Integral Of Tracking Error Research Articles

Variable Cut-Off Frequency Algorithm-Based Nonlinear Position Controller for Magnetic Levitation System Applications

In this article, the position-tracking problem for magnetic levitation (MAGLEV) systems is addressed by handling the model nonlinearities and uncertainties of parameters and loads. The first feature is devising a variable cut-off frequency algorithm enhancing the transient tracking performance by updating the feedback gain accordingly. The second is introducing the disturbance observer (DOB) improving the disturbance attenuation performance with the offset-free property, which corresponds to the replacement of tracking error integrators. The simulation results numerically demonstrate the effectiveness of the proposed technique considering model-plant mismatches and load variations.

Additive Uncertainty Consideration for Nonlinear and Multivariable Bioprocess Control

Biological processes are becoming more frequent nowadays due to the wide variety of products obtained from them and their possibility of making environmentally friendly some processes while high standard products are obtained. Nevertheless, controlling them has many difficulties due to their complex dynamic (multivariable and highly nonlinear systems) subject to modeling uncertainties and external disturbances presence. In this paper, two possibilities of improvement for a previously presented technique are proposed. In the first one, an approach based on the error estimation using Newtons backward interpolation is included in the design equations to decrease the uncertainties effect; while in the second one, some tracking error integrators are added in the control action calculation. Alternatives are applied in a bioethanol system, tested under different conditions and compared to show the improvements.

Velocity-sensorless proportional–derivative trajectory tracking control with active damping for quadcopters

The proposed observer-based control mechanism solves the trajectory tracking problem in the presence of external disturbances with the reduction in sensor numbers. This systematically considers the quadcopter nonlinear dynamics and parameter and load variations by adopting the standard controller design approach based on a disturbance observer (DOB). The first feature is designing first-order observers for estimating the velocity and angular velocity error, with their parameter independence obtained from the DOB design technique. As the second feature, the resultant velocity observer-based control action including active damping and DOBs secures first-order tracking behavior for the position and attitude (angle) loops through pole zero cancellation, thereby forming a proportional–derivative control structure. Closed-loop analysis results reveal the performance recovery and steady-state error removal properties in the absence of tracking error integrators. The numerical verification confirms the effectiveness of the proposed mechanism using MATLAB/Simulink.

Trajectory tracking control with preview action for a class of continuous-time Lur\u2019e-type nonlinear systems

A novel preview control scheme is developed for the trajectory tracking problem of continuous-time Lur’e-type nonlinear systems. With the aid of the translation approach, the state augmentation technique along with some special mathematical manipulations, an augmented error system including preview information is constructed. The tracking control problem is thereby reduced to a standard H_{infty } controller design problem. Meanwhile, the integrator is introduced to eliminate the steady-state tracking error. The controller design condition is established in terms of a linear matrix inequality (LMI). As for the original system, the tracking controller is a state feedback controller with tracking error integral plus preview action. Finally, an example is given to illustrate the tracking performance of the proposed method.

Multivariable Tracking Control of a Bioethanol Process under Uncertainties

Bioethanol is one of the most studied alternative fuels nowadays. Due to its production process complexity and the low quality of the mathematical models that describe it, a reliable controller is needed to maximize the fuel production and minimize its environmental impact, even in the presence of uncertainty. Here, a controller for tracking optimal profiles considering model errors and external perturbations is proposed. This work is an improvement of a previously presented technique. To reduce the earlier mentioned uncertainties’ effect during the fermentation, some tracking error integrators are added in the control action calculation. This simple modification ensures the tracking error convergence to zero, even in the presence of uncertainties (demonstration available). Different tests are carried out and a performance comparison with the original controller is shown to highlight improvements in the tracking error of up to 98% when integrators are incorporated. Furthermore, a classical PI controller is contrasted with the proposed techniques.

Auto-Tuner-Based Controller for Quadcopter Attitude Tracking Applications

This brief offers a nonlinear advanced attitude tracking controller for quadcopter applications. The proposed technique incorporates an auto-tuner and disturbance observers instead of tracking error integrators. The offset-free convergence and performance recovery properties are rigorously proved using the Lyapunov stability theorem. Through realistic simulations, the closed-loop performance is numerically evaluated, focusing on showing the effectiveness of the auto-tuner.

Track-keeping observer-based robust adaptive control of an unmanned surface vessel by applying a 4-DOF maneuvering model

The present study addresses the speed and steering controller design for the maneuvering motions of an unmanned surface vessel (USV). Based on a 4-DOF nonlinear mathematical model for the maneuvering motions of the proposed USV with multi-inputs and multi-outputs, an adaptive sliding mode controller based on Lyapunov analysis is designed to follow the desired velocity and to estimate unknown parameters for the separated surge motion. In addition, for the steering motion control, an augmented model including the heading motion and output tracking error integral is presented. In accordance with the proposed model, an observer-based model reference adaptive controller is developed, leading to a convex optimization problem subject to matrix inequalities. The reference heading angle is extracted from an adaptive line-of-sight (LOS) guidance algorithm based on waypoints. Finally, the simulation results of tracking several maneuvering motion paths indicate the efficiency of the proposed approach is satisfactory and superior compared with PID controller.

Self-Tuning Proportional-Type Performance Recovery Property Output Voltage-Tracking Algorithm for DC–DC Boost Converter

This article exhibits an output voltage-tracking control algorithm incorporating a self-tuning algorithm and disturbance observers (DOBs) for dc–dc boost converters without tracking error integrators, considering model nonlinearities, parameter variations, and load uncertainties. The proposed algorithm is designed such that it forces the output voltage to track its target trajectory driven by a time-varying low-pass filter (LPF), despite model-plant mismatches. This paper makes two main contributions. First, it constructs the self-tuning algorithm by updating the closed-loop cut-off frequency in the time-varying LPF to improve the transient tracking performance. Second, it embeds first-order DOBs in the proportional-type nonlinear controller to achieve both performance recovery and the offset-free properties. The experimental verifications are carried out to illustrate the effectiveness of the closed-loop system driven by the proposed technique with a 3-kW prototype dc–dc boost converter; the 46% improvement of the tracking performance is observed, compared with the conventional feedback-linearization controller.

Adaptive finite time servo control for automotive electronic throttle with experimental analysis

In order to meet the rigorous requirement for transient and static performance of automobile electronic throttle control systems, an adaptive finite time servo control (AFTSC) strategy is investigated by integrating adaptive backstepping recursive technique into the framework of finite-time stability theory. The required transient performance of the throttle opening trajectory tracking is guaranteed theoretically by the finite convergence time and the convergence rate related to the adjustable control parameters. The static performance is enhanced by introducing the tracking error integral into the system state variables. The robustness of the satisfactory transient and static performance is improved by the adaptive update law in the light of system parameter uncertainties due to production deviations, different working conditions and aging. Meanwhile, the advantage of the proposed AFTSC strategy is validated by demonstrating the comparison results with the existing strategies both in the critical operating cases under Matlab/Simulink simulation environment and in the actual operating cases on the dSPACE rapid-control-prototype (RCP) test platform for a real electronic throttle system.

Passivity-Based Robust Output Voltage Tracking Control of DC/DC Boost Converter for Wind Power Systems

This paper exhibits a passivity-based robust output voltage controller for DC/DC boost converters for wind power system applications. The proposed technique has two features. The first one is to introduce a nonlinear disturbance observer for estimating the disturbances arising from the load and parameter variations. The second one is to derive a proportional-type passivity-based output voltage tracking controller incorporating the disturbance observer output, which simplifies the control algorithm by removing the use of tracking error integrators and an anti-windup algorithm. These two features constitute the useful closed-loop properties called the performance recovery and offset-free properties. Numerical simulation results confirm the efficacy of the proposed scheme, where a wind power system including the proposed controller is emulated using the PowerSIM software.

Robust Offset-Free Speed Tracking Controller of Permanent Magnet Synchronous Generator for Wind Power Generation Applications

This article presents a robust speed tracking algorithm for a permanent magnet synchronous generator utilized for wind power generation systems, considering the machine parameter and load uncertainties. There are two major contributions: (a) a disturbance observer is designed to exponentially estimate disturbances from the model-plant mismatches and severe load torque variations, and (b) it is included in a nonlinear cascade-type proportional speed tracking controller to establish the performance recovery and offset-free properties without the use of tracking error integrators. A simulation result numerically verifies the effectiveness of the proposed technique, where the PowerSIM software emulates a wind power generation system.

Robust iterative learning control for batch processes with input delay subject to time‐varying uncertainties

A robust iterative learning control (ILC) method is proposed for industrial batch processes with input delay subject to time-varying uncertainties, based on a two-dimensional (2D) system description of batch process operation. To compensate the input delay, a 2D state predictor is established to predict the augmented system states, such that a 2D ILC design is developed for the ‘delay-free’ 2D system based on using only the measured output errors of current and previous cycles. Delay-dependent stability conditions for the resulting 2D system are established in terms of matrix inequalities by defining a comprehensive 2D Lyapunov–Krasovskii functional candidate along with free-weighting matrices. By solving these matrix inequalities using a cone complementarity linearisation method, the ILC controller is explicitly derived together with an adjustable H infinity performance index. An important merit is that perfect tracking can be realised for a batch process with arbitrarily long input delay if the delay-free part of the 2D system can be stabilised, in no presence of time-varying uncertainties. Moreover, the time integral of tracking error can be added as an extended 2D system state for ILC design to eliminate steady-state output error for all batches. An illustrative example of injection moulding process is given to demonstrate the effectiveness of the proposed method.

Disturbance observer based robust mixed H2/H∞ fuzzy tracking control for hypersonic vehicles

This paper introduces a disturbance observer (DO) based mixed H2/H∞ robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle (HV) with modeled and unmodeled disturbances. A Takagi–Sugeno (T–S) fuzzy model is firstly employed to approximate the nonlinear dynamics of HV. Subsequently, based on the fuzzy model, a DO is constructed to estimate the modeled disturbance. Next, by integrating the HV dynamics, the tracking error integral and the disturbance estimation error dynamics, an augmented system is established for the control design. Then, a DO-based mixed H2/H∞ robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed H2/H∞ control performance of the augmented system. The proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral, a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error, and a DO-based compensator for the modeled disturbance cancellation. The outcome of the DO-based mixed H2/H∞ robust fuzzy control problem is formulated in terms of linear matrix inequalities (LMIs). Furthermore, by utilizing the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of H2 performance. Finally, simulation results on an HV demonstrate the effectiveness of the proposed design method.

A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos

A novel sliding mode nonlinear proportional-integral control (SMNPIC) scheme is proposed for driving a class of time-variant chaotic systems with uncertainty to arbitrarily desired trajectory with high accuracy. The SMNPIC differs from the previous sliding mode techniques in the sense that a nonlinear proportional-integral action of sliding function is involved in control law, so that both the steady-state error and the high-frequency chattering are reduced and meanwhile, robustness and fastness are guaranteed. In addition, the proposed SMNPIC actually acts as a class of nonlinear proportional-integral-differential (PID) controller, in which the tracking error and its derivatives up to (n-1)th order as well as the integral of tracking error are considered, so that more useful information than traditional PID can be implemented and better dynamic and static characteristics can obtained. Its good performance for chaotic control is illustrated through a Duffing–Holmes system with uncertainty.