To present an application of optimal controller design to a block-ice production process using dynamic programming. First, we develop mathematical models for such a process by employing system identification techniques. In particular, we build two parametric models, namely, linear model and neural network model. Linear models are built with Auto-Regressive model with exogenous inputs (linear ARX model). Feedforward neural networks (NNARX model) are constructed using the information provided by the linear ARX models. In addition, the Optimal Brain Surgeon (OBS) method is employed to prune the neural network models. Comparing the experimental results obtained from these models, it indicates that linear ARX models yield reasonably good performance in terms of the model fit. Then, using the obtained models, we investigate the energy consumption and operation cost of an ice factory when using time of use (TOU) tariff and time of day (TOD) tariff. Specifically, we develop an optimal control design for block-ice production process. The optimal strategy aims to minimize the electricity cost over a finite-time horizon and is subjected to constraints involving the control input of compressors, the brine temperature, and the number of block-ices ready for sales. Moreover, various factors in the design criteria have been analyzed with respect to the energy consumption and the operation cost. We compare the performance of the optimal controllers and the conventional control strategy. The simulation reveals that the proposed optimal control design has better performance than that of the conventional control. Furthermore, the optimal control using TOU tariff can reduce the operation cost when comparing to the one using TOD tariff.
42Nudging electricity consumption using TOU pricing and feedback: evidence from Irish households
Nudging electricity consumption using TOU pricing and feedback: evidence from Irish households
21Interval Methods for Optimal Control
Bellman’s discrete dynamic programming is one of the most general approaches to solve optimal control problems. For discrete-time dynamical systems, it is, at least theoretically, capable to determine globally optimal control laws. In most practical cases, both state and control variables are subject to constraints. Due to the necessity for gridding of the range of both state and control variables in numerical implementations of dynamic programming, the computational effort grows exponentially with increasing system dimensions. This fact is well known as the curse of dimensionality. Furthermore, gridding of intervals representing uncertain system parameters is inevitable, if dynamic programming is used for the design of optimal controllers for systems with uncertainties. In this contribution, an interval arithmetic procedure for the design of optimal and robust controllers is presented. This procedure relies on the basic concepts of dynamic programming. Sophisticated techniques for the exclusion of non-optimal control strategies significantly reduce the computational burden. Since interval techniques can be applied to both continuous-time and discrete-time dynamical systems, the interval arithmetic optimization approach presented in this chapter is applicable to both cases. In addition, the inclusion of effects of uncertain parameters in the underlying optimality criteria is demonstrated. For that purpose, interval arithmetic routines for analysis and design of optimal and robust controllers have been developed. Details about computationally efficient implementations of interval arithmetic optimization procedures and numerical results for a mechanical positioning system with statedependent switchings between different dynamical models for viscous and Coulomb friction are summarized.
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169Public acceptability of domestic demand-side response in Great Britain: The role of automation and direct load control
Domestic demand-side response (DSR), if widely adopted, could help make electricity more secure, clean and affordable. However, little is known about consumer demand for different approaches to achieving DSR. This study aimed to gauge the acceptability of a range of DSR tariffs, and explore factors affecting it. An online between-subjects survey experiment was deployed to a representative sample of bill payers in Great Britain (N=2002), testing five tariffs including static/dynamic time of use (TOU) pricing (with/without automated response to price changes) and direct load control (DLC) of heating on a below-average flat rate.The tariff permitting limited DLC of heating was significantly (p<.01) more popular than the TOU tariffs. This was surprising given evidence for concern around loss of control in DLC, and suggests that for many people DLC is acceptable in principle (within tight bounds and with override ability). The option of automated response made dynamic TOU (otherwise the least popular tariff) as acceptable as static TOU. This is important because dynamic TOU offers additional network benefits, while automation can improve duration and reliability of response. The TOU tariffs were rated highly for giving people control over spending on electricity, but other factors were more associated with overall acceptance.
Read more13Computational Optimal Control.
1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.
Read more3Computational approach to optimal damping controller design for a GCSC
Summary form only given. This paper presents a computational approach for an offline measurement based design of an optimal damping controller using adaptive critics for a new type of FACTS device - the gate controlled series capacitor (GCSC). Remote measurements are provided to the controller to damp out system modes. The optimal controller is developed based on the heuristic dynamic programming (HDP) approach. Three multi-layer perceptron (MLP) neural networks are used in the design - the identifier/model network to identify the dynamics of the power system; the critic network to evaluate the performance of the damping controller; and the controller network to provide optimal damping. This measurement based technique provides an alternative to the classical linear model based optimal control design. The eigenvalue analysis of the closed loop system is performed with time domain responses using the Prony method. Analysis of the simulation results show potential of the HDP based optimal damping controller on a GCSC for enhancing the stability of the power system.
Read moreThe optimal controller design for uncertain chaotic systems based on quadratic performance index
The issue of optimal controller design which is based on exact linearization of state feedback in the uncertain and chaotic systems with external disturbances is researched. First, based on the mature quadratic optimal control theory, the nonlinear chaotic system model with disturbance is converted to an equivalent linear system model without disturbance. Second, an optimal controller design method based on quadratic performance index is given which aims at pseudo-linear-system. The optimal control rate is shown after equation solution, and then the nonlinear chaotic system is changed into an equivalent linear system with Lie derivative transformation which makes the project simple and easily realized. With the simulation for parameter uncertainty in Liu chaotic systems, the result shows that the control quality has been greatly improved.
Read more22Observer-based dynamic optimal recoil controller design for deepwater drilling riser systems
Observer-based dynamic optimal recoil controller design for deepwater drilling riser systems
6Optimal controller approximation using neural and fuzzy-neural networks
A feedforward neural network has been shown to possess the ability of approximating an optimal controller over a subspace of initial conditions. In addition to a feedforward neural network the fuzzy logic/neural network hybrid ANFIS (adaptive network based fuzzy inference system) structure has been shown to be a universal approximator. This paper discusses briefly the use of ANFIS to approximate an optimal feedback controller for the nontrivial problem of guiding a high-speed vehicle (glider) to a ground target and compares results to a three layer feedforward neural network controller. The controllers are trained using optimal open loop state and control data generated by VF02AD. Simulation results show that both controller types guide the vehicle to within 1000 ft of the target with practically no degradation in the optimal impact velocity over a range of initial conditions. The advantages and disadvantages of both controllers are discussed together with some practical limitations of the ANFIS optimal feedback controller.
Read more85Optimal fuzzy controller design: local concept approach
In this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory. The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties.
Read more4H∞-Optimal Tracking Controller for Three-Wheeled Omnidirectional Mobile Robots with Uncertain Dynamics
In this paper, we present an optimal control approach using Linear Matrix Inequalities (LMIs) for trajectory tracking control of a three-wheeled omnidirectional mobile robot in the presence of external disturbances on the robot's actuators and noise in the robot's sensor measurements. First, a state-space representation of the omnidirectional robot dynamics is derived using a point-mass dynamic model. Then, we propose an LMI-based full-state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller for the tracking problem. The robot's tracking performance with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is compared to its performance with a classical full-state feedback tracking controller in simulations with circular and bowtie-shaped reference trajectories. In order to evaluate our proposed controller in practice, we also implement the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal and classical controllers for these reference trajectories on a three-wheeled omnidirectional robot. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller guarantees stabilization of the robot motion and attenuates the effects of frictional disturbances and measurement noise on the robot's tracking performance. Using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller, the robot is able to track the reference trajectories with up to a 47.8% and 45.8% decrease in the maximum pose and twist errors, respectively, over a full cycle of the trajectory compared to the classical controller. The simulation and experimental results show that our LMI-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.
Read moreOptimal Controller Use Adaptive Dynamic Programming E -- Greedy Iteration
Adaptive Dynamic Programming (ADP) is a new way for the complex nonlinear system optimal controller design. But the iteration step requires infinite ensure to find the optimal control law. In this paper, the greed iterative ADP algorithm was improved by adopting-approximate method. Further, the strict mathematical analysis and proof is given. The improved algorithm based in initial state points iterative limited steps to find approximate optimal control law. So reduces the computational complexity, and beneficial to outcome of the project. Simulation illustrate to the algorithm is effective to overcome the difficulty of the infinite iteration.
Read more35Integrated operations planning in highly electrified container terminals considering time-of-use tariffs
Integrated operations planning in highly electrified container terminals considering time-of-use tariffs
25Integration of Optimal Time-of-Use Pricing in Stochastic Programming for Energy and Reserve Management in Smart Micro-grids
In this paper, the optimal operation problem of smart micro-grids integrated with the pricing of Time-of-Use (TOU) demand response (DR) program is modeled as a two-stage stochastic programming problem with the aim of minimizing the cost of MG operation and running TOU in the presence of renewable resources and incentive-based DR programs. Here, TOU as the most common type of time-based DR programs is implemented using a linear function based on the concept of self- and cross-price elasticity of load demand. In the presented model, the forecasting errors of generation of renewable resources are modeled by probability density functions. The operator of MG decides on two stages for optimal management of its network; the first stage refers to the operation of base condition of MG and the second one is pertaining to after the realization of different scenarios for generation of renewable resources. The base condition of MG refers to the situation in which the active power productions of renewables are equal to the predicted values. The proposed model is solved by Particle Swarm Optimization algorithm. A typical MG is employed to investigate and analyze the different features of the method. By varying the demand response potential of MG consumers, TOU tariffs are determined, and their impact on the results of energy and reserve cost as well as voltage and load profiles of MG are analyzed. Numerical results show the efficiency of DR in reducing costs as well as covering the uncertainty resulting from renewables.
Read more15Direct Optimal Vibration Control of a Piezoelastic Plate
An optimal control method for distributed parameter systems is developed and applied to active vibration control of a plate. Piezoelectric material is used as an actuator. The structural dynamics are modeled using the space—time assumed mode expansion technique (a Rayleigh—Ritz method applied to both time and space variables). In particular, the generalized coordinates (both mechanical and electrical) and all generalized forces are described in terms of expansion functions. Using Hamilton's law of varying action along with the space—time assumed mode expansion results in algebraic equations of motion. These are then used as the constraint equations in the optimal controller design. Using space—time expansion, the usual variational optimal control problem is transformed into an equivalent algebraic problem. Optimal solutions are then obtained in a closed form and the solution is global within the time period considered. The solution procedure does not lead to a Riccati equation as is the case in the conventional optimal control solutions. The direct optimal control problem of a vibrating plate is illustrated through simulations where a parametric study is undertaken to check the controller performance. This study shows that the developed optimal control method is simple and the structure—control interaction is an inherent property of the method.
Read moreSimulation on the tactics of energy storage in power generation sector in context of the time of use tariff
In July 2021, the NDRC (National Development and Reform Committee) launched the Notice to Further Better Off the ToU (Time of Use) Mechanism [1]. The notice is aimed to create a better environment for the development of the renewables and the construction of the renewables-based new power system by deepening the reform of the power market. This paper stands in the point of view of the power plants to address how does the power supply side, especially the coal fired power plants, tackle the challenges coming out in the context of the widening tariff difference between the peak and valley loads. This paper analyzed the operational tactics of the energy storage in the power supply side. With the model analysis and the simulation of the energy storage tactics, it tried to usher the power supply side to grasp the opportunity to adopt new energy storage facilities and apply the storage operational tactics, to enhance the reliability of the system, and meanwhile increase the proportion of the renewables into the power grid, ultimately help our power industry drive a successful energy transition and form a solid new power system in near future.
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