arXiv subjects

Ahmad F. Taha

Publications and source records attributed to Ahmad F. Taha.

At least 55 records · Page 3Linked to original sources

arXiv2023

On Scaling Robust Feedback Control and State Estimation Problems in Power Networks

Many mainstream robust control/estimation algorithms for power networks are designed using the Lyapunov theory as it provides performance guarantees for linear/nonlinear models of uncertain power networks but comes at the expense of scalability and sensitivity. In particular, Lyapunov-based approaches rely on forming semi-definite programs (SDPs) that are (i) not scalable and (ii) extremely sensitive to the choice of the bounding scalar that ensures the strict feasibility of the linear matrix inequalities (LMIs). This paper addresses these two issues by employing a celebrated non-Lyapunov approach (NLA) from the control theory literature. In lieu of linearized models of power grids, we focus on (the more representative) nonlinear differential algebraic equation (DAE) models and showcase the simplicity, scalability, and parameter-resiliency of NLA. For some power systems, the approach is nearly fifty times faster than solving SDPs via standard solvers with almost no impact on the performance. The case studies also demonstrate that NLA can be applied to more realistic scenarios in which (i) only partial state data is available and (ii) sparsity structures are imposed on the feedback gain. The paper also showcases that virtually no degradation in state estimation quality is experienced when applying NLA.

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arXiv2023

Robust Feedback Control of Power Systems with Solar Plants and Composite Loads

Due to the rapid developments in synchronized measurement technologies, there exist enormous opportunities to attenuate disturbances in future power grids with high penetration of renewables and complex load demands. To that end, this paper investigates the effectiveness of new robust feedback controllers for interconnected power systems with advanced power electronics-based models of photovoltaic (PV) power plants, composite load dynamics, and detailed higher-order synchronous generator models. Specifically, we design new, advanced control-theoretic wide-area controllers to improve the transient stability of nonlinear differential-algebraic models. Thorough simulation studies are carried out to assess the performance of the proposed controllers. Several fundamental questions on the proposed controllers' computational complexity and disturbance attenuation performance are raised and addressed. Simulation results demonstrate that with the proposed controllers as a secondary control layer, the overall transient stability and system robustness against load and renewables disturbances/uncertainties can be significantly improved compared to the state-of-the-art.

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arXiv2023

Comprehensive Framework for Controlling Nonlinear Multi-Species Water Quality Dynamics

Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of 1- D advection-reaction (AR) partial differential equations (PDEs). With the absence of analytical solutions in many scenarios, numerical solutions require high-resolution time- and spacediscretizations resulting in large model dimensions. This adds complexity to the water quality control problem. In addition, considering multi-species water quality dynamics rather than the single-species dynamics produces a more accurate description of the reaction dynamics under abnormal hazardous conditions (e.g., contamination events). Yet, these dynamics introduces nonlinear reaction formulation to the model. To that end, solving nonlinear 1-D AR PDEs in real time is critical in achieving monitoring and control goals for various scaled networks with a high computational burden. In this work, we propose a novel comprehensive framework to overcome the large-dimensionality issue by introducing different approaches for applying model order reduction (MOR) algorithms to the nonlinear system followed by applying real-time water quality regulation algorithm that is based on an advanced model to maintain desirable disinfectant levels in water networks under multi-species dynamics. The performance of this framework is validated using rigorous numerical case studies under a wide range of scenarios demonstrating the challenges associated with regulating water quality under such conditions.

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arXiv2023

State-Robust Observability Measures for Sensor Selection in Nonlinear Dynamic Systems

This paper explores the problem of selecting sensor nodes for a general class of nonlinear dynamical networks. In particular, we study the problem by utilizing altered definitions of observability and open-loop lifted observers. The approach is performed by discretizing the system's dynamics using the implicit Runge-Kutta method and by introducing a state-averaged observability measure. The observability measure is computed for a number of perturbed initial states in the vicinity of the system's true initial state. The sensor node selection problem is revealed to retain the submodular and modular properties of the original problem. This allows the problem to be solved efficiently using a greedy algorithm with a guaranteed performance bound while showing an augmented robustness to unknown or uncertain initial conditions. The validity of this approach is numerically demonstrated on a $H_{2}/O_{2}$ combustion reaction network.

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arXiv2023

CAV Traffic Control to Mitigate the Impact of Congestion from Bottlenecks: A Linear Quadratic Regulator Approach and Microsimulation Study

This work investigates traffic control via controlled connected and automated vehicles (CAVs) using novel controllers derived from the linear-quadratic regulator (LQR) theory. CAV-platoons are modeled as moving bottlenecks impacting the surrounding traffic with their speeds as control inputs. An iterative controller algorithm based on the LQR theory is proposed along with a variant that allows for penalizing abrupt changes in platoons speeds. The controllers use the Lighthill-Whitham-Richards (LWR) model implemented using an extended cell transmission model (CTM) which considers the capacity drop phenomenon for a realistic representation of traffic in congestion. The impact of various parameters of the proposed controller on the control performance is analyzed. The effectiveness of the proposed traffic control algorithms is tested using a traffic control example and compared with existing proportional-integral (PI)- and model predictive control (MPC)- based controllers from the literature. A case study using the TransModeler traffic microsimulation software is conducted to test the usability of the proposed controller as well as existing controllers in a realistic setting and derive qualitative insights. It is observed that the proposed controller works well in both settings to mitigate the impact of the jam caused by a fixed bottleneck. The computation time required by the controller is also small making it suitable for real-time control.

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arXiv2023

Load and Renewable-Following Control of Linearization-Free Differential Algebraic Equation Power System Models

Electromechanical transients in power networks are mostly caused by a mismatch between power consumption and production, causing generators to deviate from the nominal frequency. To that end, feedback control algorithms have been designed to perform frequency and load/renewables-following control. In particular, the literature addressed a plethora of grid- and frequency-control challenges with a focus on linearized, differential equation models whereby algebraic constraints (i.e., power flows) are eliminated. This is in contrast with the more realistic nonlinear differential algebraic equation (NDAE) models. Yet, as grids are increasingly pushed to their limits via intermittent renewables and varying loads, their physical states risk escaping operating regions due to either a poor prediction or sudden changes in renewables or demands -- deeming a feedback controller based on a linearization point virtually unusable. In lieu of linearized differential equation models, the objective of this paper is to design a simple, purely decentralized, linearization-free, feedback control law for NDAE models of power networks. The aim of such a controller is to primarily stabilize frequency oscillations after a significant, unknown disturbance in renewables or loads. Although the controller design involves advanced NDAE system theory, the controller itself is as simple as a decentralized proportional or linear quadratic regulator in its implementation. Case studies demonstrate that the proposed controller is able to stabilize dynamic and algebraic states under significant disturbances.

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arXiv2023

Data-Driven Identification of Dynamic Quality Models in Drinking Water Networks

Traditional control and monitoring of water quality in drinking water distribution networks (WDN) rely on mostly model- or toolbox-driven approaches, where the network topology and parameters are assumed to be known. In contrast, system identification (SysID) algorithms for generic dynamic system models seek to approximate such models using only input-output data without relying on network parameters. The objective of this paper is to investigate SysID algorithms for water quality model approximation. This research problem is challenging due to (i) complex water quality and reaction dynamics and (ii) the mismatch between the requirements of SysID algorithms and the properties of water quality dynamics. In this paper, we present the first attempt to identify water quality models in WDNs using only input-output experimental data and classical SysID methods without knowing any WDN parameters. Properties of water quality models are introduced, the ensuing challenges caused by these properties when identifying water quality models are discussed, and remedial solutions are given. Through case studies, we demonstrate the applicability of SysID algorithms, show the corresponding performance in terms of accuracy and computational time, and explore the possible factors impacting water quality model identification.

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arXiv2022

Robust Dynamic State Estimation of Multi-Machine Power Networks with Solar Farms and Dynamics Loads

Conventional state estimation routines of electrical grids are mainly reliant on dynamic models of fossil fuel-based resources. These models commonly contain differential equations describing synchronous generator models and algebraic equations modeling power flow/balance equations. Fuel-free power systems that are driven by inertia-less renewable energy resources will hence require new models and upgraded estimation routines. To that end, in this paper we propose a robust estimator for an interconnected model of power networks comprised of a comprehensive ninth order synchronous generator model, advanced power electronics-based models for photovoltaic (PV) power plants, constant power loads, constant impedance loads, and motor loads. The presented state estimator design is based on Lyapunov stability criteria for nonlinear differential algebraic equation (DAE) models and is posed as a convex semi-definite optimization problem. Thorough simulations studies have been carried out on IEEE-39 bus test system to showcase the robustness of the proposed estimator against unknown uncertainty from load demand and solar irradiance.

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arXiv2022

On Differential Privacy and Traffic State Estimation Problem for Connected Vehicles

This letter focuses on the problem of traffic state estimation for highway networks with junctions in the form of on- and off-ramps while maintaining differential privacy of traffic data. Two types of sensors are considered, fixed sensors such as inductive loop detectors and connected vehicles which provide traffic density and speed data. The celebrated nonlinear second-order Aw-Rascle- Zhang (ARZ) model is utilized to model the traffic dynamics. The model is formulated as a nonlinear state-space difference equation. Sensitivity relations are derived for the given data which are then used to formulate a differentially private mechanism which adds a Gaussian noise to the data to make it differentially private. A Moving Horizon Estimation (MHE) approach is implemented for traffic state estimation using a linearized ARZ model. MHE is compared with Kalman Filter variants namely Extended Kalman Filter, Ensemble Kalman Filter and Unscented Kalman Filter. Several research and engineering questions are formulated and analysis is performed to find corresponding answers.

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arXiv2022

Dynamic State Estimation of Nonlinear Differential Algebraic Equation Models of Power Networks

This paper investigates the joint problems of dynamic state estimation of algebraic variables (voltage and phase angle) and generator states (rotor angle and frequency) of nonlinear differential algebraic equation (NDAE) power network models, under uncertainty. Traditionally, these two problems have been decoupled due to complexity of handling NDAE models. In particular, this paper offers the first attempt to solve the aforementioned problem in a coupled approach where the algebraic and generator states estimates are simultaneously computed. The proposed estimation algorithm herein is endowed with the following properties: (i) it is fairly simple to implement and based on well-understood Lyapunov theory; (ii) considers various sources of uncertainty from generator control inputs, loads, renewables, process and measurement noise; (iii) models phasor measurement unit installations at arbitrary buses; and (iv) is computationally less intensive than the decoupled approach in the literature.

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arXiv2022

Control-Theoretic Modeling of Multi-Species Water Quality Dynamics in Drinking Water Networks: Survey, Methods, and Test Cases

Chlorine is a widely used disinfectant and proxy for water quality (WQ) monitoring in water distribution networks (WDN). Chlorine-based WQ regulation and control aims to maintain pathogen-free water. Chlorine residual evolution within WDN is commonly modeled using the typical single-species decay and reaction dynamics that account for network-wide, spatiotemporal chlorine concentrations only. Prior studies have proposed more advanced and accurate descriptions via multi-species dynamics. This paper presents a host of novel state-space, control-theoretic representations of multi-species water quality dynamics. These representations describe decay, reaction, and transport of chlorine and a fictitious reactive substance to reflect realistic complex scenarios in WDN. Such dynamics are simulated over space- and time-discretized grids of the transport partial differential equation and the nonlinear reaction ordinary differential equation. To that end, this paper (i) provides a full description on how to formulate a high fidelity model-driven state-space representation of the multi-species water quality dynamics and (ii) investigates the applicability and performance of different Eulerian-based schemes (Lax-Wendroff, backward Euler, and Crank- Nicolson) and Lagrangian-based schemes (method of characteristics) in contrast with EPANET and its EPANET-MSX extension. Numerical case studies reveal that the Lax-Wendroff scheme and method of characteristics outperform other schemes with reliable results under reasonable assumptions and limitations.

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arXiv2022

Flood Risk Mitigation and Valve Control in Stormwater Systems: State-Space Modeling, Control Algorithms, and Case Studies

The increasing access to non-expensive sensors, computing power, and more accurate forecasting of storm events provides unique opportunities to shift flood management practices from static approaches to an optimization-based real-time control (RTC) of urban drainage systems. Recent studies have addressed a plethora of strategies for flood control in stormwater reservoirs; however, advanced control theoretic techniques are not yet fully investigated and applied to these systems. In addition, there is an absence of a coupled integrated control model for systems composed of watersheds, reservoirs, and channels for flood mitigation. To this end, we develop a novel state-space model of hydrologic and hydrodynamic processes in reservoirs and one-dimensional channels. The model is tested under different types of reservoir control strategies based on real-time measurements (reactive control), and based on predictions of the future behavior of the system (predictive control) using rainfall forecastings. We apply the modeling approach in a system composed by a single watershed, reservoir, and a channel connected in series, respectively, for the San Antonio observed rainfall data. Results indicate that for flood mitigation, the predictive control strategy outperforms the reactive controls not only when applied for synthetic design storm events, but also for a continuous simulation. Moreover, the predictive control strategy requires smaller valve operations, while still guaranteeing efficient hydrological performance. From the results, we recommend the use of the model predictive control strategy to control stormwater systems due to the ability to handle different objective functions, which can be altered according to rainfall forecasting and shift the reservoir operation from flood-based control to strategies focused on increasing detention times, depending on the forecasting.

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arXiv2022

Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond

Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following function set classifications: bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic inner-boundedness, and quadratic boundedness. These function sets are characterized by constant scalars or matrices bounding the NDS' nonlinearities. These constants (i) depend on the NDS' operating region, topology, and parameters, and (ii) are utilized to synthesize observer/controller gains. Unfortunately, there is a near-complete absence of algorithms to compute such bounding constants. In this paper, we develop analytical then computational methods to compute such constants. First, for every function set classification, we derive analytical expressions for these bounding constants through global maximization formulations. Second, we utilize a derivative-free, interval-based global maximization algorithm based on branch-and-bound framework to numerically obtain the bounding constants. Third, we showcase the effectiveness of our approaches to compute the corresponding parameters on some NDS such as highway traffic networks and synchronous generator models.

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arXiv2022

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound

Sensor and actuator selection problems (SASP) are some of the core problems in dynamic systems design and control. These problems correspond to determining the optimal selection of sensors (measurements) or actuators (control nodes) such that certain estimation/control objectives can be achieved. While the literature on SASP is indeed inveterate, the vast majority of the work focuses on linear(ized) representation of the network dynamics, resulting in the placements of sensors or actuators (SA) that are valid for confined operating regions. As an alternative, herein we propose a new general framework for addressing SASP in nonlinear dynamic systems (NDS), assuming that the inputs and outputs are linearly coupled with the nonlinear dynamics. This is investigated through (i) classifying and parameterizing the NDS into various nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations, and (iii) designing a new customized branch-and-bound (BnB) algorithm that exploits problem structure of the SASP. The newly designed BnB routines are computationally more attractive than the standard one and also directly applicable to solve SASP for linear systems. In contrast with contemporary approaches from the literature, our approach is suitable for finding the optimal SA combination for stable/unstable NDS that ensures stabilization of estimation error and closed-loop dynamics through a simple linear feedback control policy.

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arXiv2022

Where Should Traffic Sensors Be Placed on Highways?

This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find placements that result in optimized network-wide, traffic observability. Consequently, this results in accurate traffic density estimates on segments where sensors are not installed. The substantial contribution of this paper is the utilization of control-theoretic observability analysis -- jointly with integer programming -- to determine traffic sensor locations based on the nonlinear dynamics and parameters of traffic networks. In particular, the celebrated asymmetric cell transmission model is used to guide the placement strategy jointly with observability analysis of nonlinear dynamic systems through Gramians. Thorough numerical case studies are presented to corroborate the proposed theoretical methods and various computational research questions are posed and addressed. The presented approach can also be extended to other models of traffic dynamics.

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arXiv2022

Model Order Reduction for Water Quality Dynamics

A state-space representation of water quality dynamics describing disinfectant (e.g., chlorine) transport dynamics in drinking water distribution networks has been recently proposed. Such representation is a byproduct of space- and time-discretization of the PDE modeling transport dynamics. This results in a large state-space dimension even for small networks with tens of nodes. Although such a state-space model provides a model-driven approach to predict water quality dynamics, incorporating it into model-based control algorithms or state estimators for large networks is challenging and at times intractable. To that end, this paper investigates model order reduction (MOR) methods for water quality dynamics with the objective of performing post-reduction feedback control. The presented investigation focuses on reducing state-dimension by orders of magnitude, the stability of the MOR methods, and the application of these methods to model predictive control.

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arXiv2021

Feedback Stabilization and Output Tracking for Discrete-Time Lipschitz Nonlinear Systems via Iterative Convex Approximations

The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs for dynamic systems in which the nonlinearity belongs to Lipschitz functions have been proposed. However, most of them only focus on output feedback and consequently, state feedback design remains less developed. To that end, this paper is dedicated to the problem of full-state feedback controller design for discrete-time Lipschitz nonlinear systems. In addition, we present a simple iterative method for improving the convergence of the closed-loop performance. It is later demonstrated that our approach can be conveniently extended and utilized for output tracking.

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arXiv2021

Probabilistic State Estimation in Water Networks

State estimation in water distribution networks (WDN), the problem of estimating all unknown network heads and flows given select measurements, is challenging due to the nonconvexity of hydraulic models and significant uncertainty from water demands, network parameters, and measurements. To this end, a probabilistic modeling for state estimation (PSE) in WDNs is proposed. After linearizing the nonlinear hydraulic WDN model, the proposed PSE shows that the covariance matrix of unknown system states (unmeasured heads and flows) can be linearly expressed by the covariance matrix of three uncertainty sources (i.e., measurement noise, network parameters, and water demands). Instead of providing deterministic results for unknown states, the proposed PSE approach (i) regards the system states and uncertainty sources as random variables and yields variances of individual unknown states, (ii) considers thorough modeling of various types of valves and measurement scenarios in WDNs, and (iii) is also useful for uncertainty quantification, extended period simulations, and confidence limit analysis. The effectiveness and scalability of the proposed approach is tested using several WDN case studies.

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