Reduced-order Controller Research Articles

Robust load frequency control in interval power systems via reduced-order generalized active disturbance rejection control

Abrupt load changes, structural discrepancies, and parametric uncertainties cause degraded performance of the high-order power systems. This situation creates a problematic endeavor while analyzing the performance of such high-order systems. Hence, a simple and efficient lower-order control methodology can be deployed to sort out the issues related to load frequency control (LFC) in such systems. This study resolves the LFC problem in parametric bounded power systems by developing a worst-case reduced-order generalized active disturbance rejection control (WRGADRC) method. The core concept of the proposed technique entails that a controller will perform well in nominal scenarios if it performs satisfactorily in worst-case conditions. Therefore, an interval system’s worst-case reduced-order model is first obtained from its different uncertain models; the reduced order controller is then designed using the GADRC technique. The proposed scheme is rigorously validated on various parametric bounded minimum and non-minimum phase single-area and multi-area power systems, instilling confidence in its ability to achieve minimum frequency deviation in multiple scenarios. The supremacy of the proposed scheme is highlighted over some well-established control techniques in the literature related to the LFC problem.

Direct Synthesis of Reduced-Order Controllers With Integrating Action for a Class of Norm-Bounded Uncertain Plants

Direct Synthesis of Reduced-Order Controllers With Integrating Action for a Class of Norm-Bounded Uncertain Plants

The Supplementary Damping Method for CLCC HVDC Based on Projective Control Theory

This paper proposes a design method for an additional damping reduced-order controller based on the projective control theorem. Improvements are made to the projective theorem to achieve additional damping control through Controllable-Line-Commutated Converter (CLCC)-based High Voltage Direct Current (HVDC), which suppresses low-frequency oscillations. Using small disturbance identification techniques, the system’s linear model is first identified, and the state feedback control law of the system is then determined using the state-space pole assignment control method. Then, by retaining the dominant oscillation modes of the closed-loop system through the improved projective theorem, the state feedback is converted into output feedback. Ultimately, the sixth-order state feedback controller is reduced to a second-order one and applied in the CLCC HVDC additional damping strategy to suppress low-frequency oscillations. Simulation results based on the electromagnetic transient simulation software PSCAD demonstrate that the designed CLCC HVDC additional damping reduced-order projective control exhibits good suppression performance, strong robustness, and low order, which are of significant importance for engineering practice.

Active vibration control for flexible towers based on displacement observation and reduced-order controller in modal space: Theory and experiment

Active vibration control is not only suitable but also urgently needed in order to mitigate excessive vibration for dynamic systems such as wind turbine towers. However, there is a challenge of directly observing displacement and developing an efficient reduced-order control strategy. With this in view, a reduced-order controller based on displacement observation is developed for the vibration mitigation of flexible high towers, where the problems of low signal-to-noise ratio (SNR) and intricate acceleration-based control algorithms are eliminated completely. The displacement can be measured by laser or modern videometrics technology. A reduced-order model with an active mass damper (AMD) at the top of the tower is created using modal truncation approach based on modal participation factor (MPF), which successfully preserves the dominant modes of the original structure, and reduces the influence of high-frequency uncertainties. Considering structure uncertainties caused by environmental factors and aging process, an unscented Kalman filter (UKF) is introduced to identify the modal stiffness of the reduced-order model. The present study, using a 5 MW onshore wind turbine as an example, investigates active vibration control under wind and seismic loads and compares it with traditional tuned mass damper (TMD). From a dynamic perspective, the simplified model of wind turbine tower takes the form of a multi-degree-of-freedom series model. Consequently, a six-story steel frame platform has been constructed to experimentally validate the efficacy of the reduced-order controller. According to numerical simulation and laboratory testing, the control effect of the reduced-order controller with a few displacement states as feedback can be utilized as an active control strategy for high-rise flexible towers.

Design of reduced-order controllers for fluid flows using full-order controllers and Gaussian process regression

We propose a method to design reduced-order output-feedback controllers for fluid flows with the use of data produced by full-order controllers. First, the full-order controller is obtained by combining an ensemble Kalman filter (EnKF) and a model predictive controller (MPC) that are designed based on the Navier–Stokes equations. The full-order controller has high computational complexity and, therefore, is not suitable for real-time implementation. Hence, we use the full-order controller in offline numerical simulations to generate data for data-driven design of the reduced-order controller with low computational complexity. We find a reduced-order subspace of a closed-loop system under the full-order control from the data. This subspace underlies the reduced-order output-feedback controller. The reduced-order state-feedback law is obtained by approximating the full-order MPC with the use of its input/output data. The reduced-order observer is designed for a reduced-order model that is derived by using the Gaussian process regression (GPR). The GPR enables us to design the reduced-order observer which can evaluate uncertainty due to state-dependent residuals of the reduced-order model. We demonstrate the proposed method for a control problem of a flow around a cylinder at the Reynolds number 100. Numerical simulations reveal that the reduced-order controller performs as almost well as the full-order controller for a set of initial states. In addition, robustness of the reduced-order controller to a temporal disturbance that is not considered in the control design is confirmed in the simulations.

μ-Analysis and μ-Synthesis Control Methods in Smart Structure Disturbance Suppression with Reduced Order Control

In this study, we created an accurate model for a homogenous smart structure. After modeling multiplicative uncertainty, an ideal robust controller was designed using μ-synthesis and a reduced-order H-infinity Feedback Optimal Output (Hifoo) controller, leading to the creation of an improved uncertain plant. A powerful controller was built using a larger plant that included the nominal model and corresponding uncertainty. The designed controllers demonstrated robust and nominal performance when handling agitated plants. A comparison of the results was conducted. As an example of a general smart structure, the vibration of a collocated piezoelectric actuator and sensor was controlled using two different approaches with strong controller designs. This study presents a comprehensive simulation of the oscillation suppression problem for smart beams. They provide an analytical demonstration of how uncertainty is introduced into the model. The desired outcomes were achieved by utilizing Simulink and MATLAB (v. 8.0) programming tools.

A novel integrated differential-Routh approach to develop reduced order controller with improved performance

A novel integrated differential-Routh approach to develop reduced order controller with improved performance

An Active Power Dynamic Oscillation Damping Method for the Grid-Forming Virtual Synchronous Generator Based on Energy Reshaping Mechanism

The grid-forming virtual synchronous generator (GFVSG) with large virtual inertia can provide a friendly grid-connected operational mode for power electronic converters, but it may also introduce the active power dynamic oscillation problems similar to traditional synchronous generators. In view of this, the dynamic equivalent circuit model of the GFVSG grid-tied active power-angle is established firstly, and, then, the understanding of the GFVSG active power oscillations under variable disturbances is revealed from the perspective of circuit energy flow in this paper. On this basis, an active power dynamic oscillation damping method based on an energy reshaping mechanism for the GFVSG is proposed, and a parameter design method using the second-order equivalent reduced-order control model is given. The MATLAB 2016a simulation as well as experimental test platforms of a 100 kV·A GFVSG grid-connected system are established, then, both the feasibility and effectiveness of the proposed active power dynamic oscillation damping method are verified by using the simulation and experimental comparison results.

Dynamic Modeling and Control of a Flexible Planar Three-Link Mechanism Using Joint and Piezoelectric Actuators

Abstract This paper presents a new method of controlling the end effector position and orientation of a flexible planar three-link mechanism. The coupled dynamic model was formulated using a method based on the Udwadia–Kalaba equations of motion for constrained systems. Lyapunov's theory was used to develop a nonlinear control law using piezoelectric actuators and the unconstrained link dynamic models. Numerical simulation was used to demonstrate the system tracking performance of the end effector using a reduced order controller applied to a higher order truth dynamic model.

Developing HSS iteration schemes for solving the quadratic matrix equation AX2+BX+C=0$AX^{2}+BX+C=0$

AbstractThe quadratic matrix equation (QME) occurs in the branches such as the quadratic eigenvalue problems and quasi‐birth‐death processes. Also, the numerical solution of QMEs is an essential step in many computational methods for linear‐quadratic and robust control, filtering, controller order reduction, inner‐outer factorization, spectral factorization, and other applications. In this study, schemes are presented to solve the QME based on the Hermitian and skew‐Hermitian splitting (HSS). It is shown that the proposed schemes converge to the solutions of the QME. Finally, some examples are solved to discover the application of the schemes in comparison with Newton's method.

Output Feedback Control of Fuzzy Systems via Reduced-Order Approximation Technique

This article focuses on the problem of designing the reduced-order dynamic output feedback (DOF) controller for discrete-time T–S fuzzy plants. Differing from the existing methodologies, the reduced-order approximation technique is applied to simplify the pregiven high-order DOF controller. The key point is to construct a reduced-order closed-loop model to approximate the original high-order closed-loop system. First, a new error auxiliary system between the high-order closed-loop system and the reduced-order closed-loop model is obtained. The sufficient conditions to guarantee that the corresponding error system is asymptotically stable with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$</tex-math> </inline-formula> performance index are developed. Then, the parameters of the desired reduced-order controller are derived by utilizing the projection lemma and the cone complementary linearization algorithm. Finally, the advantages of the proposed technique are illustrated by a series of simulation analysis.

A survey on compressed sensing approach to systems and control

AbstractIn this survey paper, we review recent advances of compressed sensing applied to systems and control. Compressed sensing has been actively researched in the field of signal processing and machine learning. More recently, the method has been applied to systems and control problems, such as sparse feedback gain design, reduced-order control, and maximum hands-off control. This paper introduces these important applications of compressed sensing to systems and control. MATLAB programs for the numerical examples shown in this survey paper are available as supplementary materials.

Practical implementation of computationally-efficient machine learning-based control performance assessment system for a class of closed loop systems

This paper presents the concept of the computationally-efficient reduced order control performance assessment (RO-CPA) system for automatic detection of industrial single closed loop control systems whose performance could be not acceptable due to a poor tuning of the controller. The proposed machine learning (ML) based classification system is derived for a broad class of industrial control closed loops based on the proportional–integral–derivative (PID) controller. Apart from a high accuracy of the classification of the closed loop performance, the proposed RO-CPA system is derived to meet the requirements of low computational complexity and low memory usage. These requirements allow for practical implementation of RO-CPA in devices with low computational and memory resources, such as industrial programmable logic controllers (PLC) operating in manufacturing systems or embedded autonomous systems with dedicated PID-based control loops. This paper shows the rigorous ML-based design of the proposed RO-CPA system and the results of the validation of its classification accuracy. Additionally, an example of a practical implementation within a PLC in the form of a general purpose library function block is presented and the final experimental validation is made using a part of laboratory heat exchange and distribution setup.

Design of reduced-order and pinning controllers for probabilistic Boolean networks using reinforcement learning

In this paper, we study a stabilization method for probabilistic Boolean networks (PBNs) using Q-learning, which is one of the typical methods in reinforcement learning. A PBN is a class of discrete-time stochastic logical systems in which update functions are randomly chosen from the set of the candidates of Boolean functions. In the existing methods using reinforcement learning, a design method of structured controllers has not been studied. In this paper, we propose reward design methods to derive reduced-order controllers and pinning controllers. The key idea is to adjust the structure of controllers by the reward for the structure of the Q-table. The advantage of the proposed method is that implementation is easy, because the proposed method can be embedded in the existing Q-learning-based stabilization algorithm. In design of pinning controllers, we can calculate not only controllers but also pinning nodes in which the control input is assigned. We demonstrate through numerical examples that the controller obtained from our proposed method is simpler than that from the existing method.

Reduced-Order Static -Gain Control of Rotorcraft with Guaranteed Rotor–Fuselage Stability

A reduced-order control design method for rotorcraft is proposed in this work. Explicit constraints on the closed-loop fuselage–rotor stability are considered in the fuselage dynamics-based control design, aiming for the -gain performance for the fuselage dynamics under pole placement constraints and the guaranteed fuselage–rotor stability. Sufficient conditions for the control design problem are presented, formulated as a feasibility problem based on bilinear matrix inequalities. Such an NP-hard problem is approximated using convex relaxation techniques and the cone complementary linearization method, leading to an iterative control design algorithm. An altitude–velocity vector tracking concept is also proposed in this work, integrated with the proposed control design method to design rotorcraft trajectory controllers. Performance of the resultant rotorcraft trajectory controllers is examined via numerical simulations against representative maneuvers from the ADS-33E specification.

A non-iterative approach to Linear Quadratic Static Output Feedback

This paper considers the problem of static output feedback (SOF) synthesis for linear time-invariant (LTI) systems. Static output feedback, and more generally structured controller synthesis, is of special interest to any industrial application where a reduced-order controller is desired, e.g., high-order systems, or a specific structure is to be imposed, i.e., distributed/decentralised control. A simple two-step process is proposed, solving one Riccati equation and one optimisation problem with linear matrix inequality (LMI) constraints, enabled via a dilation using the distance to the full-state feedback optimum gain. Numerical analysis shows considerable computational savings, with negligible differences in the performance, when compared to current iterative methods.

H∞ Loop Shaping Using Polytopic Weights and Pole Assignment to Missile Autopilot

Modern missiles must deal with stringent performance requirements and ensure robustness across a wide range of operating conditions during flight time. Classic gain-scheduling designs have been successful in practice, but do not provide theoretically ensured bounds on both performance and robustness. Controllers are interpolated at intermediate operating conditions and switching them may cause instability. On the other hand, polytopic linear parameter-varying (LPV) controllers avert this switching and use real-time information about the plant, in order to smooth out the gain scheduling. We hereby propose a novel procedure to yield an output feedback LPV controller that ensures robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> performance to a missile longitudinal autopilot. Our novel approach considers the four-block loop-shaping <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> control theory with polytopic LPV weights that use polytopic coordinates of the LPV plant. One is capable of adjusting the singular values of the open-loop plant individually at the polytope vertices, and benefits from a trade-off between linear matrix inequalities (LMI) based optimization tools and the designer experience. This can be construed as a natural extension of the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}_{\infty} $ </tex-math></inline-formula> loop-shaping method that uses linear time-invariant (LTI) weights. Assuming the scheduling variables are frozen, we also include LMI conditions for assigning closed-loop poles and hence circumvent controller order reduction. Nonlinear simulations assess the proposed autopilot, and results show an improved robust stability margin, in addition to an improved response to the acceleration command, concerning the LTI-based approach.

Controller Reduction for Nonlinear Systems by Generalized Differential Balancing

In this article, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD linear quadratic Gaussian (LQG) balancing and GD <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> -balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> -balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities (LMIs).

Reduced-order controller design for Cuk converters based on objective holographic feedback

Reduced-order controller design for Cuk converters based on objective holographic feedback

Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.