Reference Tracking Control Research Articles

Control of Large Wind Energy Systems Throughout the Shutdown Process

This contribution examines the control problem for very large wind energy converters during shutdown operation and analyses the most important control approaches. The control methods make use of the built-in conventional control infrastructure, but control system reconfigurations are undertaken in order to meet the demands of the shutdown control operation. Hence, the torque controller as well as the collective pitch controller (CPC) are redesigned from their regulator functions to reference tracking control systems with constraints. In addition, the CPC is combined with a feedforward controller in order to gain responsiveness. Constraints in magnitude and rate are managed by a modified anti-windup mechanism. Simulations of a 20 MW reference wind turbine verify the performance of the approaches.

Discrete-Time Model Reference Tracking Control for A Class of Combined Spacecraft: A High-Order Fully Actuated System Approach

Discrete-Time Model Reference Tracking Control for A Class of Combined Spacecraft: A High-Order Fully Actuated System Approach

Sliding mode tracking control of a class of fractional-order nonstrict-feedback nonlinear systems

Since the Leibniz rule for integer-order derivatives of the product of functions, which includes a finite number of terms, is not true for fractional-order (FO) derivatives of that, all sliding mode control (SMC) methods introduced in the literature involved a very limited class of FO nonlinear systems. This article presents a solution for the unsolved problem of SMC of a class of FO nonstrict-feedback nonlinear systems with uncertainties. Using the Leibniz rule for the FO derivative of the product of two functions, which includes an infinite number of terms, it is shown that only one of these terms is needed to design a SMC law. Using this point, an algorithm is given to design the controller for reference tracking, that significantly reduces the number of design parameters, compared to the literature. Then, it is proved that the algorithm has a closed-form solution which presents a straightforward tool to the designer to obtain the controller. The solution is applicable to the systems with a mixture of integer-order and FO dynamics. Stability and finite-time convergence of the offered control law are also demonstrated. In the end, the availability of the suggested SMC is illustrated through a numerical example arising from a real system.

Neural network-based adaptive fault-tolerant control for nonlinear systems with uncertainties

This paper proposes a novel fault-tolerant control (FTC) scheme for real-time uncertainty estimation in nonlinear systems. It addresses the challenges arising from nonlinear dynamics in system inputs, states, and outputs, along with measurement uncertainties, within an output feedback framework. Our approach leverages two key components: 1) A neural network NN descriptor-based observer: this novel observer concurrently estimates both system states and sensor uncertainties. It is particularly capable of handling unbounded sensor uncertainties in specific situations. It utilizes NNs as universal approximators to capture the system's complex nonlinearities. 2) A robust model reference tracking controller: this controller employs the estimated states from the NN descriptor-based observer to achieve the desired system performance despite the existence of uncertainties. It exhibits robustness, guaranteeing system stability and asymptotic state tracking to a given reference model. The efficacy of the proposed FTC scheme is validated through theoretical analysis and its application to two real-world case studies.

Variable Frequency Resonant Controller Based on Generalized Predictive Control for Biased-Sinusoidal Reference Tracking and Multi-Layer Perceptron

Variable Frequency Resonant Controller Based on Generalized Predictive Control for Biased-Sinusoidal Reference Tracking and Multi-Layer Perceptron

Analysis of Power-Maximizing Region 2 Controllers for Wind and Marine Turbines

Wind and marine energy are rapidly growing and complementary technologies that share some techniques for simplified modeling and control, particularly in below-rated flow speeds. A turbine operator has several choices of controller for maximizing power in Region 2. The simple and ubiquitous KΩ2 control law is often effective but limited in its flexibility. Alternative controllers use reference tracking to split the control objectives into a low-bandwidth optimal tip-speed ratio tracking loop to maximize steady-state power and a higher-bandwidth proportional-integral control loop to reject inflow turbulence. Several options exist for identifying the slowly varying optimal set point during operation, based on estimating the inflow velocity or filtering the power or torque signals. This study compares the trade-offs between performance and other design priorities for a few choices of reference-tracking controller in the literature for reference wind and marine turbines. Analysis is performed in the frequency domain using the linearization of each controller, and the impact of turbulent disturbances on the closed-loop system is described. The controllers are simulated in OpenFAST to analyze their performance with higher-order nonlinear turbine dynamics.

Model adaptive reference tracking control for uncertain robotic manipulators with input disturbance

AbstractThis article presents a simple approach for designing a linear adaptive controller, employing the model reference systems concept, to enable the tracking of uncertain robotic manipulators under the influence of input disturbances. The combined impact of model uncertainties and matched disturbances on the robot's behavior is considered as a total matched disturbance, attributed to a double integral system. Subsequently, a novel linear disturbance estimator, augmented by a feed‐forward correction term, is employed to estimate this lumped disturbance within the double integrator system. As a result of this procedure, the requisite adaptive law, based on the model reference system, is formulated for the nominal control parameter instead of arbitrary free‐parameter selections. The effectiveness of the proposed approach is theoretically justified and further supported by its application in the analysis of an active magnetic bearing system.

Adaptive reinforcement learning-based control using proximal policy optimization and slime mould algorithm with experimental tower crane system validation

This paper presents a novel optimal reference tracking control approach resulted from the combination of a popular policy gradient Reinforcement Learning (RL) algorithm, namely Proximal Policy Optimization (PPO), and a metaheuristic Slime Mould Algorithm (SMA). One of the most important parameters in the PPO-based RL process is the learning rate, which has a big impact on how the parameters of the actor neural network (NN) are iteratively updated. In every episode of the RL process, the weights and the biases of the actor NN are multiplied with the learning rate, determining how much the learning agent will step into a certain direction computed based on previous experiences. The classical PPO algorithm usually relies on fixed values for the learning rates which rarely change, or not at all, during the learning process. However, its main drawback is that the learning agent cannot take advantage of positive momentum in the learning process by accelerating towards good learning experiences or slow down and quickly change the direction in the case of consecutive negative learning experiences. The main objective of the combination proposed in this paper is to create an adaptive SMA-based PPO approach applied to control systems, which instead of using fixed learning rate values, it uses the SMA to compute optimal values of the learning rates in each time step of the learning process based on the progress of the learning agent. This paper investigates if the adaptive SMA-based PPO control approach can be considered as an alternative to the classical PPO version, which employs fixed values of the learning rate. A comparison is carried out using control system performance indices gathered while performing an optimal reference tracking control task on tower crane system laboratory equipment.

Improved Immune Moth-Flame Optimization Based on Gene Correction for Automatic Reverse Parking.

During the process of reverse parking, it is difficult to achieve the ideal reference trajectory while avoiding collision. In this study, with the aim of establishing reference trajectory optimization for automatic reverse parking that smooths and shortens the trajectory length and ensures the berthing inclination angle is small enough, an improved immune moth-flame optimization method based on gene correction is proposed. Specifically, based on the standard automatic parking plane system, a reasonable high-quality reference trajectory optimization model for automatic parking is constructed by combining the cubic spline-fitting method and a boundary-crossing solution based on gene correction integrated into moth-flame optimization. To enhance the model's global optimization performance, nonlinear decline strategies, including crossover and variation probability and weight coefficient, and a high-quality solution-set maintenance mechanism based on fusion distance are also designed. Taking garage No.160 of the Dalian Shell Museum located in Dalian, Xinghai Square, as the experimental site, experiments on automatic parking reference trajectory optimization and tracking control were carried out. The results show that the proposed optimization algorithm provides higher accuracy for reference trajectory optimization and can achieve better tracking control of the reference trajectory.

Observer-based differential evolution constrained control for safe reference tracking in robots

Big torque inputs in controls could increase energy consumption, and big estimated perturbations in observers could produce device damages. Therefore, it would be interesting to propose a constrained control for safe reference tracking and a constrained observer for safe perturbation estimation in robots. Furthermore, the best gains in controls produce a balance between safe reference tracking and save energy consumption. Therefore, it would be interesting to propose a method to find the best gains. In this paper, an observer-based differential evolution constrained control is proposed for safe reference tracking in robots. The contributions are described as follows: (1) a constrained observer is proposed for safe perturbation estimation in robots, (2) a constrained control is proposed for safe reference tracking in robots, (3) a differential evolution optimizer is used to find the best gains in an observer-based constrained control, (4) the robust stability in an observer-based constrained control is assured, (5) the pseudo-code of an observer-based differential evolution constrained control is detailed. The proposed observer-based differential evolution constrained control is applied for safe reference tracking in two robots.

Discrete Switching Sequence Control for Converter Reference Tracking With Zero Steady-State Errors

This letter proposes a discrete switching sequence control (dSSC) to achieve zero steady-state error tracking for L-type converters. Considering switching characteristics of power electronics, a discrete-time model is established and dSSC is designed step-by-step. A strict mathematical proof ensures that the proposed dSSC achieves reference tracking with zero steady-state errors. Meanwhile, the theoretical discussion shows that the expected dynamics is obtained by choosing the control parameter of dSSC. Compared with classical methods such as pulse width modulation (PWM) and model predictive control (MPC), the proposed dSSC systemically analyzes and designs the dynamics and steady-state accuracy of converters, from a switching theoretical viewpoint. Simulations and experiments verify the effectiveness of the proposed dSSC.

Exponentially stable adaptive optimal control of uncertain LTI systems

SummaryA novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time‐invariant systems is proposed. Such an approach is based on the direct self‐tuning regulators design framework and the exponentially stable adaptive control technique developed earlier by the authors. Unlike the known solutions, a procedure is proposed to obtain a non‐overparametrized regression equation (RE) with respect to the unknown controller parameters from an initial RE of the LQ‐based reference tracking control system. On the basis of such result, an adaptive law is proposed, which under mild regressor finite excitation condition provides monotonous convergence of the LQ‐controller parameters to an adjustable set of their true values, which bound is defined only by the machine precision. Using the Lyapunov‐based analysis, it is proved that the mentioned law guarantees the exponential stability of the closed‐loop adaptive optimal control system. The simulation examples are provided to validate the theoretical contributions.

Robust model reference tracking control for high‐order descriptor linear systems subject to parameter uncertainties

AbstractThis paper investigates the robust model reference tracking control problem for high‐order descriptor linear systems (HODLS) subject to norm‐bounded parameter uncertainties. The problem is divided into two subproblems: a robust proportional plus derivative state feedback stabilization (RPPDSFS) problem and a robust feed‐forward compensation (RFFC) problem. In the presence of uncertainties, by using the controller consisting of RPPDSFS part and RFFC part, all the signals of the closed‐loop system are bounded. The latter is equivalent to seeking three coefficient matrices such that a series of linear matrix equations are satisfied, and simultaneously the effect caused by uncertainties is minimized. Based on the right coprime factorization, the RFFC problem is further converted into a minimization problem with a quadratic performance index and some linear constraints. Thereafter, a linear matrix equation that determines the optimal solution is achieved. The restrictive condition that the coefficient matrix of the augmented reference system is non‐defective is relaxed, which reduces the conservativeness. A numerical example and the application of a three‐axis dynamic flight motion simulator manifest the effectiveness and the practicability of the proposed algorithm.

Robust integral terminal sliding mode controller for model reference tracking control of matched/mismatched uncertain nonlinear time-delay systems

Robust integral terminal sliding mode controller for model reference tracking control of matched/mismatched uncertain nonlinear time-delay systems

Experimentally validated frequency shifted internal model cascade control strategy for magnetic levitation system

Magnetic levitation systems (MLS) provide friction-less, dependable, quick, and affordable operations in a variety of real life applications. One of the often-employed control strategies for the MLS is traditional cascade control, which uses internal model control (IMC)-based proportional–integral–derivative (PID) and proportional–integral (PI) controllers in its primary and secondary loops, respectively. Though this control structure succeeds in achieving levitation, it falls short in terms of set point tracking and disturbance rejection performance. To overcome this limitation, a bi-loop frequency shifted IMC proportional–derivative (FSIMC-PD) strategy is used in the primary loop retaining the conventional IMC-based PI controller in the secondary loop. Routh stability constraints are used to build the PD controller for stabilizing the MLS. Once the MLS is stabilized, an FSIMC-based PID controller for reference tracking is designed for the outer loop. In addition to simulation-based performance comparison of IMC-based PID-PI cascade scheme and the proposed scheme, experimental validation is also carried out on a laboratory scaled MLS setup. Furthermore, performance evaluation based on metrics like the integral of absolute error, integral of square error, integral of time weighted absolute error, total variation of the control signal and its maximum value are also carried out to vindicate the effectiveness of the suggested design. Robust stability analysis is carried out in addition to Nyquist stability considerations to vindicate that the FSIMC-based design is capable of yielding stable closed-loop response amid uncertainties in plant model parameters.

Fuzzy Small-Gain Approach for the Distributed Optimization of T-S Fuzzy Cyber-Physical Systems.

The distributed optimization problem (DOP) of Takagi-Sugeno (T-S) fuzzy cyber-physical systems is studied under the framework of weight-balanced graphs and quasistrongly connected characteristics. The objective is to drive the outputs of all agents to the optimal solution of a given global objective function regarded as the desired output, based on the partial information of the local objective functions. To this end, distributed optimal coordinators (DOCs) are used to generate optimal solutions of local objective functions that converge to the desired output, and fuzzy reference-tracking controllers are designed to ensure that all agents can track the optimal solutions. As novel technical results, two Lyapunov-based fuzzy input-to-state stability (ISS) small-gain theorems are proposed for the T-S fuzzy interconnected system. Thus, the overall closed-loop system is an interconnected system involving the modules of optimal coordinators and fuzzy tracking controllers with T-S fuzzy subsystems. The fuzzy ISS cyclic-small-gain theorem is applied to analyze the system stability. The DOP of T-S fuzzy cyber-physical systems is solved using the DOCs and fuzzy reference-tracking controllers through the fuzzy small-gain approach. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed method.

Distributed Optimization for Uncertain High-Order Nonlinear Multiagent Systems via Dynamic Gain Approach

In this article, we investigate the distributed output optimization for general uncertain high-order nonlinear multiagent systems (MASs), where nonlinear functions are constrained by a linear growth condition. The dynamic gain approach is utilized to cope with the influence of the unknown optimal solution. First, the distributed optimal coordinators (DOCs) with an adjustable parameter are constructed to steer the generated signals converging to the optimal solution. By developing the iterative design strategy, the dynamic reference-tracking controllers are then designed so that the output of each agent follows the generated value of coordinators, respectively. It is proved that all states are globally bounded, as well as the tracking error between the outputs and optimal solution can be bounded in a finite time by an arbitrarily small constant. Simulation studies demonstrate the validness of the main idea.

Reinforcement learning-based unknown reference tracking control of HMASs with nonidentical communication delays

Reinforcement learning-based unknown reference tracking control of HMASs with nonidentical communication delays

Markov data-based reference tracking control to tensegrity morphing airfoils

This paper presents a data-based control approach to the tensegrity morphing airfoils. We first collect the Markov parameters of the system based on the I/O tests. Then, using the Markov parameters, we formulate a data-based LQG controller for reference tracking. The proposed approaches are investigated on tensegrity morphing airfoils whose topology has been described in detail in this paper. A NACA 2412 airfoil with specified morphing targets is chosen to verify the developed design. The methods developed in this paper also apply to other tensegrity structures and structural control problems.

Distributed optimization for nonlinear multi-agent systems with an upper-triangular structure

This paper proposes a new two-step distributed optimization framework with a low-gain parameter for a class of upper-triangular nonlinear multi-agent systems. Specifically, distributed optimal coordinators are first established to generate signals close to the optimal solution by using the real-time values of gradient functions. Then, reference-tracking controllers are designed to make system outputs converge to the generated signals by coordinators. Correspondingly, system outputs can converge to the optimal solution by choosing the appropriate low-gain parameter. Finally, simulation results illustrate the proposed control scheme.