduced order model corresponds to a bilinear control system. Based on quasi-linearization of the optimality conditions derived from Pontryagin’s maximum principle, and stated as a two boundary value problem, we propose an iterative scheme for suboptimal closed-loop control. We take advantage of linear synthesis methods in each iteration step to construct a sequence of controllers. The convergence of the controller sequence is proved in appropriate functional spaces. When compared with previous iterative schemes for optimal control of bilinear systems, the proposed scheme avoids repeated numerical computation of the Riccati equation and therefore reduces significantly the number of ODEs that must be solved at each iteration step. A numerical simulation study shows the effectiveness of this approach.     

Energy-based control of a distributed solar collector field

Model-based control of the outlet temperature of a distributed solar collector field is studied. An energy-based controller is derived using internal energy as a controlled variable. The controller relies on a distributed parameter nonlinear plant model and includes feedforward from the solar irradiation and inlet temperature. Convergence of the closed loop is proved, and the method is experimentally verified to perform well on a pilot-scale solar power plant.     

Feedback linearization control for a distributed solar collector field

This article describes the application of a feedback linearization technique for control of a distributed solar collector field using the energy from solar radiation to heat a fluid. The control target is to track an outlet temperature reference by manipulating the fluid flow rate through the solar field, while attenuating the effect of disturbances (mainly radiation and inlet temperature). The proposed control scheme is very easy to implement, as it uses a numerical approximation of the transport delay and a modification of the classical control scheme to improve startup in such a way that results compared with other control structures under similar conditions are improved while preserving short commissioning times. Experiments in the real plant are also described, demonstrating how operation can be started up efficiently.     

Wavelet based approximations in the optimal control of parabolic problems

We consider optimal control of a bilinear parabolic equation. The determination of such control requires to minimize a given energy performance measure. The performance measure of the system is taken as a combination of its modified total energy and the penalty term describing the approach used in the control process. Using an appropriate transformation modal expansion, the optimal control of a distributed parameter system (DPS) is simplified into the optimal control of a bilinear time-varying lumped parameter system (LPS). A computational efficient formulation to evaluate the optimal trajectory and control of the system is determined. It is based on the parametrization of the state and control variables by using finite wavelets. Numerical examples are provided to demonstrate the applicability and the efficiency of the proposed method and the results are quite satisfactory.     

无限长概周期过程的虚拟寻优控制

一类无限长过程具有概周期特性,为其最优控制的求解提供了可能,其核心问题是周期初态的寻优.本文提出一种虚拟寻优法,再配上周期之间适当的状态连接,既大大减少了计算量和存储量,又收到了较好的优化效果.水厂最优控制的仿真说明,本文方法能收到很好的节能效果.     

Repetitive control of tubular heat exchangers

Effective operation of heat exchangers involves optimum control of the fluid outlet temperature. Several ideas have been proposed in the literature to cope with intrinsic resonance dynamics aimed at widening the bandwidth of the closed-loop system to achieve fast, well-damped responses in controlling the outlet fluid temperature by means of the steam temperature. This is also the main purpose of this article, in which the use of a repetitive control scheme is proposed to take resonance dynamics into account when residence time is variable, as in this case the control variable is the fluid flow rate and not the steam temperature. The scheme is based on a model of the tubular heat exchanger dynamics in which the explicit terms of resonance are cancelled out by the controller. Simulation results are provided both for a typical tubular heat exchanger and for a special sort of heat exchanger, the distributed collector field of a solar power plant.     

Stabilisation of infinite-dimensional bilinear systems using a quadratic feedback control

This article discusses feedback stabilisation of bilinear systems defined on a Hilbert state space. We show that stabilising such a system reduces stabilising only its projection on a suitable subspace. Then we give a new stabilising control that minimises a quadratic cost and allows the decay estimate of the optimal trajectories. An illustrating example is presented.     

A Mixed Suspension System for a Half-Car Vehicle Model

Inthis paper we realize the design of a mixed suspension system(an actuator in tandem with a conventional passive suspension)for the axletree of a road vehicle based on a linear model withfour degrees of freedom. We propose an optimal control law thataims to optimize the suspension performance while ensuring thatthe magnitude of the forces generated by the two actuators andthe total forces applied between wheel and body never exceedgiven bounds. The solution we derive takes the form of an adaptivecontrol law that switches between different constant state feedbackgains. The results of our simulations show that the bound onthe active forces is a design parameter useful for establishinga trade-off between performance and power requirement.     

Decentralized preview control for multiple disturbance rejection in HVAC systems

A decentralized preview controller is designed for temperature control of multizone indoor environmental spaces. A two-zone space heating system is considered. The physical system consists of a boiler, heat pumps, distribution network and two environmental zones. By assuming that the outdoor temperature variations are “previewable”, a decentralized preview controller is designed by using a parameter optimization method. The output responses of the resulting decentralized closed-loop bilinear system acted upon by single and multiple disturbances with and without preview action are compared. Also, results showing the robustness property of the controller, and the 24-hour building operation with unoccupied and occupied setpoint tracking using preview control are given.     

Time optimal control of a dielectrophoretic system

This paper examines a time optimal control problem for a dielectrophoretic system. The system consists of a neutrally buoyant and neutrally charged particle in a chamber filled with a fluid flowing with a low Reynolds number. At the bottom of this chamber is a series of parallel electrodes with a controlled time‐varying voltage. The voltage on the electrodes creates a time‐varying nonuniform electric field inducing a dipole moment in the particle. This induced dipole moment interacts with the electric field to generate a force on the particle. There are two state variables x and y, where x is the position of the particle and y is the induced dipole moment in the particle. The system has two parameters α and c which depend on the electric characteristics of the particle and the ambient fluid. The parameter c is always positive by the laws of physics, but α can have either sign. We solve the time optimal control problem for this system when α≥0 and y(0) is arbitrarily prescribed. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

甘油生物歧化为1,3-丙二醇过程的H∞控制

A robust controller is designed by using the bilinear transformation and H∞ mixed sensitivity method for bio-dissimilation process of glycerol to 1,3-propanediol. Under the controller the system works near an optimal steady-state for the volumetric productivity of 1,3-propanediol attaining its maximization. The design procedure is carried out by tuning the transformation parameter and DC gain of the performance weighted function, which is an iterative and optimal search process. Simulation results are presented which show that the designed robust controller not only ensures the robust stability of the system in face of the parametric variations in the model, but also makes the system have a favourable robust tracking performance. The validity of the proposed H∞ controller has been tested.     

Robust incoherent control of qubit systems via switching and optimisation

A robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state. This scheme consists of two main steps: projective measurement on the initial mixed state and optimal control between two pure states. The first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states. The second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state. The connection between the two steps is accomplished by a switching strategy. To accomplish the second step, two approaches are presented in detail. These approaches are time-optimal transition with unbounded control and bang-bang control with minimal switches. The minimal time and minimal number of switches in these approaches can be calculated by simple analytical expressions. The proposed approaches provide two relatively straightforward optimal design methods.     

基于切换机制的多模型自适应混合控制

针对多模型自适应混合控制的性能依赖系统参数估计误差大小的缺点,本文提出了基于切换机制的多模型自适应混合控制.首先对被控系统进行辨识,然后根据参数估计值进行判断.当参数估计值不在最优参数集内时,实行切换策略,重置参数估计值到最优参数集内,用以减小暂态误差,提高暂态性能;当参数估计值在最优参数集内时,实行混合控制,用以平滑过渡过程.文中给出了系统的稳定性和收敛性的证明,最后的仿真实验结果验证了所提出方法的可行性.