Reduce Tracking Errors Research Articles

Data Driven Distributed Bipartite Consensus Tracking for Nonlinear Multiagent Systems via Iterative Learning Control

This article explores a data-driven distributed bipartite consensus tracking (DBCT) problem for discrete-time multi-agent systems (MASs) with coopetition networks under repeatable operations. To solve this problem, a time-varying linearization model along the iteration axis is first established by using the measurement input and output (I/O) data of agents. Then a data-driven distributed bipartite consensus iterative learning control (DBCILC) algorithm is proposed considering both fixed and switching topologies. Compared with existing bipartite consensus, the main characteristic is to construct the proposed control protocol without requiring any explicit or implicit information of MASs' mathematical model. The difference from existing iterative learning control (ILC) approaches is that both the cooperative interactions and antagonistic interactions, and time-varying switching topologies are considered. Furthermore, through rigorous theoretical analysis, the proposed DBCILC approach can guarantee the bipartite consensus reducing tracking errors in the limited iteration steps. Moreover, although not all agents can receive information from the virtual leader directly, the proposed distributed scheme can maintain the performance and reduce the costs of communication. The results of three examples further illustrate the correctness, effectiveness, and applicability of the proposed algorithm.

Repetitive Control Process for Periodic Disturbance Cancellation Using Data Classification With a Fuzzy Regression Approach

The utilization of a repetitive controller to cancel periodic disturbance or noise in mechanical systems has become increasingly important for industrial applications. In this study, a repetitive control process was developed using a data classification method, with a fuzzy regression approach and basis function, to reduce tracking errors in feedback controllers. First, a system model using the basis function is illustrated to compute the matched basis functions and their associated coefficients. A real case example of improving the focus of an electron beam subjected to periodic fluctuations has been described for verification and error analysis. Next, model algorithms containing pure and fuzzy regression are introduced into a repetitive feedback control system to reduce tracking errors caused by a periodic disturbance. System output data are categorized using fuzzy inference rules as similar data forming a single group are typically more reliable than the entire output data. The fuzzy theorem approach adopts a Gaussian membership function for system output variables owing to uncertainties that arise from modeling errors, environmental noise, etc. It is determined that the repetitive control process based on data classification with a fuzzy regression approach is more effective than using a pure regression approach. Increasing the number of data classifications initially improves accuracy; however, this decreases when the number of data classifications continues to increase. The optimal root-mean-square output tracking error convergence value was determined as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-14.09</sup> when the system output data was classified into four categories, demonstrating the satisfactory reduction of a periodic disturbance. Similar results were obtained using the pure regression algorithm, where the lowest averaged verification error was 2.71% for the linear basis function model, with data classified into four categories, and this corresponded to an average prediction error of 3.86%.

Optimal Tuning of Model Predictive Controller Weights Using Genetic Algorithm with Interactive Decision Tree for Industrial Cement Kiln Process

Energy intense nature of cement kiln demands optimal operation to minimize the energy requirement. Optimal control of cement kiln is achieved by proper tuning of the model predictive controller (MPC), which is addressed in this work. Genetic algorithm (GA) is used to determine the MPC weights that minimize the overall energy utilization with reduced tracking error. Single objective function has been formulated using importance weighted performance metrics like energy utilization and integral absolute error in tracking the desired response. Importance weights are determined in specific to the control scenarios using an interactive decision tree (IDT). It interacts with the operator to detect the weaker metrics and raises the importance level for further improvement. The algorithm terminates after attending all the metrics with the consent from the operator. Five control scenarios that predominantly occur in industrial cement kiln have been considered in this study. It includes tracking, measured, and unmeasured disturbance rejection of pulse and Gaussian type noises. The results illustrate the minimized energy operation with the use of the proposed single objective function as compared with the multi-objective function-based GA tuning procedure.

A Model Predictive Controller with Longitudinal Speed Compensation for Autonomous Vehicle Path Tracking

Autonomous vehicle path tracking accuracy faces challenges in being accomplished due to the assumption that the longitudinal speed is constant in the prediction horizon in a model predictive control (MPC) control frame. A model predictive control path tracking controller with longitudinal speed compensation in the prediction horizon is proposed in this paper, which reduces the lateral deviation, course deviation, and maintains vehicle stability. The vehicle model, tire model, and path tracking model are described and linearized using the small angle approximation method and an equivalent cornering stiffness method. The mechanism of action of longitudinal speed changed with state vector variation, and the stability of the path tracking closed-loop control system in the prediction horizon is analyzed in this paper. Then the longitudinal speed compensation strategy is proposed to reduce tracking error. The controller designed was tested through simulation on the CarSim-Simulink platform, and it showed improved performance in tracking accuracy and satisfied vehicle stability constrains.

Design of an evolving Fuzzy-PID controller for optimal trajectory control of a 7-DOF redundant manipulator with prioritized sub-tasks

Articulated manipulators constitute a major fraction of industrial robots. With the increase in the need to perform complex tasks requiring a higher degree of accuracy, such manipulators require a more robust and efficient control. In this paper, an evolving Fuzzy-PID control design for the trajectory tracking problem of a redundant 7-DOF serial manipulator is proposed. The scaling factors of the Fuzzy controller are evolved over time by using recent meta-heuristic techniques, namely, Moth-Flame Optimisation (MFO), Novel Bat Algorithm (NBA) and Sine Cosine Algorithm (SCA). The proposed technique which utilizes Intelligent control methods combined with meta-heuristics provides a promising hybrid control design, which has been found to be more efficient in our software implementation, in terms of reduced tracking error of the manipulator for its kinematic control in the joint space as compared to other controllers of the same nature that are generally used in practise. The performance of the controller is compared in the time-domain responses under external disturbances and have been found to outperform standard controllers without the need of any additional training.

Hierarchical Control for Trajectory Generation and Tracking Via Active Front Steering

Abstract A new hierarchical model predictive controller (HMPC) for autonomous vehicle steering control is presented. The controller generates a path of shortest distance by determining lateral coordinates on a longitudinal grid, while respecting road bounds. This path is then parameterized by arc length before being optimized to restrict the normal acceleration values along the trajectory's arc length. The optimized trajectory is then tracked using a nonlinear MPC scheme using a bicycle plant model to calculate an optimal steering angle for the tires. The proposed controller is evaluated in simulation during a double-lane-change maneuver, where it generates and tracks a reference trajectory while observing the road boundaries and acceleration limits. Its performance is compared to a controller without path optimization, along with another that uses a smooth, predetermined, reference path instead of creating its own initial reference. It is shown that the proposed controller improves the tracking compared to a controller without path optimization, with a four-times reduction in average lateral tracking error. The average lateral acceleration is also reduced by 6%. The controller also maintains the tracking performance of a controller that uses a smooth reference path, while showing a much greater flexibility due to its ability to create its own initial reference path rather than having to follow a predetermined trajectory.

A Simplified Model Predictive Control of Four-Leg Two-Level Inverter

This article proposes current control strategy for four-leg two-level voltage source inverters (VSI). This strategy is based on model predictive control (MPC) approach and presents its comparison with finite control set (FCS) model technique. Besides providing a fast dynamic response, proposed technique replaces complex modulation stage and PI controller being used in earlier classical control techniques. Moreover, the proposed methodology selects the switching sequence which reduces tracking error between output and applied reference currents using cost function optimization. This shows the improvement of system response like FCS model technique. However, FCS model technique results in calculation stress and computation burden; resulting computational delay and extra power consumption by the processor. This problem is solved with the help of proposed single predictive technique which makes the inverter more suitable for large time horizon operations and small sampling time instants. The computational delay is reduced up to 6% compared to the case of FCS-MPC controlled inverter. Performance of proposed simplified technique is analyzed and compared with FCS-MPC controlled system with the help of different types of reference signals. This work will boost the industrial application of four-leg two-level VSI by increasing dynamic response and removing complex modulation stage.

Finite-Time Control of a Linear Motor Positioner Using Adaptive Recursive Terminal Sliding Mode

Payload variations, friction, and external disturbances deteriorate the control performance of linear motor (LM) positioners. To provide high-speed and high-precision performance for the LM, an adaptive recursive terminal sliding-mode (ARTSM) controller is proposed in this article. For the controller, a fast nonsingular terminal sliding function and a recursive integral terminal sliding function are developed in a recursive structure such that the sliding surfaces are arrived successively and ultimately the tracking error can converge to zero in a finite time. Furthermore, by setting an appropriate initial value for the integral element of the ARTSM controller, the control system is enforced to start on the sliding surface at the initial time such that the reaching time is reduced. Stability analysis is presented to prove the finite-time convergence and zero tracking error of the closed-loop system under the proposed ARTSM controller. Experimental results also demonstrate the effectiveness of the controller in terms of significantly reduced tracking errors and faster disturbance rejection in comparison with a recently reported fast nonsingular terminal sliding-mode (FNTSM) controller for the LM positioner.

Automated Ice-Bottom Tracking of 2D and 3D Ice Radar Imagery Using Viterbi and TRW-S

Multichannel radar depth sounding systems are able to produce two-dimensional (2D) and three-dimensional (3D) imagery of the internal structure of polar ice sheets. Information such as ice thickness and surface elevation is extracted from these data and applied to research in ice flow modeling and ice mass balance calculations. Due to a large amount of data collected, we seek to automate the ice-bottom layer tracking and allow for efficient manual corrections when errors occur in the automated method. We present improvements made to previous implementations of the Viterbi and sequential tree-reweighted message passing (TRW-S) algorithms for ice-bottom extraction in 2D and 3D radar imagery. These improvements are in the form of novel cost functions that allow for the integration of further domain-specific knowledge into the cost calculations and provide additional evidence of the characteristics of the ice sheets surveyed. Along with an explanation of our modifications, we demonstrate the results obtained by our modified implementations of the two algorithms and by previously proposed solutions to this problem, when compared to manually corrected ground truth data. Furthermore, we perform a self-assessment of tracking results by analyzing differences in the estimated ice-bottom for surveyed locations where flight paths have crossed and, thus, two separate measurements have been made at the same location. Using our modified cost functions and preprocessing routines, we obtain significantly decreased mean error measurements from both algorithms, such as a 47% reduction in average tracking error in the case of 3D imagery between the original and our proposed implementation of TRW-S.

The effects of electromyography-assisted modelling in estimating musculotendon forces during gait in children with cerebral palsy

Neuro-musculoskeletal modelling can provide insight into the aberrant muscle function during walking in those suffering cerebral palsy (CP). However, such modelling employs optimization to estimate muscle activation that may not account for disturbed motor control and muscle weakness in CP. This study evaluated different forms of neuro-musculoskeletal model personalization and optimization to estimate musculotendon forces during gait of nine children with CP (GMFCS I-II) and nine typically developing (TD) children. Data collection included 3D-kinematics, ground reaction forces, and electromyography (EMG) of eight lower limb muscles. Four different optimization methods estimated muscle activation and musculotendon forces of a scaled-generic musculoskeletal model for each child walking, i.e. (i) static optimization that minimized summed-excitation squared; (ii) static optimization with maximum isometric muscle forces scaled to body mass; (iii) an EMG-assisted approach using optimization to minimize summed-excitation squared while reducing tracking errors of experimental EMG-linear envelopes and joint moments; and (iv) EMG-assisted with musculotendon model parameters first personalized by calibration. Both static optimization approaches showed a relatively low model performance compared to EMG envelopes. EMG-assisted approaches performed much better, especially in CP, with only a minor mismatch in joint moments. Calibration did not affect model performance significantly, however it did affect musculotendon forces, especially in CP. A model more consistent with experimental measures is more likely to yield more physiologically representative results. Therefore, this study highlights the importance of calibrated EMG-assisted modelling when estimating musculotendon forces in TD children and even more so in children with CP.

Genetic algorithm-based multi-objective design of optimal discrete sliding mode approach for trajectory tracking of nonlinear systems

In this paper, a novel multi-objective design of optimal control for robotic manipulators is considered. Generally, robots are known by their highly nonlinearities, unmodeled dynamics, and uncertainties. In order to design an optimal control law, based on the linear quadratic regulator, the robotic system is described as a linear time varying model. The compensation of both disturbances and uncertainties is ensured by the integral sliding mode control. The problem of deciding the optimal configuration of the linear quadratic regulator controller is considered as an optimization problem, which can be solved by the application of genetic algorithm. The main contribution of this paper is to consider a multi-objective optimization problem, which aims to minimize not only the chattering phenomenon but also other control performances including the rise time, the settling-time, the steady-state error and the overshoot. For that, a novel dynamically aggregated objective function is proposed. As a result, a set of nondominated optimal solutions are provided to the designer and then he selects the most preferable alternative. To demonstrate the efficacy and to show complete performance of the new controller, two nonlinear systems are treated in this paper: firstly, a selective compliance assembly robot arm robot is considered. The results show that the manipulator tracing performance is considerably improved with the proposed control scheme. Secondly, the proposed genetic algorithm-based linear quadratic regulator control strategy is applied for pitch and yaw axes control of two-degrees-of-freedom laboratory helicopter workstation, which is a highly nonlinear and unstable system. Experimental results substantiate that the weights optimized using genetic algorithm, result in not only reduced tracking error but also improved tracking response with reduced oscillations.

Head-Trajectory-Tracking Control of a Snake Robot and Its Robustness Under Actuator Failure

This brief considers the problem of trajectory tracking of a planar snake robot without a lateral constraint. The reference trajectory of the head position and the orientation of link 1 are given, and torque control is determined to reduce tracking errors. The performance of the controller was tested in a number of simulations. The robustness during actuator failure was also studied. We assumed that one of the actuators was broken and the corresponding joint became passive. Furthermore, as a more realistic situation, we considered an instance when some of the states were not readily accessible from the sensor readings and needed to be estimated by an observer. The extended Kalman filter was employed for this purpose, and the performance of the closed-loop system with the observer was also tested in simulations.

Research on Adaptive Trajectory Tracking Algorithm for a Quadrotor Based on Backstepping and the Sigma-Pi Neural Network

In this paper, adaptive tracking control is applied to improve performances of an underactuated quadrotor helicopter with respect to attitude and position control. Firstly, the dynamic model is presented. Then a new trajectory tracking algorithm is designed by using the sigma-pi neural network and backstepping. The paper designs the sigma-pi neural network compensation control law and gives the Lyapunov-type stability analysis. Then the corresponding numerical simulations are performed by using MATLAB. Simulation results are shown to demonstrate the effectiveness of the proposed control strategy, which could reduce tracking error, decrease tracking time, and improve the anti-interference ability of the system.

Particle swarm optimization-tuned adaptive fuzzy output feedback motion tracking control of piezo-positioning mechanism with unknown hysteresis

This paper considers the problem of observer-based adaptive fuzzy output feedback control for a piezo-positioning mechanism with unknown hysteresis. In this paper, fuzzy logic systems (FLSs) are used to estimate the unknown nonlinear functions, and also Nussbaum function is utilized to overcome the unknown direction hysteresis. Based on the Lyapunov method, the control scheme is constructed by using the backstepping and adaptive technique. In order to better control performance in reducing tracking error, the particle swarm optimization (PSO) algorithm is utilized for tuning the controller parameters. Proposed adaptive controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded (SGUUB) and the tracking error can converge to a small neighborhood of the origin. Finally, the simulation results are provided to demonstrate the effectiveness and robustness of the proposed approach.

Observer-based fractional-order adaptive type-2 fuzzy backstepping control of uncertain nonlinear MIMO systems with unknown dead-zone

A new problem of observer-based fractional adaptive type-2 fuzzy backstepping control for a class of fractional-order MIMO nonlinear dynamic systems with dead-zone input nonlinearity is considered in the presence of model uncertainties and external disturbances where the control scheme is constructed by combining the backstepping dynamic surface control (DSC) and fractional adaptive type-2 fuzzy technique. First, a linear state observer estimates immeasurable states. Second, the unknown nonlinear functions of the uncertain system are approximated with interval type-2 fuzzy logic systems. Third, to avoid the complication of backstepping design process, the DSC is used. Fourth, by using the fractional adaptive backstepping, fractional adaptive laws are constructed, the proposed method is applied to a class of uncertain fractional-order nonlinear MIMO system. In order to have a better control performance in reducing tracking error, the controller parameters are tuned by using the PSO algorithm. Stability of the system is proven by the Mittag-Leffler method. It is presented that the proposed design guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the zero. The simulation examples are given to show the efficiency of the proposed controller.

Adaptive type-2 fuzzy backstepping control of uncertain fractional-order nonlinear systems with unknown dead-zone

A new problem of adaptive type-2 fuzzy fractional control with pseudo-state observer for commensurate fractional order dynamic systems with dead-zone input nonlinearity is considered in presence of unmatched disturbances and model uncertainties; the control scheme is constructed by using the backstepping and adaptive technique. To avoid the complexity of backstepping design process, the dynamic surface control is used. Also, Interval type-2 Fuzzy logic systems (IT2FLS) are used to approximate the unknown nonlinear functions. By using the fractional adaptive backstepping, fractional control laws are constructed; this method is applied to a class of uncertain fractional-order nonlinear systems. In order to better control performance in reducing tracking error, the PSO algorithm is utilized for tuning the controller parameters. Stability of the system is proven by the Mittag–Leffler method. It is shown that the proposed controller guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the origin. The efficiency of the proposed method is illustrated with simulation examples.

Rollover prevention for a heavy vehicle using optimised slide mode steering control

For a heavy vehicle, active steering can effectively prevent rollover, however, it also changes the operation of the vehicle away from the driver's intentions. To improve rollover stability and reduce tracking error, an optimised slide mode steering control strategy is proposed. Four degrees of freedom linear model is used, which includes lateral, yaw, and roll motions of the sprung mass and unsprung mass. This model is also validated to describe heavy vehicle rollover dynamics. From the model, slide mode control based roll angle and lateral displacement strategies are developed, respectively, and the optimised slide mode steering control strategy is presented to track the set routes and prevent vehicle rollover. Furthermore, some typical numerical cases are simulated to demonstrate the effectiveness of the control strategies. The results show that the optimised strategy can effectively prevent vehicle rollover and significantly improve the performance of tracking the driver's intention for a heavy vehicle.

Iterative Learning Approaches for Discrete-Time State and Disturbance Observer Design of Uncertain Linear Parameter-Varying Systems

Iterative learning approaches are well developed for the design of feedback controllers of dynamic systems which perform identical control tasks during multiple successive executions. Such tasks are characterized by identical reference trajectories in each of the iterations to be run. Exploiting this information, it becomes possible to reduce tracking errors by adapting the control signal not only on the basis of information of the state variables from the current iteration but also by accounting for the history of the tracking errors from previous trials. Although such control strategies are part of an active field of research, the corresponding dual task, namely, the design of state and disturbance observers for systems with successively repeated state trajectories has not yet received the same amount of attention. Therefore, a discrete-time iterative learning observer design, aiming at the combined state and disturbance estimation, is presented in this paper. The resulting approach is validated in numerical simulations for the simplified model of the charging/discharging dynamics of Lithium-Ion battery systems.

Optimal Trajectory Scheme for Robotic Welding Along Complex Joints Using a Hybrid Multi-Objective Genetic Algorithm

The problem of trajectory planning is relevant for the proper use of costly robotic systems to mitigate undesirable effects such as vibration and even wear on the mechanical structure of the system. The objective of this study is to design trajectories that are devoid of collision, velocity, acceleration, jerk and snap discontinuities so that the cycle time required to complete the process can be reduced. The trajectory design was constructed for all the six joints, using a 9th order Bezier curve to accommodate the ten boundary conditions required to satisfy the continuity constraints for joints displacement, velocity, acceleration, jerk and snap. The scheme combines the multi-objective genetic algorithm and the multi-objective goal attainment algorithm to solve the problem of total tracking error reduction during arc welding. The use of a hybrid multi-objective algorithm shows an improved average spread, average distance, number of iteration and computational time. Also, it can be concluded from the constraints studied, that the optimal path in terms of the robots dynamic constraints can achieve the expected tracking ability in terms of the optimal joint angles, velocities, acceleration, jerk, snap and torque.

Application of Iterative Machine Learning for Output Tracking With Magnetic Soft Actuators

This paper presents experimental results of output tracking for soft magnetic actuators using iterative machine learning (IML) to estimate the model and its uncertainty. A challenge is that parameters of dynamic-response models of such soft actuators are sensitive to the operating point. To overcome this challenge and improve the tracking performance, a complex-valued Gaussian process regression (CGPR) is used to estimate a system inverse model; additionally, the CGPR approach provides an uncertainty measure, which is used to design the frequency-dependent iteration gain to ensure convergence. This approach leads to convergence even when data near resonance (where models tend to be sensitive) is not available. Moreover, a method to improve the model estimation is proposed, in which the initial training signal is augmented with additional frequency content to increase the input and output signal size compared to the noise. Using this augmented approach, the IML approach results in a ${\text{95}\%}$ reduction in the maximum tracking error compared to using the dc gain alone. The final maximum tracking error is ${\text{1.8}\%}$ , which is near the sensor resolution limit.