Dynamic Reference Model Research Articles

Model reference adaptive controller with interpretable fuzzy rules for linear MIMO systems

This paper presents a method for fuzzy model reference adaptive control system design for a partially known multi-input multi-output (MIMO) linear dynamic plant. Differential or convolutional equations can describe the plant to be controlled, and the fuzzy controller is assumed to be from the MIMO sector-bounded nonstationary nonlinearities class. The task is to obtain robust adaptive stabilization. Some absolute stability theorems and integral evaluations of the state and control vectors are applied in the MIMO fuzzy adaptive controller design procedure for the first time. A method for automatically obtaining a near-optimal nonlinear dynamic reference model is described. A practical step-by-step procedure of the MIMO adaptive fuzzy controller design is proposed, resulting in highly interpretable MIMO fuzzy control rules based on triangular fuzzy sets and strong triangular fuzzy partition. An example of the fuzzy controller design according to the proposed procedure is given.

Design of robust pre‐compensators for decoupling polytopic linear systems

SummaryThis work proposes a new approach for designing dynamic pre‐compensators to reduce interactions of multivariable uncertain square systems. The proposed method is based on the minimization of the norm of the difference between the compensated system and a diagonal reference model. The main appeal of the technique is to propose a systematic procedure to obtain the reference model dynamics, in contrast to methods that use the identity matrix as a reference, and to obtain diagonal dominance in a frequency range of interest employing the generalized Kalman‐Yakubovich‐Popov (KYP) Lemma. The design conditions are expressed as linear matrix inequalities (LMI) thanks to a new general parametrization on the decision variables in bilinear products to reduce the conservatism of the solutions compared to standard approaches from the literature. Numerical examples verify the robustness of the proposed method, showing significant decoupling of the uncertain plant.

Experimental model validation and predictive control strategy for an industrial fire-tube boiler

This paper presents a flexible control structure for fire-tube boilers based on a suitable integration of the typical decentralized PI control structure and model predictive control technique. First, a dynamic nonlinear reference model of the fire-tube boilers is developed combining models available in the technical literature, based on first principle laws. The overall system model is considered as a gray-box model, and it has been validated with real data. Then, a suitable control-oriented model is derived out of the nonlinear reference model, in order to design a hybrid cascade MPC-PI control structure capable of guaranteeing stability, improving performances and enforcing real-time constraints. The flexibility of such a structure can be exploited to impose different types of functional behavior to the boiler itself, from the performance-related ones to the efficiency increase ones. While the reference non-linear model is large and detailed, the control-oriented one is simplified so that a few process parameters are identified to reduce dramatically the implementation in the MPC controller hardware and software framework. A sensitivity analysis with respect to these process parameters highlights the robustness and easy implementation of such a strategy. Two MPC configurations have been developed and tested in simulation over the validated boiler model. Then, a customized algorithm has been developed to understand a massive quantization phenomenon on the boiler pressure measurement. Finally, a test session conducted on a real fire-tube boiler quantifies the performance benefits of one configuration of the MPC-PI control structure with respect to the PI control. • Tuning of a dynamic nonlinear reference model of the fire-tube boilers with real data. • A hybrid cascade MPC-decentralized PID control structure, easly tunable. • Sensitivity analysis to test the robustness and easy implementation of such a control strategy. • A customized algorithm to reject a massive quantization on the boiler pressure measurement. • Implementation of the optimal control strategy and test session on a real fire-tube boiler.

Weighting Factor Free Model Predictive Control for a Flying Capacitor Converter in a DC Microgrid

This paper presents a single-objective model predictive control for a bidirectional DC-DC flying capacitor (FC) converter, which integrates a battery to the microgrid. The presence of multiple FCs facilitates the converter to interface a low-voltage battery to a high-voltage DC bus at reduced voltage stress on its power switches. However, such converter requires a controller that fulfils multiple objectives, namely DC bus and FC voltage regulations, and bidirectional power flow. The key feature of the proposed controller is that it utilizes a model predictive control with a single-objective cost function based on battery current and a redundant state selection scheme to attain these multiple objectives. Adopting such a strategy not only reduces computational burden but also eliminates the need for weighting factors and requirement of complex numerical models for its estimation. Another notable aspect is that the controller employs an improved dynamic reference model to generate appropriate battery current reference for the DC bus voltage regulation, without necessitating a secondary control loop and additional current sensors. Finally, experimental results of the proposed system for a step-response of the DC bus voltage, varying PV power, and loads are validated and compared against finite control set model predictive control.

Saturated full model capability of virtual synchronous generator to improve transient stability of hybrid power system

In hybrid power system (HPS), there are many inverter-based generators (IBGs) that inject renewable energy into the system as electrical power. Transient stability analysis of HPS in which synchronous generators (SGs) are operated in parallel with IBGs is necessary to operate the network safely under large disturbances. This paper examines the transient behaviour of IBGs with effective strategies, in which constraint on output current of IBGs is strictly considered to bring the results closer to reality. The control strategy is based on reference model tracking and substitution theory for networks, including parallel SG-IBGs to full IBGs. First, for a network with full IBGs, a constant power model reference is proposed as a static model. Then a dynamic reference model called saturated full model of virtual synchronous generator (VSG) or simply SFMVSG is introduced as the final solution for the controller of IBG in HPS. The SFMVSG has all existing VSG features and provides virtual damping torque created by the interaction of virtual damping fluxes. The simulation results confirm that the study is efficient.

Modelling and Simulation of Vehicle ESP System Based on CarSim and Simulink

In this paper, the simulation of the vehicle ESP system is carried out, and the linear two-degree-of-freedom dynamic reference model of the vehicle is established in MATLAB/Simulink. Combined with the method of direct yaw moment control, the yaw rate and the yaw angle are selected as the control variables. Based on the fuzzy PID control theory, the control strategy of the ESP system is designed to calculate the additional yaw moment required when the vehicle deviates from the desired trajectory. In order to verify the effectiveness of the ESP system designed in this paper, the vehicle dynamics model in CarSim software is used to build a joint simulation platform of CarSim and Simulink, and the model is tested at a speed of 120 km/h on a double lane change road with low adhesion rate. The simulation results show that the designed controller can significantly improve the manoeuvrability and stability of the vehicle.

Improving MRAC Transient Response Using Generalized Dynamic Inversion and Nullspace Parametrization

We demonstrate how the transient response of Model Reference Adaptive Control (MRAC) is improved by utilizing Generalized Dynamic Inversion (GDI) and the corresponding nullspace parametrization in the powerful Greville formula. The proposed approach neither alters the reference model structure, nor it modifies it through feedback. Rather, the proposed approach utilizes the control redundancy in matching the reference model for the purpose of designing an MRAC control law that yields good transient closed loop adaptive control response. The adaptive GDI-MRAC control law is composed of two parts: a particular part that enforces the reference model dynamics, and an auxiliary part that is affine in a null control vector. The particular and the auxiliary parts of the adaptive control law are confined in the range space of the transposed control matrix and its orthogonal complement nullspace, respectively. The null control vector is projected onto the nullspace of the control matrix via a nullprojection matrix. Hence, the null control vector design does not interfere with the reference model following, yet it can be designed via state feedback to improve closed loop state transient response. An improved Lyapunov control function is used to design the adaptation gains such that asymptotic vanishing of the state error dynamics is guaranteed. Extensive simulations are conducted to demonstrate the efficacy of the proposed method.

A Single-Objective Modulated Model Predictive Control for a Multilevel Flying Capacitor Converter in a DC Microgrid

This paper presents a single-objective modulated model predictive control for a bi-directional DC-DC flying capacitor (FC) converter in a microgrid. The presence of FC facilitates the converter to integrate a low-voltage battery to a high-voltage DC bus at reduced voltage stress on its power switches. The converter in such a configuration demands a multi-objective controller to accomplish DC bus and FC voltage regulations, and bi-directional power flow. The proposed controller realizes these multiple control objectives by determining optimum duty ratio for the power switches using a single-objective cost function based on battery current. In doing so, the converter realizes its multiple control objectives without weighting factors in the cost function and operates its power switches at a fixed switching frequency. The proposed controller also eliminates an additional control loop by utilizing an improved dynamic reference model to generate appropriate battery current reference for the DC bus voltage regulation and bi-directional power flow. Finally, the proposed system is validated experimentally under step-response of DC bus voltage, load, PV power, and system parameter variations, and compared with a finite control set model predictive control to prove its effectiveness.

Online capacitor early ageing monitoring and detection using a dynamic reference model

This study deals with a new approach for real-time detection of early ageing in DC-link electrolyte capacitors of DC–DC converters. The method is based on the comparison between the slope of the inductor current derived from a reference dynamic model and that of measurement. All of the normal deviations of the system parameters including gradual ageing of the capacitor and impact of the operating temperature are taken into account in the reference model. Since parameters of the reference model are set in accordance with the datasheets of the components, the reference slope represents normal gradual ageing of the capacitor. Therefore, any early ageing emerges in the measured slope. An accelerated ageing test bench was implemented to assess the proposed method, by which early ageing is emulated by experiments. The results confirm the performance of the method for the early ageing detection.

A dynamic process reference model for sparse networks with reciprocity

ABSTRACT Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network models built on top of simple Bernoulli baseline (or reference) measures often behave unrealistically in this respect, leading to the development of sparse reference models that preserve features such as mean degree scaling. In this paper, we generalize recent work on the micro-foundations of such reference models to the case of sparse directed graphs with non-vanishing reciprocity, providing a dynamic process interpretation of the emergence of stable macroscopic behavior.

Online optimal and adaptive integral tracking control for varying discrete‐time systems using reinforcement learning

SummaryConventional closed‐form solution to the optimal control problem using optimal control theory is only available under the assumption that there are known system dynamics/models described as differential equations. Without such models, reinforcement learning (RL) as a candidate technique has been successfully applied to iteratively solve the optimal control problem for unknown or varying systems. For the optimal tracking control problem, existing RL techniques in the literature assume either the use of a predetermined feedforward input for the tracking control, restrictive assumptions on the reference model dynamics, or discounted tracking costs. Furthermore, by using discounted tracking costs, zero steady‐state error cannot be guaranteed by the existing RL methods. This article therefore presents an optimal online RL tracking control framework for discrete‐time (DT) systems, which does not impose any restrictive assumptions of the existing methods and equally guarantees zero steady‐state tracking error. This is achieved by augmenting the original system dynamics with the integral of the error between the reference inputs and the tracked outputs for use in the online RL framework. It is further shown that the resulting value function for the DT linear quadratic tracker using the augmented formulation with integral control is also quadratic. This enables the development of Bellman equations, which use only the system measurements to solve the corresponding DT algebraic Riccati equation and obtain the optimal tracking control inputs online. Two RL strategies are thereafter proposed based on both the value function approximation and the Q‐learning along with bounds on excitation for the convergence of the parameter estimates. Simulation case studies show the effectiveness of the proposed approach.

Linear Transfer Functions Extraction for a Power Generation Three-Shaft Gas Turbine Based on Actual Specifications

The design and testing of various types of controllers require accurate and reliable transfer functions that are compatible with the performance condition of the system. In this paper, the linear and the nonlinear methods have been utilized for extracting the transfer functions for a three-shaft industrial gas turbine. The main variables are the fuel input and environment temperature, while the main outputs are the LPT exhaust gas temperature and the generated power. According to the nonlinear structure of the system and the input variation intervals, the quasi-amplitude-modulated pseudo random binary sequence signals have been utilized for generating input parameters. Finally, the results extracted from the selected methods were compared to the outputs of real performance data under loading and unloading conditions. Based on the comparison between the accuracies obtained by the results, the auto-regressive moving average with eXogenous, try and error transfer function and linearized Hammerstein model methods are proposed, respectively. The outcome of using the controller indicated higher compatibility from transfer functions as compared to the reference dynamic model.

Stability analysis for time delay control of nonlinear systems in discrete-time domain with a standard discretisation method

This paper provides stability analysis results for discretised time delay control (TDC) as implemented in a sampled data system with the standard form of zero-order hold. We first substantiate stability issues in discrete-time TDC using an example and propose sufficient stability criteria in the sense of Lyapunov. Important parameters significantly affecting the overall system stability are the sampling period, the desired trajectory and the selection of the reference model dynamics.

Stochastic Robust Team Formation Tracking Design of Multi-VTOL-UAV Networked Control System in Smart City Under Time-Varying Delay and Random Fluctuation

In this study, the robust H∞ event-triggered team formation tracking control design of multi-VTOL-UAVs in networked system is investigated. To describe the realistic networked system and UAV model, the intrinsic continuous Wiener random fluctuation, discontinuous Poisson random fluctuations, external disturbances and time-varying delays of wireless network are formulated in the proposed nonlinear stochastic jump diffusion system structure. By combining the event-triggered multi-UAV dynamic models and reference model into an augmented system, the robust H∞ event-triggered multi-UAV networked team tracking problem can be transformed to a Hamilton-Jacobi inequality(HJI)-constraint optimization problem. Due to the difficulties in solving HJI-constraint optimization problem, for practical application, the T-S fuzzy techniques are adopted to efficiently approximate the nonlinear multi-UAVs system by a set of local linearized networked systems. Thus, the HJI-constraint optimization problem for the H∞ event-triggered robust formation team tracking control can be transformed to a linear matrix inequality(LMI)-constraint optimization problem and can be easily solved by the convex optimization techniques. Finally, a simulation example is given to validate the effectiveness of the proposed event-triggered robust H∞ team formation tracking control for the multi-VTOL-UAV system.

Context-aware data-centric misbehaviour detection scheme for vehicular ad hoc networks using sequential analysis of the temporal and spatial correlation of the consistency between the cooperative awareness messages

Vehicular ad hoc Networks (VANETs) have emerged mainly to improve road safety, traffic efficiency, and passenger comfort. The performance of most VANET applications and services relies on the availability of accurate and up-to-date mobility-information, through so-called Cooperative Awareness Messages (CAMs), shared by neighbouring vehicles. However, sharing false mobility information can disrupt any potential VANET application. As cryptographic techniques used to protect CAMs in VANETs are expensive, complicated, and vulnerable to internal misbehaviour, security lapses are inevitable. Although several misbehaviour detection solutions have been proposed, those solutions assume that the VANET's context is stationary, which does not hold for VANETs in a real scenario, as the vehicle's context changes continuously. The use of static and predefined security thresholds in highly dynamic and harsh environments is the major drawback of those solutions. To address this issue, a context-aware data-centric misbehaviour detection scheme (CA-DC-MDS) is proposed, using sequential analysis of temporal and spatial correlation of the consistency between neighbouring vehicles' mobility information. The static thresholds have been replaced by a dynamic context reference model that is constructed online and updated in a timely fashion using statistical techniques. Firstly, the Kalman filter algorithm is used to track the mobility information received from neighbouring vehicles. Then, the innovation errors of the Kalman filter are utilized to construct a temporal consistency assessment model for each neighbouring vehicle, using a box-and-whisker plot. After that, the Hampel filter is used to construct a spatial consistency assessment model that represents the current context reference. Similarly, plausibility assessment reference models are built online and updated in a timely fashion using the Hampel filter and by utilizing the consistency assessment reference model of neighbouring information. Finally, a message is classified as suspicious if its consistency and plausibility scores deviate significantly from the context reference model. The proposed context-aware scheme achieved a 73% reduction in the false alarm rate while achieving a 37% improvement in the detection rate. This demonstrates the effectiveness of the proposed context-aware scheme compared with the existing static solutions.

Position‐heading quadrotor control using LPV techniques

This work presents a solution to the position-heading control problem of a small quadrotor. The main idea of this study is to exploit the advantages of the linear parameter varying (LPV) control approach together with a feedback linearisation approach for designing a cascade control structure without the need to perform simplifications with respect to the reference dynamic model used in the literature. The use of a LPV representation of the attitude subsystem allows to consider it as independent of the position one, allowing the use of a cascade control structure. For the inner attitude control loop, the proposed quasi-LPV-linear-quadratic regulator (LQR) controller and proportional-integral observer (PIO) are solved in an optimal manner by solving a set of linear matrix inequalities (LMIs). While for the outer position control loop, a feedback linearisation approach is developed before designing the corresponding controller and PIO also minimising the LQR problem by means of LMIs. Furthermore, another outer loop, interchangeable with the position one, such that controls the velocities in the body frame is proposed. This velocities controller is also solved in an optimal manner using a combination of feedback linearisation and LPV techniques. The proposed solutions are applied to an AscTec Hummingbird unmanned aerial vehicle in simulation.

Lateral stability integrated with energy efficiency control for electric vehicles

Abstract A hierarchical controller is designed to enhance the lateral stability of electric vehicles (EVs) with as low dissipation energy as possible in this paper. In particular, a reference dynamic model based on the estimated tire cornering stiffness is established for different driving conditions, the lateral stability control can be transformed into tracking the desired sideslip angle and yaw rate by the reference dynamic model. At the upper-level, the controller is consisted of an integral terminal sliding mode (ITSM) controller and a speed tracking controller. The ITSM controller considering parameter uncertainties is proposed to quickly achieve the lateral stability, the speed tracking is used to stabilize the longitudinal dynamics. At the lower-level, in order to reduce the computational burden of the tire energy consumption, a penalty function with the longitudinal slip ratio is introduced to automatically modulate the weight factor of each wheel torque. Then, an optimal torque control allocation (CA) strategy utilizes the designed penalty function to allocate the control command from the upper-level controller. Simulation results show that the designed controller can guarantee the lateral stability under different driving conditions. Moreover, compared to other CA methods, the tire dissipation energy can be effectively decreased by the proposed CA based on the longitudinal slip ratio.

Computing stability limits for adaptive control laws with high-order actuator dynamics

A challenge in the design of adaptive control laws for uncertain dynamical systems is to achieve system stability and a prescribed level of command following performance in the presence of actuator dynamics. It is well-known that if the actuator dynamics do not have sufficiently high bandwidth, their presence cannot be practically neglected in the design since they limit the achievable stability of adaptive control laws. In this paper, we consider the design of model reference adaptive control laws for uncertain dynamical systems in the presence of high-order actuator dynamics. Specifically, a linear matrix inequalities-based hedging approach is proposed, where this approach modifies the ideal reference model dynamics to allow for correct adaptation that is not affected by the presence of actuator dynamics. The stability of the modified reference model is then computed using linear matrix inequalities, which reveals the fundamental stability interplay between the parameters of the actuator dynamics and the allowable system uncertainties. In addition, we analyze the convergence properties of the modified reference model to the ideal reference model. The presented theoretical results are finally illustrated through a numerical example.

Development of a brake by wire system design for car stability controls

The paper presents the development of a vehicle stability control system that is able to operate in real time, ensuring to enhance vehicle dynamics and safety in all vehicle motion conditions, even at limit of handling. The commercial cars have an Electronic Stability System, ESC, that acts actuating the brakes autonomously to correct the vehicle dynamics at limit of adhesion conditions. In this study it will be shown how the stability control system proposed can operate autonomously and constantly during vehicle motion, thanks to a controller based on a simplified vehicle model and a brake unit that operates in continuous.The control system consists of a high-level control and four Brake-By-Wire actuators. The high-level control is an Linear Quadratic Regulator, LQR, that ensures to stabilize the yaw rate and the side slip angle minimizing the errors between the actual car values and the values given by a steady state dynamic reference model. To reach this aim the LQR gives the values of longitudinal forces that each wheel has to achieve. These values of force are sent by a CAN signal to the Cornering Brake Actuators, CBA, that with their own logic and proximity to the wheels ensure a vary fast actuation, stabilizing the vehicle and providing safety.To validate the control system a series of manoeuvres have been carried out on a case-study test bench, that has been installed on a static driving simulator equipped with a concurrent real-time machine, the complete vehicle network and the full steering system. The control system has been design to be used as a stability system on commercial cars, requiring of common vehicle sensors, ensuring better performances and stability even in driving at limit of adhesion conditions, but also to be installed in an autonomous vehicle being able to act independently from the driver.

Distributed adaptive control and stability verification for linear multiagent systems with heterogeneous actuator dynamics and system uncertainties

ABSTRACTThe contribution of this paper is a control synthesis and stability verification framework for linear time-invariant multiagent systems with heterogeneous actuator dynamics and system uncertainties. In particular, we first propose a distributed adaptive control architecture in a leader-follower setting for this class of high-order multiagent systems. The proposed architecture uses a hedging method, which alters the ideal reference model dynamics of each agent in order to ensure correct adaptation in the presence of heterogeneous actuator dynamics of these agents. We then use Lyapunov stability theory and linear matrix inequalities to analyse the proposed architecture. This analysis reveals a stability condition, where evaluation of this condition with respect to a given graph topology allows stability verification of the controlled multiagent system. From a practical point of view, this condition also shows a fundamental tradeoff between heterogeneous agent actuation capabilities and unknown parameters in agent dynamics. Several illustrative numerical examples are also provided to demonstrate the efficacy of the proposed architecture.