Wavelet-based Control Research Articles

Resilient Control for Macroeconomic Models.

This paper derives a macroeconomic resilient control framework that provides the optimal feedback fiscal and monetary policy responses in response to a potentially large negative external incident. We simulate the model for the U.S. under the conditions that prevailed throughout the 2020 economic crisis that occurred due to the government lockdown that was caused by the coronavirus pandemic. We develop a discrete-time soft-constrained linear-quadratic dynamic game under a worst-case design with multiple disturbances. Within this context, we introduce a resilience feedback response and compare the case where the policymakers counter in response the external incident with the case when they do not counter. This framework is especially applicable to large-scale macroeconomic tracking control models and wavelet-based control models when formulating the magnitudes of the policy changes necessary for the unemployment rate and national output variables to maintain acceptable tracking errors in the periods following a major disruption. Our policy recommendations include the maintenance of “rainy day” funds at appropriate levels of government to mitigate the effects of large adverse events.

Okun’s law revisited in the time–frequency domain: introducing unemployment into a wavelet-based control model

This paper integrates the Okun’s law (OL) relationship into a wavelet-based control (WBC) model to compare simulated optimal fiscal and monetary policy for the US when the policymakers place varying emphasis on the primary macroeconomic targets of unemployment, output growth, and inflation. The simulation results show that the unemployment rate is impacted differently across frequency ranges. We find that fiscal policy is the most aggressive when economic growth is emphasized as a policy objective, whereas monetary policy is relatively more aggressive when the inflation rate is emphasized. Given that the US inflation rate was below target for the start of the simulation exercises, when it is emphasized, that leads to lower interest rates, a depreciated exchange rate, and larger aggregate investment. We also find that introducing OL into a WBC model leads to less expansionary fiscal and monetary policies when unemployment is initially low.

Novel Improved Adaptive Neuro-Fuzzy Control of Inverter and Supervisory Energy Management System of a Microgrid

In this paper, energy management and control of a microgrid is developed through supervisor and adaptive neuro-fuzzy wavelet-based control controllers considering real weather patterns and load variations. The supervisory control is applied to the entire microgrid using lower–top level arrangements. The top-level generates the control signals considering the weather data patterns and load conditions, while the lower level controls the energy sources and power converters. The adaptive neuro-fuzzy wavelet-based controller is applied to the inverter. The new proposed wavelet-based controller improves the operation of the proposed microgrid as a result of the excellent localized characteristics of the wavelets. Simulations and comparison with other existing intelligent controllers, such as neuro-fuzzy controllers and fuzzy logic controllers, and classical PID controllers are used to present the improvements of the microgrid in terms of the power transfer, inverter output efficiency, load voltage frequency, and dynamic response.

Is the Taylor rule optimal? Evaluation using a wavelet-based control model

ABSTRACT This paper extends the wavelet-based control (WBC) model of Crowley and Hudgins (2015) to compare the simulated performance of jointly optimal fiscal and monetary policy, where the policymakers place emphasis on a variety of macroeconomic targets, with the case where monetary policy follows a modified Taylor rule. The results show that the Taylor rule is likely to render higher interest rates, diminished investment, and appreciated real exchange rates compared with an unconstrained baseline simulation. We therefore find that the Taylor rule is suboptimal since it results in higher fiscal deficits due to substitution by policy authorities, thus confirming recent research on the interaction of fiscal and monetary policies. The analysis also compares the baseline and Taylor rule simulated forecasts when the central bank adopts a ‘hawkish’ inflation policy compared to a more ‘dovish’ policy stance.

Real-Time Optimization Energy Management Strategy for Fuel Cell Hybrid Ships Considering Power Sources Degradation

In order to protect the marine environment, the fuel cell has become a good candidate for the main energy source of marine vehicles due to its remarkable performance of high efficiency, quietness, and cleanness. However, the fuel cell of the hybrid power system has a critical drawback of short lifetime. For this reason, the development of the energy management strategy considering power sources degradation becomes significant and urgent. In addition, the power system configuration has a strong link with the control strategy. In this vein, a sizing method of the hybrid energy storage system for a fuel cell hybrid excursion ferry is proposed to prolong the fuel cell lifetime. Based on the configuration of the power system, a real-time optimization control strategy considering efficiency and durability is developed. To verify the control strategy, the mathematical model of the hybrid power system is established. Compared with the wavelet-based control strategy and rule-based control strategy, the proposed strategy has better performance in terms of the fuel economy, the system durability as well as the dynamic property.

Dynamic Optimization for Copper Removal Process With Continuous Production Constraints

The copper removal process (CRP) aims to reduce the copper ion concentration in zinc sulphate solution to a specific range by zinc addition. The satisfaction of production constraints and minimization of zinc consumption are vital but difficult to achieve. In this article, the dynamic optimization for CRP is conducted for optimal zinc control trajectory design considering constraints at least cost. First, a dynamic optimization problem with both state and control constraints is constructed for CRP. Then, a constrained dynamic optimization method is proposed, where a wavelet-based control parameterization method and a smooth penalty method are adopted. Specially, a hybrid optimization strategy is proposed to achieve a robust and efficient optimization performance. Numerical experiments are provided to illustrate the effectiveness of the proposed method. Results show that the proposed method can produce not only the optimal control trajectory with a qualified outlet ion concentration but also the less zinc consumption.

Open Economy Dynamics in a Floating Exchange Rate Developing Country Context

ABSTRACTThis article develops a wavelet-based control model to simulate fiscal, monetary, and real exchange rate scenarios in an open economy developing country with an inflation-targeting regime. We use South African macro data to jointly simulate optimal fiscal and monetary policy under varying scenarios for real exchange rate stability with interest rate parity. As real exchange rate stability increases, the model simulates the effects on the trade balance under both a constant and depreciating real exchange rate. We find that short-term cycle stability problems are somewhat mitigated by allowing the real exchange rate to depreciate.

Wavelet-based Controller Design for Dynamic Positioning of Vessels

This paper presents design and evaluation of a wavelet-based multi-resolution proportional integral derivative controller (MRPID) for dynamic positioning (DP) of vessels under noise and environmental disturbances. In the proposed MRPID controller, the errors with position and orientation are decomposed into different frequency components using discrete wavelet transform. The different scales of wavelet transform represent details such as external disturbances, process noise and measurement noise. A set of sub-PID controllers are assigned to selected error components and the commands generated by all controllers are added together to produce the control command for dynamic positioning of the vessel. Performance of the controller is evaluated in simulation and compared with the conventional PID controller with acceleration feedback. Nonlinear state estimation is performed by using an unscented Kalman filter assuming a typical sensor package for localization.

Modelling a Small Open Economy Using a Wavelet-Based Control Model

This paper develops a wavelet-based control system model that can be used to simulate fiscal and monetary strategies in an open economy context in the time-frequency domain. As the emphasis on real exchange rate stability is increased, the model simulates the effects on both the aggregate and decomposed trade balance under both constant and depreciating real exchange rate targets, and also the effects on the real GDP expenditure components. This paper adds to recent research in this area by incorporating an external sector via the use of a real effective exchange rate as a driver of output. The research is also the first to analyze exchange rate effects within a time-frequency model with integrated fiscal and monetary policies in an open-economy applied wavelet-based optimal control setting. To demonstrate the usefulness of this model, we use post-apartheid South African macro data under a political targeting design for the frequency range weights, where we simulate jointly optimal fiscal and monetary policy under varying preferences for real exchange rate stability.

Exploitation of the control switching structure in multi-stage optimal control problems by adaptive shooting methods

The adaptive switching structure approach is generalized from single-stage problems and single-shooting to multi-stage problems and multiple-shooting. This generalization is based on previous work on the exploitation and detection of the control switching structure and wavelet-based control grid refinement for single-stage problems. Here, single-shooting is employed to transcribe the multi-stage optimal control problem (OCP) into a nonlinear programming problem. The proposed multi-stage formulation is also capable to represent the transcription of single-stage OCP stemming from multiple-shooting. Thus, the previously reported adaptive multiple-shooting approach is extended by an adaptation of the switching structure. Finally, a new stopping criterion is introduced that measures the intermediate constraint violation at the optimal solution.The proposed adaptive switching structure detection is illustrated for a multi-stage and a multiple-shooting problem using the Williams–Otto semi-batch reactor. A solution of user-specified accuracy in the objective and the path-constraints can be obtained using only few decision variables.

Adaptive Robot Control – An Experimental Comparison

This paper deals with experimental comparison between stable adaptive controllers of robotic manipulators based on Model Based Adaptive, Neural Network and Wavelet -Based control. The above control methods were compared with each other in terms of computational efficiency, need for accurate mathematical model of the manipulator and tracking performances. An original management algorithm of the Wavelet Network control scheme has been designed, with the aim of constructing the net automatically during the trajectory tracking, without the need to tune it to the trajectory itself. Experimental tests, carried out on a planar two link manipulator, show that the Wavelet-Based control scheme, with the new management algorithm, outperforms the conventional Model-Based schemes in the presence of structural uncertainties in the mathematical model of the robot, without pre-training and more efficiently than the Neural Network approach.

Implementation of Wavelet-Based Controller for Battery Storage System of Hybrid Electric Vehicles

This paper presents a wavelet-based multiresolution proportional integral derivative (MRPID) controller for temperature control of the ambient air of battery storage system of the hybrid electric vehicles. In the proposed wavelet MRPID controller, the discrete wavelet transform (DWT) is used to decompose temperature error into frequency components at various resolution of the error signal. The wavelet transformed coefficients are scaled by suitable gains and then added together to generate the control signal of thermal system. The proposed wavelet controller is implemented for battery storage system in both simulation and experiments. The digital signal processor board is used for real-time implementation of the proposed controller. The performance of the proposed wavelet-based MRPID controller is compared with conventional proportional-integral-derivative (PID) and adaptive neural network controllers. The proposed wavelet controller for battery storage system is found more robust and quicker than the conventional and adaptive controllers.

Implementation of a Wavelet-Based MRPID Controller for Benchmark Thermal System

This paper presents a comparative analysis of the intelligent controllers for temperature control of a benchmark thermal system. The performances of the proposed wavelet-based multiresolution proportional-integral derivative (PID) (MRPID) controller, which can also be stated as a multiresolution wavelet controller, are compared with the conventional PID controller and the adaptive neural-network (NN) controller. In the proposed MRPID temperature controller, the temperature error of actual and command temperatures of a thermal system is decomposed into different frequency components at various scales of the discrete wavelet transform (DWT). The wavelet-transformed coefficients of temperature error at different scales of the DWT are scaled by their respective gains and then are added together to generate the control signal for the thermal system. The performances of these intelligent controllers are investigated in both simulation and experiments for different operating conditions of the thermal system. The performances of the wavelet-based MRPID controller are found superior to the conventional PID and adaptive NN controllers for temperature control of the thermal systems.

MONITORING AUTOCORRELATED PROCESSES WITH WAVELETS

This paper develops a wavelet control chart for monitoring autocorrelated processes. The procedure uses the discrete wavelet transform of the original series, and traditional control charts are applied to the stream of wavelet coefficients. Unlike other control charts for monitoring autocorrelated processes found in the literature, the wavelet control chart does not require that a model be specified for the process data. The wavelet-based control chart is simple enough that it can be easily automated. Real and simulated data are used to illustrate the effectiveness of the proposed wavelet control chart.

Online implementation of wavelet-based identification and dynamic matrix control in a heat exchanger unit

This paper presents an online implementation of wavelet-based least-square identification (WLSI) and wavelet-based dynamic matrix control (WDMC) in a plate-type heat exchanger unit. Wavelet domain 'blocking' and 'condensing' (B&C) techniques are used to reduce the computation time for optimisation of dynamic matrix control (DMC) performance index. Algorithms for WLSI and WDMC are developed and implemented in the online identification and control of temperature in a heat exchanger unit. The results are compared with conventional PID and DMC controllers. It is observed that the WDMC is better and robust than the other controllers.

A New Wavelet-based Speed Controller for Induction Motor Drives

This article presents a novel speed controller based on multi-resolution decomposition analysis of the discrete wavelet transform for vector-controlled induction motor drives. The field-oriented control principle is used to decouple the flux and torque components of the induction motor dynamics. In the proposed controller, the discrete wavelet transform is used to decompose the speed error between the actual and command speeds at various scales. The control signal is generated using the wavelet-transformed coefficients of speed error of different scales. It has been found that these coefficients can represent the cumulative effect of motor drive uncertainties such as parameter variations, measurement noise, frictional variation, and external torque disturbances. The performance of this controller is evaluated in both simulation and experiments. The complete vector-control scheme incorporating the proposed controller is successfully implemented in real time using the ds1102 digital signal processor board (dSPACE, GmbH, Paderborn, Germany) for the laboratory 1-hp induction motor. The experimental results validate the robustness and, hence, justify the applicability of the proposed controller for the induction motor drive to be used in high-performance drive applications. In order to prove the superiority of the proposed controller, a comparison between the proposed and the conventional proportional-integral and proportional-integral-derivative controller-based systems is made at different dynamic operating conditions.

Wavelet-based Neighborhood Control for Self-Sizing Networks

The exponential growth of the Internet has turned it into a multiservice complex network of heterogeneous elements with dynamically changing traffic conditions. To regulate such a large scale network it is necessary to place intelligence in the nodes and find simple distributed rules and strategies that can produce meaningful and consistent behavior. These control mechanisms must be adaptive to effectively respond to continually changing network conditions. A “self-sizing” network can allocate link/switch capacity automatically and adaptively using online traffic data. Such adaptive, distributed, localized mechanisms are crucial to provide a scalable solution for controlling large, complex networks. In this paper, we propose a new, distributed self-sizing framework for locally controlled networks, which can support the stringent requirements of real-time applications in the Internet. Our unified and critical study of online resource allocation algorithms of two different classical approaches, led us to the use of adaptive multi-resolution decomposition (“wavelet”) algorithms. Our results show that by performing online resource allocation at each node based on their local knowledge, we can achieve considerable bandwidth savings and also satisfy QoS at the packet level. In our novel “neighborhood control” technique, we establish that by increasing the knowledge of some nodes so that higher self-sizing gains can be attained.

Can Wavelets Improve the Representation of Forecast Error Covariances in Variational Data Assimilation?

Abstract Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude–height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet-based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.