State-space Mathematical Model Research Articles

Distributed joint parameter and state estimation algorithm for large‐scale interconnected systems

SummaryThis paper proposes a distributed joint parameter and state variables estimation algorithm for large‐scale state‐space interconnected systems. In this distributed estimation scheme, each interconnected sub‐system is described by a linear discrete‐time state space mathematical model. Each sub‐system is supposed to be controlled by an intelligent controller that can communicate with its interconnected neighbors and exchange information, such as state variables. The proposed approach comprises two recursive estimation algorithms, a parameter estimation algorithm considering the state space model and a distributed Kalman filter for state variables estimation. It is a fully distributed cooperative approach that allows to reduce complexity and saves computational and communication resources. Theoretical analysis and numerical examples are provided to prove the feasibility and effectiveness of this joint estimation algorithm.

State-Spatial Viewpoint of Stress in Thermally Postbuckled and Nonlinearly Bent FG Saturated Poroelastic Circular Plates

A dimensionless discrete state-space mathematical model is proposed for stress analysis of an axially-symmetric saturated poroelastic circular plate being loaded by temperature rise of one of the flat faces. Computation of stress by means of this model is free from a need for differentiation. The curves of thermal postbuckling, thermal nonlinear bending, radial stress, circumferential stress and resultant radial force have been achieved by means of six state-space variables and differential quadrature procedure. The effects of loading temperature, boundary conditions, porosity, pore distribution and fluid pore pressure on the thermal post buckling and nonlinear bending phenomena have been investigated. The critical postbuckling thermal load has been determined by means of a numerical algorithm that does not converge to trivial solution because it starts from a relatively great numerical thermal load. Contrary to the governing equation in usual form, the governing equations in state space together with the state equations equalize the number of the governing assembled difference equations and that of the unknowns, and eventually do not require to apply the so-called auxiliary extra boundary conditions at the nodes adjacent to the boundary nodes. As another advantage, in state-spatial viewpoint, there is not any necessity for computing the coefficients of derivatives with order higher than unity.

Design a Robust Proportional-Derivative Gain-Scheduling Control for a Magnetic Levitation System

This study focuses on the design of a robust PD gain-scheduling controller (PD-GS-C) for an unstable SISO (single-input, single-output) magnetic levitation system with two electromagnets (MLS2EM). Magnetic levitation systems offer various advantages, including friction-free, reliable, fast, and cost-effective operations. However, due to their unstable and highly nonlinear nature, these systems require sophisticated feedback control techniques to ensure optimal performance and functionality. To address these challenges, in this study, we derive the nonlinear state-space mathematical model of the MLS2EM and linearize it around five different operating points. The PD-GS-C controller aims to stabilize the system and improve steady-state control error. The strategy for obtaining the PD controller gains involves a parameter space technique, which specifies performance requirements. This technique results in ranges of proportional (KP) and derivative (KD) gains that are used by the PD-GS-C structure. To optimize the controller’s performance further, we utilize the big bang–big crunch optimization technique (BB-BC) to determine the optimal PD gains within the specified ranges. The optimization process focuses on achieving optimal performance in terms of a specific performance index function. This function quantifies the system’s time-domain step response criteria, which include minimizing overshoot percentage, settling time, and rising time. The index function is inversely proportional to the desired performance criteria, meaning that the goal is to maximize the index function to optimize the system’s performance. To validate the effectiveness and viability of the proposed strategy, we conducts MATLAB simulations and real-time experiments. The simulations and experimental findings serve to demonstrate the controller’s performance and verify its capabilities in stabilizing the MLS2EM magnetic levitation system.

Synchronization control of blanket remote maintenance robot based on MPC-CCC algorithm

AbstractThis paper studies the synchronization control of the blanket remote maintenance robot (BRMR) of the China fusion engineering test reactor (CFETR). First, the general state space mathematical model of BRMR was established by using a physical-based method. Second, based on the receding horizon optimization of model predictive control (MPC) and cross-coupling error reduction in cross-coupling control (CCC), the innovative MPC-CCC controller was proposed to realize the single-system and multisystem error convergence and high accuracy transportation of blanket through the high accuracy synchronization control of BRMR. Third, to verify the control effectiveness of the MPC-CCC controller, two types of simulations and experiments were implied compared with the original proportional-integral (PI) controller in Mover. Results showed that simulation and experiments were highly consistent. It is found that the use of an MPC-CCC controller can result in up to a 70% reduction in displacement error and up to a 59% reduction in synchronization error compared to the PI controller. And the accuracy of the MPC-CCC controller satisfies the real requirement of the maintenance process of the blanket. This work provides the theoretical basis and practical experience for the highly stable, safe, and efficient maintenance of blankets in the future.

Distributed parameter identification algorithm for large‐scale interconnected systems

AbstractThis paper deals with parameter estimation problem of large‐scale systems. A recursive distributed parameter estimation algorithm, based on the minimization of the prediction estimation error method, is developed. Specifically, the class of large‐scale systems that are composed of several interconnected sub‐systems is considered. Each interconnected sub‐system is modelled by a linear discrete‐time state space mathematical model with unknown parameters. The convergence analysis is then achieved using the Lyapunov approach. The theoretical analysis and simulation results prove the effectiveness of the proposed algorithm.

Robust Subsynchronous Damping Control of PMSG-Based Wind Farm

This paper provides an H∞ robust control strategy for a permanent magnet synchronous generator (PMSG)-based wind farm to realize subsynchronous resonance suppression (SSR) subject to uncertain system distortions and parameter perturbation. Firstly, an eighth-order state space mathematical model of a PMSG-based wind farm is established, including the grid-side converter (GSC), GSC controller, and phase-locked loop (PLL) model. Secondly, the SSR characteristics of a PMSG-based wind farm are analyzed through eigenvalue analysis. Thirdly, a robust subsynchronous damping controller is designed based on eigenvalue analysis of SSR. Finally, the designed robust subsynchronous damping controller is validated with case studies of wind farms. The results show that the controller can increase the stability of PMSG-based wind farm systems and restrain SSR.

Discrete-Time Model Predictive Controller Using Laguerre Functions for Active Flutter Suppression of a 2D wing with a Flap

In this paper, a discrete-time model predictive controller using Laguerre orthonormal function-based (LMPC) for active flutter suppression of a two-dimensional wing with a flap is presented. In this work, a linear mathematical state-space model for the pitch, plunge, and flap degrees of freedom under unsteady aerodynamics is derived and used to determine the linear flutter velocity and frequency of the parameters of a selected experimental wing. To verify the model, the open-loop simulation results are compared to an experimental study using the same wing from the literature. The state-space system is then discretized and LMPC with a Kalman filter is designed and tuned using the MATLAB® simulation environment at a selected speed in the linear flutter region. The predictive control advantage of dealing with input constraints in a systematic manner is explored through a quantitative analysis of the response of both constrained and unconstrained LMPC controllers. The results indicate that theoretically both cases can give excellent performance. However, the input trajectory generated by the unconstrained LMPC is very aggressive in a way that it is considered impractical when compared to the physical limits of an experimental actuator from the literature. The potential of LMPC to achieve a reasonable performance at a significantly lower computational cost compared to the classical model predictive controller (MPC) is investigated by measuring the time required by the same computer to compute the control trajectory for both controllers. The data suggest that LMPC requires remarkably low computational power, which makes it an excellent choice for fast aeroelastic applications.

Design and Realization of Intelligent Aero-engine DDPG Controller

As the artificial intelligence technology advances, intellectualization has become an important development trend for the future aero-engine industry. The intelligent aero-engine will bring a new round of technology revolution in aviation industry. Since an aero-engine is a complex system with strong nonlinearity and coupling, it is difficult to achieve the optimal control performance with traditional PI control. Therefore, the DDPG (Deep Deterministic Policy Gradient, DDPG) algorithm belonging to the family of Deep Reinforcement Learning is hereby proposed for designing aero-engine controller. Based on the non-linear polynomial state-space mathematical model of JT9D turbofan engine, the intelligent DDPG controller is designed and then compared with the performance of PI controller. The proposed controller can achieve the optimal control effect for aero-engine through the training the neural network. The simulation results demonstrates that compared with PI control, the control method proposed in this paper achieves superior control performance in response speed, overshoot and anti-interference ability.

Dynamic compensation control strategy of DC bus voltage based on residual generator.

Aiming at the problem of bus voltage control in DC microgrid, a dynamic compensation control strategy based on a residual generator is designed to complete the voltage compensation of DC-DC converter. Firstly, based on the DC microgrid system architecture, the bus voltage fluctuations are analyzed theoretically, and then the DC-DC converter state-space mathematical models of the DC microgrid system are established to obtain the input-output relationship of the control system. Based on the theory of double coprime decomposition and Youla parameterization stable controller, the proposed control architecture based on the residual generator is obtained, and the output value generated by the current disturbance is compensated in reverse by applying model matching theory. The voltage loop compensation controller Q(s) is obtained by the linear matrix inequality method (LMI), and the current loop compensation controller H(s) is designed according to the dynamic structure diagram of the DC-DC converter. Hardware-in-the-loop simulation (HILS) results show that the architecture can improve the dynamic performance of the DC-DC converter without changing the original system structure parameters, and suppress the DC bus voltage fluctuations caused by load switching, power fluctuations, and AC-side load imbalances, and enhance the robustness of the system.

Valve Deadzone/Backlash Compensation for Lifting Motion Control of Hydraulic Manipulators

In this paper, a novel nonlinear model and high-precision lifting motion control method of a hydraulic manipulator driven by a proportional valve are presented, with consideration of severe system nonlinearities, various uncertainties as well as valve backlash/deadzone input nonlinearities. To accomplish this mission, based on the independent valve orifice throttling process, a new comprehensive pressure-flow model is proposed to uniformly indicate both the backlash and deadzone effects on the flow characteristics. Furthermore, in the manipulator lifting dynamics, considering mechanism nonlinearity and utilizing a smooth LuGre friction model to describe the friction dynamics, a nonlinear state-space mathematical model of hydraulic manipulation system is then established. To suppress the adverse effects of severe nonlinearities and uncertainties in the system, a high precision adaptive robust control method is proposed via backstepping, in which a projection-type adaptive law in combination with a robust feedback term is conducted to attenuate various uncertainties and disturbances. Lyapunov stability analysis demonstrates that the proposed control scheme can acquire transient and steady-state close-loop stability, and the excellent tracking performance of the designed control law is verified by comparative simulation results.

Modelling and Simulation of Intelligent Master Controller Model for Hybridized Power Pool Deployment

Every conceptual framework requires several developmental stages such as prototyping, preproduction and production stages. This paper considers prototype developmental stage which entails design, modelling and simulation for the conceptual system to determine suitable parameters and specifications before the production task is initiation. The inability to represent the conceptual control system with mathematical equivalence would hamper on the system operational efficiency, stability, controllability and observability; would not be guaranteed. This paper focuses on the modelling and simulation of intelligent master controller for hybridized power pool deployment. This is achieved using state space mathematical model, MATLAB/Simulink and proteus software. The state space model provides the mathematical equation for the system stability, controllability and observability criteria from the system transfer function. The MATLAB/Simulink software provides response trends and the Proteus software provides the virtual implementation platform for concept validation with its code written in Arduino (IDE). The system was demonstrated through simulation and the virtual results showed that the system capability in fostering intelligent control commands in the hybridized power pool scenario. The system stability was determined using Root locus, Nyquist and Routh Hurwitz criteria. Subsequent research efforts are being made towards implementing the design optimizable on the hardware using the design specifications.

Research on fuzzy symmetrical control of valve controlled asymmetric hydraulic cylinder system

In order to solve the problems, such as the asymmetry, complex control methods, inconsistent dynamic characteristics for positive/negative directions and poor stability for asymmetric control system, in this paper, a system symmetric control method based on state feedback was brought out and the state space mathematical model was derived for valve controlled hydraulic cylinder system. With the symmetric control method of the state feedback, the valve controlled asymmetric hydraulic system can be converted into state space symmetric system, then the unified control method can be used for positive and negative directions after conversion, finally the feedback link of the system was educed. Through simulation, the accuracy of the model and the effectiveness of the control method were verified. Through experiments, the input and output characteristics and load response characteristics of the system before and after conversion were compared. It was concluded that the system had symmetric characteristics for inputs and outputs, and better load response characteristics after conversion. This study can be a base for the application of symmetric control theory to large asymmetric hydraulic systems and was of great help to realize symmetric control of large asymmetric hydraulic systems.

Linear System Identification and Vibration Control of End-Effector for Industrial Robots

This paper presents the discrete state space mathematical model of the end-effector in industrial robots and designs the linear-quadratic-Gaussian controller, called LQG controller for short, to solve the low frequency vibration problem. Though simplifying the end-effector as the cantilever beam, this paper uses the subspace identification method to determine the output dynamic response data and establishes the state space model. Experimentally comparing the influences of different input excitation signals, Chirp sequences from 0 Hz to 100 Hz are used as the final estimation signal and the excitation signal. The LQG controller is designed and simulated to achieve the low frequency vibration suppression of the structure. The results show that the suppression system can effectively suppress the fundamental natural frequency and lower vibration of end-effector. The vibration suppression percentage is 95%, and the vibration amplitude is successfully reduced from ±20 μm to ±1 μm. The present work provides an effective method to suppress the low frequency vibration of the end-effector for industrial robots.

A nonlinear time-delay realization for gastroparesis in patients with diabetes

The realization problem is fundamental in control systems theory and is well understood for linear systems. The situation is quite different for nonlinear systems with or without time delays. New results are given herein either as an abstract characterization of the class of delay–free nonlinear systems which are known to admit a realization, or by characterizing the existence of a realization for a wider class of retarded type or neutral type time delay nonlinear systems. The problem is motivated by the very practical modelling and realization problem of diabetes with or without gastroparesis. Up to 4% to 12% patients with diabetes are affected by the so-called gastroparesis which delays the digestion process. Several concurrent state space mathematical models do exist for diabetes and require a re-evaluation based on physiologic facts. These are reviewed herein to derive a (minimal) realization.

A New Parametric Estimation Algorithm for Large-Scale Systems Described by State-Space Mathematical Models

This paper is concerned with the parametric estimation problem for large-scale systems composed of several interconnected systems, which are described by linear discrete-time state-space mathematical models with unknown parameters. A new recursive parametric estimation algorithm with a particular adaptive gain is proposed for estimating the interconnected system parameters. The stability analysis of the developed parametric estimation scheme is treated by using the Lyapunov method. The proposed recursive parametric estimation algorithm is applied to estimate the parameters of a large-scale systems composed of three interconnected systems. The obtained numerical simulation results show the good performance of this algorithm.

Analysis and implementation of a step–up power converter with input current ripple cancelation

SummaryThis paper proposes a power electronics converter capable of canceling the input current ripple at preselected duty cycle. The proposed converter is an extended topology of a buck–boost converter aided by a boost‐type converter that improves the quality of the current drawn from the direct current source. The voltage gain of the proposed converter is increased as well, with a minimum of extra component added to the original buck–boost power converter. These features make the proposed converter ideal for low voltage generation sources, such as photovoltaic panel and fuel cell applications. Along this paper, the state space mathematical model is developed to provide the key design guidelines. The theoretical analysis is validated through computer simulation and hardware prototyping.

Improvement of control precision for ship movement using a multidimensional controller

ABSTRACTThis paper presents the influence of a first stage inertial element on the operation of a state space controller for a third dimension object. First chapter presents a brief introduction to linear matrix inequalities as one of the methods of controller analysis and synthesis, with examples, and helps to places the below paper in this wide field of science. Chapter two presents the controlled object, which is a model of a very large crude carrier (VLCC) ship, called Blue Lady, along with its mathematical state space model. Chapter three shows state space controller design using numerical methods of linear equalities optimization, where the given values are u longitudinal, v lateral and r rotational velocities. Presented there is also the implementation method of an inertial element to a multidimensional object for space state controller synthesis. Chapter four shows computer simulation results and focuses on showing influence of the proposed design on control error of the multidimensional closed loop system. Finally, chapter five concludes and comments simulation results and shows possible direction of future studies.

Attitude algorithm and initial alignment method for SINS applied in short-range aircraft

This paper presents an attitude solution algorithm based on the Micro-Electro-Mechanical System and quaternion method. We completed the numerical calculation and engineering practice by adopting fourth-order Runge–Kutta algorithm in the digital signal processor. The state space mathematical model of initial alignment in static base was established, and the initial alignment method based on Kalman filter was proposed. Based on the hardware in the loop simulation platform, the short-range flight simulation test and the actual flight test were carried out. The results show that the error of pitch, yaw and roll angle is fast convergent, and the fitting rate between flight simulation and flight test is more than 85%.

Modeling and Analysis of a Novel Boost Derived Multilevel Hybrid Converter

Multilevel inverters (MLI) offer high power capability connected with lower output harmonics and lower conduction and switching losses. Conventional cascaded H-bridge (CHB) MLI produces AC output which can be employed for a single load. But for smart residential nanogrid applications, dual load (AC and DC) is required concurrently. This paper has introduced a new topology of boost derived multilevel hybrid converter (BDMHC) which produces multilevel AC and DC output simultaneously. Thus the converter required the lesser number of switches to supply both AC and DC load. This proposed topology of BDMHC is constituted one H-bridge seven-level symmetrical MLI with three separate boost converters. State space mathematical model has been developed for the proposed converter and validated with simulated circuit using MATLAB/Simulink.

Tracking control of electro-hydraulic servo multi-closed-chain mechanisms with the use of an approximate nonlinear internal model

This paper studied the trajectory-tracking problem of a hydraulic servo multi-closed-chain mechanism. The nonaffine nonlinear characteristic of the electro-hydraulic actuator and its time-varying uncertainty load resulting from the multi-closed-chain mechanism was taken into consideration in the proposed novel nonlinear control algorithm, that is, the approximate internal model control (AIMC) integrated with a position feedback control in cascade control design. This algorithm improves the trajectory-tracking performance of the hydraulic servomechanism (HSM). To reduce the difficulty in directly utilizing the AIMC for the HSM position trajectory, the complex electro-hydraulic mechanical system was divided into two subsystems: nonaffine nonlinear, and linear. The AIMC controller was designed for the nonaffine nonlinear subsystem to realize velocity trajectory tracking control, whereas a position feedback control was derived for the linear subsystem. The position trajectory tracking control was achieved by congruently combining the AIMC, and the position feedback control based on a recursive design idea. In addition, a complete state-space mathematical model for the HSM was developed and illustrated through simulations and experiments. Based on the proposed approach and the AIMC, the desired position and velocity trajectory tracking was examined on a hydraulic forging manipulator. The stability of the proposed method was analytically derived. Results of the simulations and experiments performed with the hydraulic manipulator demonstrated the effectiveness of the proposed approach.