Steady-state Tracking Error Research Articles

A Study on Accelerating Average Consensus Algorithms Using Delayed Feedback

This article studies accelerating a Laplacian-based dynamic average consensus algorithm by splitting the conventional delay-free disagreement feedback into a weighted summation of current and outdated terms. When determining the weighted sum, there is a range of time delay that results in a higher convergence rate for the algorithm. For such weights, using the Lambert <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$W$</tex-math></inline-formula> function, we obtain the rate-increasing range of the time delay, obtain the maximum reachable rate, and characterize the value of the corresponding maximizer delay. We also study the effect of using the outdated feedback on the control effort of the agents. We show that only for some specific affine combination of the immediate and outdated feedback, the control effort of the agents does not go beyond that of the delay-free algorithm. In addition, we demonstrate that using outdated feedback does not increase the steady-state tracking error of the average consensus algorithm. Finally, we determine the optimum combination of the current and the outdated feedback weights to achieve the maximum increase in the rate of convergence without increasing the control effort of the agents. We demonstrate our results through a numerical example.

Zero Steady-state Error Tracking Control for Ball and Plate System Based on Principle of Internal Model

Zero Steady-state Error Tracking Control for Ball and Plate System Based on Principle of Internal Model

Reinforcement Learning-Based Adaptive Position Control Scheme for Uncertain Robotic Manipulators with Constrained Angular Position and Angular Velocity

Aiming at robotic manipulators subject to system uncertainty and external disturbance, this paper presents a novel adaptive control scheme that uses the time delay estimation (TED) technique and reinforcement learning (RL) technique to achieve a good tracking performance for each joint of a manipulator. Compared to conventional controllers, the proposed control scheme can not only handle the system parametric uncertainty and external disturbance but also guarantee both the angular positions and angular velocities of each joint without exceeding their preset constraints. Moreover, it has been proved by using Lyapunov theory that the tracking errors are uniformly ultimately bounded (UUB) with a small bound related to the parameters of the controller. Additionally, an innovative RL-based auxiliary term in the proposed controller further minimizes the steady state tracking errors, and thereby the tracking accuracy is not compromised by the lack of asymptotic convergence of tracking errors. Finally, the simulation results validate the effectiveness of the proposed control scheme.

Fault-Tolerant Current Control of Six-Phase Permanent Magnet Motor With Multifrequency Quasi-Proportional-Resonant Control and Feedforward Compensation for Aerospace Drives

To improve the current tracking performance, this article proposes a new fault-tolerant current control for the six-phase fault-tolerant permanent magnet synchronous motor (FTPMSM) system with multifrequency quasi-proportional-resonant (QPR) control and back electromotive force (EMF) feedforward compensation, which can track the time-varying sinusoidal and nonsinusoidal reference currents in the stationary reference frame (SRF) under normal and fault conditions. First, the multifrequency QPR current controller with shunt topology is proposed to track the time-varying reference current in SRF, which can guarantee the current control performance regardless of the motor speed variation and the load torque change. Second, the optimized feedforward compensation method for the back EMF is proposed to further reduce the steady-state current tracking error, which takes the time delay of the digital implementation into consideration. Finally, the effectiveness of the proposed approach is verified on a 3 kW six-phase FTPMSM platform. The resulting six-phase FTPMSM system with the proposed current control has great current tracking performance, strong robustness to various external/internal disturbance, as well as low computational burden, which can guarantee the multiphase FTPMSM system performance in normal and fault conditions.

Composite Adaptive Synchronous Control of Dual-Drive Gantry Stage With Load Movement

In gantry systems, load usually moves according to different production tasks. The continuous change of the beam centroid position is a non-negligible factor for achieving high-performance synchronous control. Therefore, it cannot be simply treated as an external disturbance. In addition, advanced controller design and model parameter identification are very important for precision motion control systems. This article addresses the synchronous control of dual-drive gantry platforms with load movement to improve their steady-state and transient performance. Based on the analysis of the rigid and flexible characteristics of gantry mechanical components, a rigid-flexible coupling dynamic model is proposed, which provides a theoretical basis for the control system design. To ensure zero steady-state tracking error and parameter convergence in the presence of parameter uncertainties and unknown disturbances, a composite adaptive control method integrating excellent output tracking performance and parameter estimation is presented. Furthermore, the bridge between load movement and centroid position is established through frequency domain identification, which facilitates reasonable thrust distribution. Comparative experimental results are presented that confirm the effectiveness and advantages of the proposed synchronous control scheme.

Application of Adaptive Integral Robust Controller in Laser Galvanometer Motor

High-speed motion control of the galvanometer has become a very important part of laser processing. Due to the parameter uncertainty of the galvanometer itself, non-linearity can affect the friction compensation effect. In this paper, we propose to reduce the steady-state tracking error of the galvanometer system by means of an integral control term, while estimating the friction behavior using a nonlinear modified LuGre observer. Then an adaptive integral robust control scheme is used to eliminate the effects of nonlinear friction and external disturbances. And the stability of the galvanometer system is proved by the Lyapunov theorem. Simulation verification by MATLAB shows that the control scheme proposed in this paper can accurately follow the system commands. And the controller can effectively suppress the effects of unknown disturbances and parameter uncertainties compared with traditional control strategies. The simulation results show that the proposed control scheme significantly improves the response speed and tracking accuracy of the galvanometer system.

A novel electromagnetic recuperator used in the artillery: Structural and control algorithm design

Aiming at the problem that the traditional artillery recuperator is difficult to maintain and control, a novel electromagnetic recuperator based on the principle of tubular permanent magnet synchronous linear motor is proposed. First, the structural scheme of the electromagnetic recuperator is designed, and the maximum thrust required for the artillery counter-recoil motion process is determined by force analysis. Secondly, according to the requirements of the artillery type and design, the analytical model of the electromagnetic recuperator is established by the subdomain method, and the main structural parameters can be obtained quickly. Then, the correctness of the analytical model is verified by the finite element method. Considering the complex uncertainties in the artillery counter-recoil control process, an adaptive robust control is proposed. The uncertainty of the system is estimated online using a leaky adaptive rate α, and the controller is compensated. Finally, the simulation results show that the designed electromagnetic recuperator meets the thrust requirements of the artillery counter-recoil process; adaptive robust control can effectively solve the uncertainty problem in the system and provides smaller stabilization time and steady-state tracking error compared to PID control.

Command filter-based adaptive fuzzy integral backstepping control for quadrotor UAV with input saturation

This paper presents an adaptive fuzzy integral backstepping control strategy combined with command filter to solve trajectory tracking problem of quadrotor unmanned aerial vehicle (UAV). By using Fuzzy logic system to approximate uncertain disturbance. The tracking error integral term is introduced to reduce the steady-state tracking error. The backstepping approach is combined with the command filter to solve the “computational explosion” problem, and the error compensation mechanism is introduced to reduce the influence of filtering error. The hyperbolic tangent function is used to solve the problem of input saturation. By choosing the appropriate Lyapunov function to calculate the adaptive law for tuning the adjustable parameters of the fuzzy logic system. Morever, the stability of the controller is analyzed by using Lyapunov stability theory. Numerical simulation results are provided to illustrate the effectiveness and superiority of the proposed control method.

Practical Position Tracking for 3D Unicycle Model

This paper considers practical position tracking for the 3D unicycle model. In contrast to the existing hand position coordinate transformation, a novel modified hand position coordinate transformation is proposed for the 3D unicycle model which can guarantee that the induced velocity transformation matrix is nonsingular for all the possible orientations. By employing the proposed modified hand position coordinate transformation, the nonlinear 3D unicycle position kinematics can be converted into the single integrator form, which enables arbitrary position reference trajectory tracking given any prespecified upper bound for the steady-state tracking error. The control performance is examined by numerical examples.

Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds

Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds

Prescribed performance dynamic surface control for nonlinear systems subject to partial and full state constraints

This paper discusses prescribed performance dynamic surface control (DSC) problems for nonlinear systems subject to state constraints. Incorporating the prescribed performance control (PPC) with DSC methods, we present a neural adaptive control method that characterizes the steady-state tracking error and its convergence rate. By constructing a type of funnel error variables, the error variables can be limited in the boundary of funnel functions, and the violations of the conditions of partial and full state constraints are shunned. In the latter case, a new assumption is proposed to handle the circular design problem in the design procedure. Under the control scheme designed, the considered nonlinear systems can be stabilized with the Lyapunov stability theory, and it can be guaranteed that all variables are semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation results verify that the proposed prescribed performance DSC-based control scheme can ensure stability and prescribed performance metrics in the existence of partial and full-state constraints.

Motion Trajectory Control System for Production Line Robots Based on Variable Domain Fuzzy Control

Mechatronics production line is widely used in the production and operation of all walks of life, which greatly reduces the amount of labor of employees, improves the production level of enterprises, and creates great social and economic benefits for enterprises. The traditional manipulator system has modeling uncertainty and is vulnerable to external interference. In this paper, a compound control scheme is designed by combining the torque controller and fuzzy compensator, which effectively improves the system's response speed and greatly reduces the steady-state tracking error of the system. At the same time, the tracking process of the scheme is stable and flexible, and the chattering is minimal, which effectively improves the trajectory tracking performance of the system. Experiments show that the algorithm effectively solves the contradiction between computational complexity and control accuracy, improves the system's response speed, and reduces the system's steady-state tracking error.

Trajectory Control Algorithm of Flexible Joint Manipulator Based on Random Matrix and Screw Theory

Flexible articulated manipulators are often used for the task of tracking reference trajectories in space and have attracted much attention. Aiming at the uncertainty of the robot system, based on random matrix and screw theory, this paper constructs a trajectory control model of a flexible joint manipulator. In order to reduce the steady-state tracking error, a random matrix variable structure control method is introduced into the model, and a nonlinear spinor-like random matrix function is designed to improve the traditional random matrix surface. In the simulation process, the dynamic model of the series robot is firstly obtained according to the screw and random matrix equation, and the dynamic characteristics are analyzed. Combined with dynamic surface control technology, a neural network controller is designed to solve the problem of dimensional explosion and ensure that the tracking error converges to a small neighborhood of zero. The experimental results show that by using the observation value to replace the unmeasurable state of the system, combining it with the random matrix network to identify the unknown dynamics of the system, and designing the random matrix network controller, the tracking control of the system can be realized, and the tracking error can be ensured to converge to a small neighborhood of zero. The control system has a better control effect than traditional PID, the peak time is shortened by 45.83%, the adjustment time is shortened by 46.91%, the maximum overshoot is reduced by 51.35%, and the steady-state error after filtering is only 0.049, which is reduced by 47.31%. Effective interference signal and measurement noise are suppressed, and the quantitative observation performance of the flexible joint manipulator system is improved.

Linear Proportional-Integral-Differential-Robustified Continuous-Time Optimal Predictive Control for a Class of Nonlinear Systems

This paper presents a novel robust optimal predictive control approach for a class of nonlinear continuous-time systems perturbed by unknown disturbances. First, a new error state with a linear proportional-integral-differential (PID) structure considering current, accumulative, and derivative tracking errors is defined. Second, prediction of the error state within the predictive periods is expressed by the error state and its high-order derivatives according to the Taylor series expansion. Last, the proposed control law as well as the main result of this paper are derived by minimizing the prediction of the error state. Numerical validation for designing a missile autopilot shows that, due to minimizing the accumulative tracking error included in the PID-structuralized new error state, the proposed approach can generate smaller steady-state tracking errors than two commonly applied continuous-time optimal predictive control approaches whether the disturbances encountered by the missile are constant or time-varying.

An Effective DC-Link Voltage Control Strategy for Grid-Connected PMVG-Based Wind Energy Conversion System

This study presents an effective control strategy for regulating the DC-link voltage in a variable-speed direct-driven (DD) wind energy conversion system (WECS) using a permanent magnet vernier generator (PMVG). To do this, at first, the overall system is configured using back-to-back (BTB) voltage source converters, and the whole system’s dynamical equations are modeled and presented. Following that, a non-linear sliding mode control strategy is introduced as the grid-side converter’s DC-link voltage controller to improve the dynamic performance of the PMVG system and achieve the stable power transfer with the grid. To accomplish this, a proportional and integral (PI)-based sliding surface is designed, and a hybrid reaching law is proposed to suppress chattering and deliver a faster response of DC-link voltage with negligible steady-state tracking error. Finally, the effectiveness and superiority of the proposed control strategy are validated through comparisons with existing methods using simulation and experimental results from a 5-kW PMVG system.

A Robust Dynamic Control Strategy for Standalone PV System under Variable Load and Environmental Conditions

Dual-stage standalone photovoltaic (PV) systems suffer from stability, reliability issues, and their efficiency to deliver maximum power is greatly affected by changing environmental conditions. A hybrid back-stepping control (BSC) is a good candidate for maximum power point tracking (MPPT) however, there are eminent steady-state oscillations in the PV output due to BSC’s recursive nature. The issue can be addressed by proposing a hybrid integral back-stepping control (IBSC) algorithm where the proposed integral action significantly reduces the steady-state oscillations in the PV array output under varying temperature and solar irradiance level. Simultaneously, at the AC stage, the primary challenge is to reduce both the steady-state tracking error and total harmonic distortion (THD) at the output of VSI, resulting from the load parameter variations. Although the conventional sliding mode control (SMC) is robust to parameter variations, however, it is discontinuous in nature and inherit over-conservative gain design. In order to address this issue, a dynamic disturbance rejection strategy based on super twisting control (STC) has been proposed where a higher order sliding mode observer is designed to estimate the effect of load disturbances as a lumped parameter which is then rejected by the newly designed control law to achieve the desired VSI tracking performance. The proposed control strategy has been validated via MATLAB Simulink where the system reaches the steady-state in 0.005 s and gives a DC–DC conversion efficiency of 99.85% at the peak solar irradiation level. The AC stage steady-state error is minimized to 0 V whereas, THD is limited to 0.07% and 0.11% for linear and non-linear loads, respectively.

Networked Active Fault-Tolerant Predictive Control for Systems With Random Communication Constraints and Actuator/Sensor Faults

This brief presents an active fault-tolerant predictive control method for the output tracking of networked control systems (NCSs) subject to random communication constraints as well as actuator and sensor faults. The system state and actuator/sensor faults are simultaneously estimated via an observer and then used to perform a fault-tolerant predictive controller. Thus, both faults and the communication constraints in the backward and forward channels are actively compensated. A closed-loop stability condition is obtained, which also guarantees a zero steady-state tracking error. Moreover, the separation principle for designing the observer-based controller holds. Finally, the numerical simulation for a mass-spring-damper system is conducted to illustrate the effectiveness of the proposed method.

Investigation of control algorithm for long-stroke fast tool servo system

Fast tool servo (FTS) is an efficient and reliable method in precision machining for fabricating freeform surfaces or microarrays with sub-micrometric form accuracy. In this paper, a Lorentz force FTS is designed where the voice coil motor is located inside the slide, and four air bearings are used as support components. Three different control algorithms, namely conventional PID control, advanced PID control with velocity/acceleration feed-forward (FF) and sliding mode control (SMC) are implemented in the system, and corresponding Simulink simulation models are built including for both mechanical and electrical systems. The results show that advanced PID and SMC can reduce phase error and overshoot, and tracking error can be controlled at 3.13% at 50 Hz. A new hybrid control algorithm (PID + SMC + FF) is developed, with system tracking error subsequently decreased to 0.871% at 50 Hz. In addition, with a suitable compensation method, the steady state tracking error is further decreased to 0.029%. Consistent results from testing with signals of different input frequency also indicate the general effectiveness of the algorithm.

Collision Avoidance and Connectivity Preservation for Time-Varying Formation of Second-Order Multi-Agent Systems With a Dynamic Leader

In this paper, the problem of time-varying formation tracking control, with collision avoidance (CA) and connectivity preservation (CP), is studied for second-order multi-agent systems. Consider the unknown control input of virtual leader, an estimator is introduced to design a distributed time-varying formation tracking control protocol, while relaxing the condition the leader&#x2019;s velocity is constant. Different from some existing results, relative velocity-based action function is designed such that both CA and CP with small negative effects on formation are achieved, and a simpler method is proposed to eliminate the large jump and discontinuity of potential field force. Furthermore, the Lyapunov-like approach is used for the stability analysis and the theoretical results are derived. Accordingly, it is demonstrated that velocity tracking errors can asymptotically converge to 0, and steady-state position tracking errors are bounded and related to initial state. Finally, two simulation examples verify the effectiveness of theoretical results.

Research on Intelligent Adaptive Control Method for Waste Heat Power Generation Stability Problem

The effective recovery and utilization of waste heat is an important part of the energy industry chain, but the gas source of waste heat has large fluctuations and strong random frequency changes, which easily affects the quality of power generation. In order to obtain more continuous and stable electricity in the process of waste heat power generation, this paper proposes an intelligent adaptive control method. This control method decouples the variables for the characteristics of strong coupling of the waste heat power generation system, which improves the anti-disturbance performance of the system on the one hand and reduces the steady-state tracking error of the system on the other hand. Experiments show that when the gas source fluctuates, the system fluctuation rate is stable within 7%; when the set value changes, the adjustment time is within 7 s, and the overshoot is small, so the performance is better than the traditional PID control method. The intelligent adaptive control method proposed in this paper is of great significance for the future development of intelligent grid-connected power generation.