Model Control Design Research Articles

Multibody Constraints in the Geometrically Nonlinear Intrinsic Formulation

Abstract The intrinsic formulation for geometrically nonlinear beam dynamics provides a compact and versatile description of slender beam-like structures. With nonlinearities limited to second-order couplings in the formulation, it has been an attractive choice in formulating nonlinear reduced-order models for dynamic analysis and control design in aeroelasticity problems involving large displacements and rotations. Owing to its rotation-free formalism, the intrinsic formulation has not been formulated to accommodate multibody constraints, limiting its use against multibody structures with kinematic constraints. This work aims to address such weakness as we present developments in introducing multibody constraints into the full and reduced-order intrinsic equations while still preserving the beneficial traits of the method. We describe the resolution of displacement-level constraints using index-1 approach and adaptation of constraint stabilization strategies to the intrinsic formulation using state projection. The numerical behavior of the full- and reduced-order implementations are assessed using test cases with large static and dynamic deformations with time-domain simulations to demonstrate validity of the approach.

Model and Fuzzy Controller Design Approaches for Stability of Modern Robot Manipulators

Robotics is a crucial technology of Industry 4.0 that offers a diverse array of applications in the industrial sector. However, the quality of a robot’s manipulator is contingent on its stability, which is a function of the manipulator’s parameters. In previous studies, stability has been evaluated based on a small number of manipulator parameters; as a result, there is not much information about the integration/optimal arrangement/combination of manipulator parameters toward stability. Through Lagrangian mechanics and the consideration of multiple parameters, a mathematical model of a modern manipulator is developed in this study. In this mathematical model, motor acceleration, moment of inertia, and deflection are considered in order to assess the level of stability of the ABB Robot manipulator of six degrees of freedom. A novel mathematical approach to stability is developed in which stability is correlated with motor acceleration, moment of inertia, and deflection. In addition to this, fuzzy logic inference principles are employed to determine the status of stability. The numerical data of different manipulator parameters are verified using mathematical approaches. Results indicated that as motor acceleration increases, stability increases, while stability decreases as moment of inertia and deflection increase. It is anticipated that the implementation of these findings will increase industrial output.

Model based aircraft design and optimization: a case study with cessna 172N aircraft

Abstract This study aims to create an interdisciplinary, multi-level design approach for fixed wing aircrafts. A case study is performed using Cessna 172N aircraft characteristics that is based on a mathematical model having six degrees of freedom (DOF). A Model Based Aircraft Design Software (MAD) is developed using a mathematical dynamic model in Python environment for use in the optimization phase of the Cessna 172N aircraft. The MAD environment is composed of analysis tools that communicate with each other by an automated process chain system. The model includes aerodynamics, engine, mass, control, atmosphere, and landing gear submodules. In addition, the model has trim and 6 DOF simulation analysis capabilities which provide a diversity of analyses that can be considered in early design phases. In order to get trimming and simulation capability, MAD software does not need any precalculated aerodynamic database. The force and moment calculations are performed instantly via DATCOM and AVL solvers for each iteration of simulation or trim. Thanks to this method, alternative aircraft geometries can be compared at the first phase of the design and optimization processes without creating an overall database. All methodologies of model submodules, performance, stability and control calculations, design, and optimization applications are implemented in the MAD environment.

PDE modelling and switch strategy controller design for a flexible detection system with output constraint and actuator failure

A novel approach for modelling a mine detection robot system is presented in this paper using partial differential equations and Hamilton’s principle. The system comprises a rigid arm, a detecting sensor module, and a flexible string. The paper addresses the challenges of boundary deflection constraint and actuator fault. To overcome these challenges, a unique controller is developed using Barrier Lyapunov function and switching strategy. This controller enables the robot system to achieve the desired position and eliminate the vibration of flexible string. The superiority of the designed control law is demonstrated through simulation results. Furthermore, the asymptotic stability of the closed-loop flexible system is established by the use of extending LaSalle’s Invariance principle to an infinite dimensional system. This principle ensures that the system will eventually reach a stable state over time.

Identifying suitable DC system models for an independent design of VSC controllers in MTDC grids

In AC-multi-terminal DC (MTDC) systems, if converter controllers are designed individually, the interactive system modes stemming from the dynamic couplings among the converters and the DC system components may result in the instability of the interconnected system (INTSYS). This paper presents a comparative system-level study to determine the suitable models for an individual design of converter controllers to prevent INTSYS instability. The goal is to identify suitable individual system (INDSYS) models that do not contain the internal dynamics of adjacent converters and only include the coupling dynamics corresponding to the interactive system modes among the converters. The use of these models for control design will result in the dynamic response of the INTSYS being close to that of the INDSYS models. Furthermore, such models can ensure INTSYS stability when converter controllers are designed individually without requiring the complete model of the INTSYS or internal dynamics of the adjacent converters. Both the master–slave and the droop control modes of operation are analyzed, and specific INDSYS models among those available in the literature are recommended for each operation mode. Time-domain simulations in PSCAD validate the accuracy of the INDSYS models. Furthermore, eigenvalue analysis along with the participation factor and sensitivity analyses for a large set of control parameters are employed to evaluate the efficacy of the recommended models.

Reinforcement Learning and Optimal Control of PMSM Speed Servo System

This article proposes a novel model-free optimal speed tracking control scheme for permanent magnet synchronous motors (PMSMs) through reinforcement learning (RL). To achieve the speed servo control, we formulate the linear quadratic regulator associated with the reduced-order model in the outer-loop controller design. Such a model is obtained in terms of singular perturbation theory, which enables the separation of slow and fast time-scale dynamics. Moreover, we develop an off-policy RL algorithm to iteratively approximate the ideal value of solution to the linear quadratic regulator without requiring any knowledge of model parameters of the PMSM and the measurement of the load torque. Both simulation and experimental tests are carried out to justify that the proposed control scheme realizes precision speed tracking performance and shape transient response in the presence of unknown model parameters.

Dynamic modeling and control of a solar sail considering large-amplitude nonlinear vibration

The solar sail spacecraft utilizes Solar Radiation Pressure (SRP) to achieve propulsion, which can realize long-term acceleration without fuel consumption, making it an appealing option for deep space exploration and polar-sitter observation. However, because of the large-scale and high-flexibility of the membrane structure, the solar sail poses challenging dynamic and control issues. Precise dynamic modeling and effective control design can provide theoretical guidance for the efficient functioning of solar sail, which are of great significance and urgently need to be studied. In this paper, a dynamic model that can describe the large-amplitude vibrations of the solar sail is established. Additionally, an attitude tracking controller and a cable-based nonlinear vibration controller are designed to control the attitude motion and flexible vibration of the solar sail. The results show that the established nonlinear rigid-flexible coupling dynamic model is more accurate compared to the linear dynamic model. The polynomial fitting method can characterize the nonlinear dynamics of the solar sail extremely effectively while cutting the program runtime to 5% of the original. Two controllers designed in this paper can make the solar sail maneuver follow the desired trajectory accurately while reducing the sail surface vibration by more than 40%. The research outcomes of this paper can provide references for the dynamic study and active control of large-scale membrane spacecraft.

Modeling and Trajectory Tracking Control for a Multi-Section Continuum Manipulator

This paper presents a dynamic modeling and trajectory tracking control design for a hyper-redundant continuum manipulator (HRM), which is able to continuously bend along its length. The HRM has the advantages of high flexibility, large workspace, and low inertia, but also poses challenges of complex kinematics, and dynamic coupling. To address these challenges, the kinematics model was developed based on the piecewise constant curvature (PCC) assumption that captures the relationship between the cable lengths, joint angles, and end-effector pose. Inverse kinematics is presented geometrically by solving trigonometric equations. The dynamic model for the continuum robot (CR) is derived using the Euler–Lagrange representation, which incorporates the effects of gravity and elasticity. Accordingly, three control strategies are developed and applied to a two-section continuum robot, which are the inverse dynamic proportional integral derivative controller (PID), fuzzy logic controller (FLC), and sliding mode controller (SMC). We validate our proposed methods through simulations on various 3D trajectories, utilized MATLAB symbolic math toolbox in conjunction with Simulink simulation; demonstrate and evaluate different close-loop dynamic control responses for different scenarios. This simulation used in the creation of a unique animated simulation for a whole 3D continuum robot while tracking its desired trajectories. Finally, the simulation results demonstrate that our proposed methods can effectively control the HRM with high tracking performance, exhibiting enhanced responses in terms of settling time, rising time, and steady-state error. While the developed SMC outperforms Poth's PID and FLC in terms of robustness and settling time (51% and 10.3%), respectively.

Predictive Control of a Wind Turbine Based on Neural Network-Based Wind Speed Estimation

Predictive control is an advanced control technique that performs well in various application domains. In this work, linearised control design models are first derived in state-space form from the full nonlinear model of the 5 MW Supergen (Sustainable Power Generation and Supply) exemplar wind turbine. Feedback model predictive controllers (FB-MPCs) and feedforward model predictive controllers (FF-MPCs) are subsequently designed based on these linearised models. A neural network (NN)-based wind speed estimation method is then employed to obtain the accurate wind estimation required for designing a FF-MPC. This method uses a LiDAR to be shared between multiple wind turbines in a cluster, i.e., one turbine is mounted with a LiDAR, and each of the remaining turbines from the cluster is provided with a NN-based estimator, which replaces the LiDAR, making the approach more economically viable. The resulting controllers are tested by application to the full nonlinear model (based on which the linearised models are derived). Moreover, the mismatch between the control design model and the simulation model (model–plant mismatch) allows the robustness of the controllers’ design to be tested. Simulations are carried out at varying wind speeds to evaluate the robustness of the controllers by applying them to a full nonlinear 5 MW Matlab/SIMULINK model of the same exemplar Supergen wind turbine. Improved torque/speed plane tracking is achieved with a FF-MPC compared to a FB-MPC. Simulation results further demonstrate that the control performance is enhanced in both the time and frequency domains without increasing the wind turbine’s control activity; that is, the controller’s gain crossover frequency (or bandwidth) remains within the acceptable range, which is about 1 rad/s.

Kernel-based regularized iterative learning control of repetitive linear time-varying systems

For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is not chosen carefully, models with either large variance or large bias would be resulted, which is one of the obstacles to further improve the modeling and tracking performances of data-driven ILC in practice. An emerging trend in the system identification community to deal with this issue is using regularization instead of the statistical tests, e.g., AIC, BIC, and one of the representatives is the so-called kernel-based regularization method (KRM). In this paper, we integrate KRM into data-driven ILC to handle a class of repetitive linear time-varying systems, and moreover, we show that the proposed method has ultimately bounded tracking error in the iteration domain. The numerical simulation results show that in contrast with the least squares method and some existing data-driven ILC methods, the proposed one can give faster convergence speed, better accuracy and robustness in terms of the tracking performance.

Fast Tube Model Predictive Control for Driverless Cars Using Linear Data-Driven Models

Model predictive control (MPC) has been widely applied to different aspects of autonomous driving, typically using nonlinear physically derived models for prediction. However, feedback control systems inherently correct for model errors, and thus in many applications it is sufficient to use a linear time-invariant (LTI) model for control design, especially when using robust control methods. This philosophy of approach appears to have been neglected in current driverless car research and is the research gap that we aim to address here. Namely, instead of deriving meticulous nonlinear physical models of vehicle dynamics and solving a correspondingly complex optimal control problem (OCP), we identify a low-order data-driven LTI model and handle its uncertainty via robust linear MPC methods. We develop a two-step control scheme for driverless cars based on tube MPC (TMPC), which introduces structural robustness, ensuring constraint compliance despite modeling error in the data-driven prediction model. Furthermore, we use fast optimization methods designed to exploit the special structure of the linear MPC problem. We evaluate the proposed control scheme using a vehicle model identified from real-world data and simulations in IPGCarmaker, where the model of the vehicle under control is inherently nonlinear and uses detailed 3-D physics. Our results show that an LTI model can be effectively used for the task of lane-keeping, that TMPC can prevent lane departure and possible collisions due to model uncertainty, and that linear models allow for several algorithmic improvements that can decrease computation time by an order of magnitude compared with naive MPC implementations.

Flight and Vibration Control of Flexible Air-Breathing Hypersonic Vehicles Under Actuator Faults.

The issue of modeling and fault-tolerant control (FTC) design for a class of flexible air-breathing hypersonic vehicles (FAHVs) with actuator faults is investigated in this article. Different from previous research, the shear deformation of the fuselage is considered, and an ordinary differential equations-partial differential equations (ODEs-PDEs) coupled model is established for the FAHVs. A feedback control is proposed to ensure flight stable and an adaptive FTC method is designed to deal with actuator faults while suppressing the system's vibrations. Besides, the stability analysis of the closed-loop system is given via the Lyapunov direct method and an algorithm that transfers the bilinear matrix inequalities (BMIs) feasibility problem to the linear matrix inequalities (LMIs) feasibility problem is provided for determining the control gains. Finally, the numerical simulation results show that the proposed controller can stabilize the flight states and suppresses the vibration of the fuselage efficiently.

Fixed-Frequency PWM Control and Stability of Series-Stacked Buffer for 2ω-Power Decoupling

Active second-harmonic ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\omega $ </tex-math></inline-formula> ) filters have become an integral technology for single-phase power converters in high-power density designs. The series-stacked buffer (SSB) has emerged as an attractive topology among the existing solutions due to its low power, high efficiency, and compact design. However, one of the challenges in adopting SSB lies in its control, where hysteresis current control has been adopted conventionally. This results in a wide variation in the switching frequency, making the digital control implementation and filter design complex. On the other hand, fixed-frequency pulsewidth modulation (PWM) control necessitates developing a model for the systematic controller design to ensure stability and desired filtering performance. The assumption of SSB modeled as a second-harmonic current source, independent of the dc bus circuit components, fails to capture the dc bus loading effect on the SSB. In this work, a dynamic model of SSB is developed where the main dc bus and its passive elements are considered. The derived model enables a systematic approach for the controller design while ensuring the desired <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\omega $ </tex-math></inline-formula> filtering. The stability limits and parameter sensitivities of the model are studied analytically and in simulations. The analytical model is validated, and the proposed controller performance and stability limit are verified experimentally on a hardware prototype. A video demonstrating the transition from stable to unstable operation is provided.

Finite-time adaptive neural network event-triggered output feedback control for PMSMs

This article investigates the finite-time adaptive neural network event-triggered output feedback control for the permanent magnet synchronous motor (PMSM) systems. The addressed PMSM systems include unknown nonlinear dynamics and immeasurable states. The neural networks are utilized to approximate the unknown nonlinear dynamics and an equivalent control design model is established, by which a neural network state observer is given to estimate the immeasurable states. By constructing an event-triggered mechanism and under the framework of adaptive backstepping control design technique and finite-time stability theory, a finite-time adaptive event-triggered output feedback control scheme is developed. It is proved that the proposed control scheme ensures the closed-loop system to be stable and the angular velocity, stator current and other state variables remain bounded in a finite time. Finally, the computer simulation is provided to confirm the effectiveness of the presented controllers.

LQG control for hydrodynamic compensation on large floating wind turbines

This work proposes a novel Linear Quadratic Gaussian (LQG)-based blade pitch control method for floating offshore wind turbines, in which a state-space model of the turbine and water hydrodynamics is included in the LQG design. The actuation considered is collective blade pitch control with the objective of generator power stabilisation and platform motion reduction. A linear Kalman filter is used to estimate un-measurable states relating to wave excitation and radiation through measurements of generator speed, platform pitch, and wind disturbance. Controller design models were validated with the full order nonlinear model under various testing conditions. The new controller design is tested on a nonlinear high-fidelity simulation model of the 15 Mega-Watt (MW) floating semi-submersible wind turbine. In simulations with realistic stochastic wind and wave disturbances, the new controller achieves 32% lower generator speed Root Mean Square Error (RMSE) and 16% lower platform pitch RMSE compared to a standard LQG controller that does not include hydrodynamic states, for equivalent levels of pitch actuation and with a 2°/sec rate limit on pitch. The inclusion of hydrodynamics in the controller design not only reduced platform pitching fluctuation, but also had a strong effect of hub-height factors such as the generator speed.

The Integrator Dual-Delay model for advanced controller design of the open canal irrigation systems with multiple offtakes

The Integrator Delay (ID) model is widely used for advanced controller design in canal automation projects, assuming that all offtakes are aggregated into one at the most downstream end for each canal pool. However, such an unrealistic assumption differs greatly from the actual location distribution of the offtakes in most open canal irrigation systems (OCIS), leading to increased uncertainties and inaccurate canal operations. For this reason, this study introduced the Integrator Dual-Delay (IDD) model, capable of innovatively considering the lag-effect of the offtake flow changes alongside the irrigation canal. To investigate the effectiveness of the modified control-oriented model in upgrading the canal automatic operating systems, two centralized model predictive controllers were designed with the ID model and the IDD model, respectively. Then the simulation tests were carried out on the Third Main Canal of the Zhanghe Irrigation System in Southern China. Two performance indicators of Non-dimensional Integrated Square of Error (NISE) and Non-dimensional Integrated Square of Discharge Change (NISQ) were adopted to measure the water level control stability and flow control stability. The results show that with the IDD model, the NISE is reduced from 3.53 × 10-5 to 1.88 × 10-5 and the NISQ is reduced from 3.23 × 10-6 to 2.88 × 10-6, indicating that the proposed IDD model can help the control stabilities of water level and flow to be improved by 46.7 % and 10.8 %, respectively. The IDD model constructs a more accurate state-space prediction process for advanced controller design and contributes to more efficient canal automatic operations, showing great potential in precision irrigation for various OCIS.

Model complexity reduction and controller design for managed pressure drilling automation

Automation of Managed Pressure Drilling (MPD) allows for fast and accurate pressure control in drilling operations. The achievable performance in automated MPD with model-based controllers is determined by the controller and, indirectly, also by the hydraulics model used for controller synthesis. On the one hand, such a hydraulics model should accurately capture essential flow dynamics of the system such as, e.g., wave propagation effects, for which typically complex models are needed. On the other hand, a suitable model should be simple enough to facilitate high-performance controller design as well as to support fast simulation studies supporting well scenario analysis. This paper shows that low-order models in terms of delay differential equations can effectively meet these requirements. Moreover, we propose a data-based model reduction technique to construct these low-order delay models. Next, based on this reduced-complexity model, a novel controller is designed to regulate the downhole pressure. Simulation results confirm that this controller outperforms existing pressure controllers in realistic drilling scenarios related to the mitigation of liquid kicks and mud losses encountered when drilling into high- or low-pressure zones.

Adaptive Koopman-Based Models for Holistic Controller and Observer Design⋆

We present a method to obtain a data-driven Koopman operator-based model that adapts itself during operation and can be straightforwardly used for the controller and observer design. The adaptive model is able to accurately describe different state-space regions and additionally consider unpredictable system changes that occur during operation. Furthermore, we show that this adaptive model is applicable to state-space control, which requires complete knowledge of the state vector. For changing system dynamics, the state observer therefore also needs to have the ability to adapt. To the best of our knowledge, there have been no approaches presently available that holistically use an adaptive Koopman-based plant model for the state-space design of both the controller and observer. We demonstrate our method on a test rig: controller and observer adequately adapt during operation, so that outstanding control performance is achieved even in the case of strong occuring systems changes.

Discrete-Time Complex-Vector Model Based Closed-Loop Current Controller for CSC-Fed PMAC Machine Systems With Low Carrier Ratios

Pulsewidth modulated (PWM) current-source converters (CSCs) have been attractive for high-power adjustable-speed machine systems with low carrier ratios. However, the high-order nonlinear model of CSC-fed machine systems, the distinct digital delay from the low carrier ratios, and the cross-coupling caused by coordinate transformation bring great challenges to design of high-performance stator current controller for such kind of machine systems. Firstly, this article derives the discrete-time complex-vector model for the CSC-fed permanent-magnet ac (PMAC) machine system with low carrier ratios considering the distinct digital delay and cross-coupling effect mentioned above. On that basis, the stator current controller is proposed with the modified controller parameters and the compensation technique to improve both dynamic performance and stability of the CSC-fed PMAC machine systems with low carrier ratios. The theoretical analysis and controller design process have been presented in detail to provide a guide for the model derivation and controller design. The experiments on a laboratory prototype are conducted to verify the effectiveness of the developed modeling and controller.

Fractional-order model identification and indirect internal model controller design for higher-order processes

Several studies have shown that fractional-order models with dead-time can be used to capture the dynamics of a wide range of processes. Also, there is more scope to improve the existing identification and control strategies. Hence, this work revisits the identification of fractional-order models (IDFOM) approach to augment the same with a robust indirect fractional-order internal model control (IFOIMC) method to formulate a new identification and control strategy. In this strategy, the fractional-order model obtained using the IDFOM approach is shifted in the frequency domain by a frequency-shifting parameter. With the help of IMC principles, the frequency-shifted model is used to design the IFOIMC controller with the frequency-shifting parameter as the only tuneable parameter. Thus, the frequency-shifting parameter/robustness parameter replaces the only tuning parameter of conventional IMC design. This frequency-shifting parameter is tuned based on maximum sensitivity considerations to ensure the robustness of the design. The resulting IFOIMC controller is further realized as a fractional-order proportional-integral controller in series with a fractional-order filter (FOPIFOF). The effectiveness of the proposed identification and control strategy is illustrated by comparing the closed-loop performance achieved by IFOIMC controllers designed using two widely used identification strategies.