State-space Equations Research Articles

Trajectory tracking control of the pushing ore truck manipulator based on adaptive sliding mode control with interference observer

An improved sliding mode controller was designed to solve the problem of low tracking accuracy caused by various disturbances and errors existing in the hydraulic-driven manipulator for pushing ore truck. The state space equation of the hydraulic system of the pushing ore truck manipulator was modeled and derived, and a sliding mode function was designed. For interference signals, use interference observers for observation. For the unobserved parts, adaptive laws are used for compensation to reduce system chattering, and system’s stability is verified using Lyapunov functions. The simulation results show that, compared with the traditional Sliding mode control and adaptive sliding mode control, the adaptive sliding mode control strategy based on interference observer proposed in this paper can effectively weaken the system chattering, reduce the uncertainty caused by external interference and modeling error, and improve the trajectory tracking accuracy of the pushing ore truck manipulator.

Free vibration analysis of fiber-reinforced composite multilayer cylindrical shells under hydrostatic pressure

With the development and application of composite materials in deepwater submersibles, the influence of high external pressure from deepwater environments on the vibration characteristics of composite pressure-resistant cylindrical shells cannot be ignored. In this paper, the free vibration characteristics of prestressed composite multilayer shells are methodically examined by establishing partial differential equations based on the three-dimensional elasticity theory. To solve these equations, the state-space technique and double Fourier series expansion are employed to transform them into state-space ordinary differential equations. These equations are utilized to analyze vibration problems of simply supported composite multilayer cylindrical shells with arbitrary layered angles. The initial stress equilibrium equation is solved to determine the prestress induced by the hydrostatic pressure. This overcomes the limitation of membrane stress and considers non-uniform distributions of radial and interlaminar prestresses. The proposed theoretical model and solution strategies are validated by comparing with theoretical and experimental results from the existing literature and the finite element method. Additionally, the present investigation reveals that the natural frequencies of thick shells can be calculated more accurately using the prestress derived by the proposed approach, especially subjected to noticeable hydrostatic pressure. Finally, the performed investigations indicate that the circumferential prestressing has a more pronounced effect on the shell's natural frequencies than axial prestressing.

State-Space Equation Model for Motion Analysis of Floating Structures Using System-Identification Methods

State-Space Equation Model for Motion Analysis of Floating Structures Using System-Identification Methods

Modified state space method for long-term behavior of viscoelastic laminated angle-ply plate

This work proposes a modified state space method (SSM) to develop the analytical solution for viscoelastic laminated angle-ply plates subjected to long-term loading situations. Within the analytical model, the plate’s stresses and displacements are governed by orthotropic elasticity theory combined with Boltzmann superposition. The convolution within the governing equation is resolved through the application of Laplace transform. The modified SSM is proposed to provide a general solution for each lamina by extracting the complex variable of the Laplace transform from the state space equation. This modification addresses a limitation of the traditional SSM where the exponential function of the state space matrix is computationally infeasible to calculate. The analytical solution of the laminated angle-ply plate is ultimately derived using the transfer matrix method followed by the inverse Laplace transform. Through comparative analysis, it is observed that the proposed solution exhibits greater accuracy than simplified solutions and higher efficiency compared to the finite element method. In addition, the work explores the bending creep and recovery behaviors of viscoelastic laminated angle-ply plate under various parameters.

Linear Parameter Varying Observer-Based Adaptive Dynamic Surface Sliding Mode Control for PMSM

This paper presents an adaptive dynamic surface sliding mode control technique to address the issue of system parameter changes in permanent magnet synchronous motor (PMSM) position servo systems. The proposed method involves adopting a linear parameter varying (LPV) observer-based parameter identification algorithm and adaptive control technique. Initially, a mathematical model of the PMSM is established, and the system parameters are divided into nominal and perturbation values. This allows for the reconstruction of the system model into a state space equation that incorporates the unknown perturbation parameters. To accurately estimate these unknown parameters, an LPV observer is designed based on the reconstructed model. Additionally, an adaptive dynamic surface sliding mode control technique is explored to achieve the desired tracking performance. Meanwhile, an exponential reaching law is introduced to expedite the dynamic behavior of the system and mitigate chattering. Finally, a suitable Lyapunov function is selected to ensure the overall stability of the system. The simulation results demonstrate the effectiveness of the parameter identification and control algorithm in achieving good identification and tracking control ability for PMSM systems.

An intelligent human-machine interaction-based longitudinal control strategy for autonomous vehicles

In the foreseeable future, the anticipation is that intelligent vehicles will transition to a mode where the intelligent driving system collaborates seamlessly with the human driver. This harmonious integration between the driver and the intelligent control system holds paramount significance for the successful execution of driving tasks, ultimately contributing to the development of more advanced and user-friendly automobiles. A pivotal element in advancing from assisted to autonomous driving lies in the establishment of a human-machine co-driving mode. This research delineates a longitudinal control strategy tailored for intelligent vehicles featuring human-machine interaction. The approach involves the creation of a personalized safe distance model for car-following by collecting driver characteristic parameters. Focused on the car-following methodology, this study formulates the kinematics state space equation, performance index function, and constraint conditions governing car-following dynamics. Subsequently, a car-following control strategy is devised based on model predictive control (MPC), which is addressed through rolling optimization techniques. Building upon this foundation, a human-machine driving control strategy is proposed to dynamically allocate driving authorities in real-time. This strategy takes into account speed and vehicle distance risk as two-dimensional inputs, employing a cooperative driving control strategy within the dual-drive dual-control system. The proposed method was validated in a simulated environment.

Networked Evolutionary Game-Based Demand Response via Feedback Controls

In this paper, the demand response considering interactive decision making between residential users and utility companies is modelled and controlled using networked evolutionary game (NEG) theory. The NEG is achieved via a widely used mathematical tool, namely the semi-tensor product (STP) of matrices, through which, feedback controls can be implemented to dynamically regulate the game-based networks. Firstly, the dynamic interactions between utility companies who provide various energy consumption packs and residential users who can intelligently choose preferable packs are modelled in the state-space form, in which both sides are consistently pursuing their maximum payoffs. Then, a quantitive analysis of such system’s equilibria is conducted using rigorous mathematical derivations, followed by the design of a profile feedback controller when the existing equilibria are not satisfactory towards the required energy consumption. Finally, an illustrative example is demonstrated, where the dynamic gaming between utility companies and users is illustrated and the effectiveness of the proposed feedback control is validated. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper addresses a very practical engineering problem, which is the demand response in the modern smart grid. Different from general optimization approaches in the existing works, the method proposed by this paper improves the demand response via feedback control of networked systems, which is based on the rigorous matrix approaches via state space equations. In addition, the work in this paper considers very practical factors in actual engineering (i.e., users with different action choices and decision logics being all together), which also provides much value to practitioners than the relevant works with similar theoretical approaches. The method proposed in this paper provides an effective regulation of the demand response in practice and can be flexibly adjusted according to actual situations.

Joint Estimation of SOC and SOH for Lithium-Ion Batteries Based on Dual Adaptive Central Difference H-Infinity Filter

The accurate estimation of the state-of-charge (SOC) and state-of-health (SOH) of lithium-ion batteries is crucial for the safe and reliable operation of battery systems. In order to overcome the practical problems of low accuracy, slow convergence and insufficient robustness in the existing joint estimation algorithms of SOC and SOH, a Dual Adaptive Central Difference H-Infinity Filter algorithm is proposed. Firstly, the Forgetting Factor Recursive Least Squares (FFRLS) algorithm is employed for parameter identification, and an inner loop with multiple updates of the parameter estimation vector is added to improve the accuracy of parameter identification. Secondly, the capacity is selected as the characterization of SOH, and the open circuit voltage and capacity are used as the state variables for capacity estimation to improve its convergence speed. Meanwhile, considering the interaction between SOC and SOH, the state space equations of SOC and SOH estimation are established. Moreover, the proposed algorithm introduces a robust discrete H-infinity filter equation to improve the measurement update on the basis of the central differential Kalman filter with good accuracy, and combines the Sage–Husa adaptive filter to achieve the joint estimation of SOC and SOH. Finally, under Urban Dynamometer Driving Schedule (UDDS) and Highway Fuel Economy Test (HWFET) conditions, the SOC estimation errors are 0.5% and 0.63%, and the SOH maximum estimation errors are 0.73% and 0.86%, indicating that the proposed algorithm has higher accuracy compared to the traditional algorithm. The experimental results at different initial values of capacity and SOC demonstrate that the proposed algorithm showcases enhanced convergence speed and robustness.

Truncated predictive tracking control design for semi-Markovian jump systems with time-varying input delays

A state tracking control problem for a class of semi-Markovian jump systems (SMJSs) with input delay and disturbances is addressed in this study. In particular, an improved-equivalent-input-disturbance estimator approach (IEIDEA)-based truncated predictive controller is designed to synchronously compensate the effect of unknown external disturbances and time-varying delay. Specifically, by making use of IEIDEA, the unknown disturbances are estimated with high precision and incorporated into the control input channel, which eases the way to achieve the desired tracking performances. Specifically, the state predictor satisfies the delay-free state-space equation and is used in controller design along with prediction. In accordance with linear matrix inequality framework and Lyapunov stability theory, a set of adequate conditions are established to guarantee the state tracking performance of SMJSs. Finally, the numerical examples with simulation results are provided to validate the efficacy and practicability of the established control technique.

Frequency Criterion for the Existence of Sliding Processes in Control Systems with an Arbitrary Variable Structure

The article proposes a criterion for the existence of sliding processes according to the frequency characteristics of the control device and the control object. It is shown that the conditions for the existence of slip are equivalent to the conditions for the absolute stability of equivalent circuits of the original systems with a variable structure. This approach is proposed by the authors as an alternative to the method of phase trajectories and state space equations used by other researchers. Frequency criteria make it possible to formulate several practical engineering provisions that are very important for the implementation of this control method in real electric drives. The main conclusions are confirmed by simulation of both processes in systems with a variable structure and in equivalent circuits.

Separable Gaussian neural networks for high-dimensional nonlinear stochastic systems

This paper extends the recently developed method of separable Gaussian neural networks (SGNN) to obtain solutions of the Fokker–Planck–Kolmogorov (FPK) equation in high-dimensional state space. Several challenges when extending SGNN to high-dimensional state space are addressed including proper definition of domain for placing Gaussian neurons and region for data sampling, and numerical integration issue of evaluating marginal probability density functions. Three benchmark nonlinear dynamic systems with increasing complexity and dimension are examined with the SGNN method. In particular, the steady-state probability density of the response is obtained with the SGNN method and compared with the results of extensive Monte Carlo simulations. It should be pointed out that some solutions of high-dimensional FPK equations for nonlinear dynamic systems would be very difficult to obtain without SGNN.

Dynamic safety control of offshore wind turbine based on model predictive control

Offshore wind power is a clean energy source with excellent development prospects that are conducive to realising China's goal of carbon neutrality. However, offshore wind turbines (WTs) are prone to failure and damage owing to their long-term operation in marine environments with high humidity, high wind speeds, and frequent extreme weather. To ensure the safe operation of offshore WTs, a modified dynamic model predictive control (MPC) method was proposed in this study. First, a dynamic model of an offshore WT was established and its nonlinear state-space equations were obtained. These state-space equations were subsequently linearised and discretised, then fast trajectory tracking of the state variables was performed according to the conventional MPC principle. Finally, a control strategy was designed to realise the safe operational control of offshore WT using the safety index as a constraint condition in the MPC. Simulation results confirmed that the proposed MPC strategy using the safety index-based constraint exhibited superior tracking of the set trajectory and achieved the minimum energy loss under varying wind speeds.

An accelerated modelling method of full-bridge modular multilevel converter considering dead-time

To avoid short-circuits of the same side switching of power converters, the dead time is of significance in the pulse trigger gating signal for full bridge modular multilevel converter (FB-MMC). However, the previous equivalent models use the binary resistance switching model to equivalent the switching state which is impossible to simulate the switching with dead time, and the detailed model (DM) with higher levels is time-consuming and inefficient in electromagnetic transient (EMT) simulation. To address this problem, based on the state-space averaging method, a speed-up average value model (AVM) of FB-MMC considering dead time is proposed. Firstly, the working state of FB-MMC is obtained through analysing the switching states with dead time and is classified into three cases according to the capacitor. Secondly, derived from state-space equation, the three cases are integrated into a unified model by introducing the duty cycle, and then the equivalent controlled source is used as the interface circuit between the external grid and capacitor. Finally, a 49-level two-terminal MMC-HVDC system consisting of FB-MMC is constructed in PSCAD / EMTDC simulations, showing that the proposed AVM compared with DM has high accuracy and operation efficiency.

Internal Modal Resonance Analysis for Full Converter-Based Wind Generation Using Analytical Inertia Model

Full converter-based wind generation (FCWG) has become a prevailing choice in new wind farms. It is usually regarded that low short circuit ratio (SCR) or weak grid is a key condition to induce oscillations associated with wind farms. However, we have recently discovered a rare phenomenon that even in a strong grid with a large SCR, the internal modal resonance of FCWG can still lead to oscillations and threaten the converter-driven stability. To determine the internal modal resonance in FCWG, a novel analytical inertia model (AIM) is derived to elaborate all oscillation modes of FCWG (FOMs) for the first time. The derived model reviews the complex relations of all FOMs in a formulaic manner, which not only provides guidance on parameter resetting, but also illuminates how FOMs interact with each other. On this basis, an equivalent transfer function is integrated into the state space equation to characterize the interaction effect, and a universal torque model is proposed to yield insights into the mechanism of internal modal resonance owing to the variation of operating conditions. Furthermore, the effectiveness of AIM is substantiated as well as the analysis method, and the unusual event of internal modal resonance is also demonstrated.

Research on Super-Twisting Sliding Mode Voltage Regulation Control of Electric Spring

The traditional control of electric spring (ES) is too complex and lack of robustness, as well as the chattering phenomenon and control accuracy of traditional sliding mode control, a second-order terminal sliding mode control based on super twisting algorithm is proposed. In this paper, the phase plane method is used to establish the mathematical model of ES, solve the state space equation, and regard the AC power supply as a simplified error analysis. Then a second-order sliding mode controller is proposed. The controller parameters are solved to obtain the second-order sliding mode control rate, and the stability is verified. Finally, three groups of comparative simulation experiments were set up by Matlab/Simulink, and the effectiveness of the model was verified by considering the voltage mutation caused by the change of power supply and circuit parameters. Compared with the traditional control method, the proposed control strategy not only ensures the voltage stability, but also improves the control accuracy and the performance of suppressing sliding mode chattering, and has better dynamic response ability.

Active vibration control of fluid-conveying pipelines: Theoretical and experimental studies

For the fluid-conveying pipeline with macro-fiber composites (MFC), relevant dynamic modeling and experimental testing studies are rarely found in previous papers. Therefore, this paper has carried out related research work. Firstly, considering the fluid-structure interaction and piezoelectric effects, a semi-analytical modeling method for the fluid-conveying pipeline with MFC attaching to any position is proposed. A new Runge-Kutta-Gear (RKG) time-domain solution method is presented for solving state-space equations with the characteristics of rigid equations, and the design methods of Linear-Quadratic Regulator (LQR) controller and Proportional-Integral-Derivative (PID) controller are introduced, respectively. Secondly, an experimental system for active control and vibration test is built, and the dynamic model and control method are verified by experiments and simulations. Finally, the influence of relevant control parameters in the controller on the active control effect is discussed, and the influence law of fluid parameters such as fluid velocity and fluid pressure on the active control is also clarified. The novelty of this work is that the active vibration control and solution methods for the fluid-conveying pipeline with MFC are proposed, and the feasibility of MFC for pipeline vibration suppression is verified by experiments, which provides a new technical idea for the vibration reduction design of the fluid-conveying pipeline.

An Integrated Model Based Prediction of Machining Accuracy for Milling Machine

The accuracy of machining can be predicted during the design process of CNC machine tools, while the prediction accuracy depends on the prediction model. However, when establishing the prediction model, the coupling effect among the machine tool’s different components is always ignored for modeling efficiency, so this will lead to its reliability cannot be guaranteed. To address this problem, the model reduction theory and the lumped parameter method are used in this study to set the state-space equations of the essential structural parts. Moreover, the electro-mechanical coupling parameter equation of the servo system is transformed into a state-space equation. Then the state-space equations of the components and the servo system are coupled to establish the machine tool dynamic model. Furthermore, a theoretical model of instantaneous undeformed chip thickness is found, and according to the linear relationship between the micro-cutting force and the instantaneous undeformed chip thickness, the instantaneous cutting force model of the cylindrical milling cutter is established. Based on these, the integrated model, which considers the mechanical structure, control system and cutting force, is obtained and further used in Simulink to build the machining accuracy prediction platform, as well as the accuracy of the integrated prediction model is verified. Moreover, the prediction model established by the integrated modeling method can effectively simulate the actual machining conditions of the machine tool, and the superiority of prediction is confirmed by comparing the simulated and measured results in peripheral milling applications. The results show the error in the system response efficiency is 14.8%, while the error in position accuracy and delay characteristics is less than 10%, the error between the predicted size of the prediction model and the actual size is within 28 μm, a minimum prediction error is 7 μm.

Optimized designed [formula omitted]-shape impedance in voltage type [formula omitted]-Source inverter based on average modeling

The Z-source inverter is a desirable power converter topology for voltage source and current source converter applications, which is an exciting alternative for replacing the popular conventional type.This paper presents a novel method for designing voltage-type Z-Source inverters that are innovated based on good voltage source and DC-Link prerequisites such as its current and voltage value. This method is caused to reduce the size of the capacitor and inductor as well as the total cost of the converter, which is applicable in hybrid electric vehicle development. Z-Source inverter‘s output based on its input variables and effects has been investigated to propose to optimize the design/control method. State space equations are obtained, and its model is analyzed to illustrate how the undesired effects of these changes can be omitted or compensated. It has been used to optimize the designed parameters. A prototype experimental Z-Source inverter with a rated power of 500W and switching frequency of 20kHz is developed to demonstrate the validity of the design process. The Simulation and experimental results verify that the proposed method successfully optimizes the x-shape Impedance design.

Generalized sequential state equation method for moving subsystem-induced structural parametric resonance

Parametric excitation is a unique type of excitation that arises from the time-varying parameters of a dynamical system, typically induced by the periodic movements of the system components. However, the structure-moving subsystems problem creates a new type of parametric excitation where the subsystems do not have exact periodic movements. Under the circumstances, dimension of the mathematical model of such a system exhibits time dependency, which prohibits the employment of conventional analytical methods to predict its stability. In this paper, we propose a novel Generalized Sequential State Equation Method that provides a distinct solution framework for analysis of the subsystem-induced parametric resonance. With the time-domain system partition and state mapping, the proposed method reconfigures the coupled system with a sequence of state space equations and solves them chronologically. The proposed method relaxes the single-subsystem-assumption in its original form and applies to a general scenario where the subsystems travel with arbitrary characteristic period. With the proposed method, occurrences of the subsystem-induced parametric resonance are precisely predicted via a set of analytical stability criteria and the steady state response is determined in an exact analytical form.

Thermal analysis for laminated plates with arbitrary supports under non-uniform temperature boundary conditions

This paper aims to investigate thermal behaviors of composite laminated plates with different supports under non-uniform temperature boundary conditions. The thermo-elastic solutions of temperature, displacements, and stresses for the laminated plate with arbitrary layer numbers and thickness are obtained based on the three-dimensional theory of thermoelasticity. By applying the Fourier law of heat conduction and the thermoelastic equations, the state-space equations are established by employing the temperature, heat flux, displacements, and stresses as state variables without the hypothesis of displacement form. The differential quadrature method is introduced to discretize the in-plane state variables. On the basis of the continuities of state variables at the interfaces in the laminated plate, the relationships of temperature, heat flux, displacements, and stresses between the top and bottom surfaces can be derived. By simultaneously considering temperature and mechanical boundary conditions applied to the surfaces of the laminated plate, the initial state variables for temperature, displacements, and stresses can be determined uniquely. The errors in the temperature, displacements and stresses resulting from the differential quadrature method can be eliminated by incrementally augmenting the number of sampling points in the convergence study. The accuracy of the present method is thoroughly verified by comparing the current results with both the finite element solutions and the findings reported in previous literature. Finally, the influences of surface temperature, length-to-thickness ratios, material properties, layer numbers, and support types for the distributions of the temperature field, displacements, and stresses in the laminated plate are discussed in detail.