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"non-linear control"
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PSO‐SMADRC for altitude test facility intake pressure environmental simulation system
To address significant disturbances, including sudden air flow variation, model uncertainty, and unavoidable measurement noises during aeroengine transient tests in the intake environmental pressure simulation system (IEPSS), a sliding mode active disturbance rejection controller (SMADRC) is designed. The sliding mode control in SMADRC can deal with unmatched disturbances that are beyond the capabilities of the extended state observer (ESO) in ADRC. And the particle swarm optimization (PSO) algorithm is introduced to tune and optimize the controller parameters to further enhance the performance. To validate the effectiveness of the proposed method, simulations are conducted on the IEPSS software platform. The simulation results clearly demonstrate PSO‐SMADRC can reduce the mean squared error by 60.9%, the input oscillation by 68.7%, and the maximum deviation by 53.9%, compared with LADRC originally applied in the IEPSS. Sliding mode (SM) control method is adopted into the active disturbance rejection controller scheme (ADRC), formulating SMADRC for the intake environmental pressure simulation system. Then the PSO method for parameter tuning is also adopted for further improvement.
Journal Article
Optimal attitude consensus control for rigid spacecraft formation based on control Lyapunov functions
In this article, the optimal attitude consensus control problem of distributed spacecraft formation through local information exchange is solved in the presence of parameter uncertainty and disturbance. The attitude dynamics model of rigid spacecraft formation is established based on unit quaternion under an undirected graph. Then, the optimal attitude consensus control scheme based on control Lyapunov functions is adopted for rigid spacecraft formation. The approach to construct an appropriate Lyapunov function for multiple spacecraft is developed. Then the lumped disturbance is estimated by an extended state observer (ESO) and using the sliding mode control approach improves the robustness of the controller. The proposed optimal controller can not only ensure the global consensus convergence of the system but also make the preset performance index function achieve the minimum value. In addition, the mathematical proof is given for the stability analysis of the system by the Lyapunov stability theory. Finally, some simulations and comparisons are presented to demonstrate the validity and advantages of the proposed controller. The optimal attitude consensus control problem of rigid spacecraft formation spacecraft is investigated based on a control Lyapunov functions for the first time. The approach to construct appropriate Lyapunov functions is given for the multiple spacecraft system. An extended state observer (ESO) is applied to estimate the uncertainty and external disturbance and using the sliding mode control approach improves the robustness of the controller. Both theoretical analysis and simulation results are presented to demonstrate the validity and advantages of the proposed method.
Journal Article
Design an omnidirectional autonomous mobile robot based on non‐linear optimal control to track a specified path
This paper explores two non‐linear control techniques for designing an effective control system for an omnidirectional autonomous mobile robot with four Mecanum wheels. Due to the unique wheel structure and four separate wheels, the robot has non‐linear dynamics, multiple inputs and outputs. The first technique uses the state‐dependent Riccati equation (SDRE) to address optimal non‐linear control while considering energy and time constraints. The second technique, using an intermediate variable θ $\\theta $ , has expanded the Hamilton‐Jacobi‐Belman equation in terms of the power series. Consequently, these equations are reduced to a set of recursive Lyapunov algebraic equations, leading to a closed‐form solution for solving the non‐linear optimal control problem. Finally, the maneuverability and path‐tracking capability of the robot are examined by highlighting the non‐linear term through numerical simulation. This paper explores two non‐linear control techniques for designing an effective control system for an omnidirectional autonomous mobile robot with four Mecanum wheels. Due to the unique wheel structure and four separate wheels, the robot has non‐linear dynamics and multiple inputs and outputs.
Journal Article
Finite‐time tracking control of disturbed non‐holonomic systems with input saturation and state constraints: Theory and experiment
This article investigates the finite‐time tracking control problem for disturbed non‐holonomic systems with input saturation and state constraints. Input saturation is ensured by utilizing saturated state feedback and designing auxiliary variables. A rigorous design procedure, which combines barrier Lyapunov function‐based backstepping and neural networks, is introduced to satisfy state constraints and overcome the influence of lumped disturbances. A finite‐time filter is developed to address the explosion of complexity problem. Together with relay switching, the designed saturated controller guarantees that the tracking errors converge to arbitrarily small neighbourhoods around zero within a finite time. Stability analysis indicates that all closed‐loop system signals maintain bounded, and the desired input and state constraints are not violated throughout the control process. To demonstrate the effectiveness of the proposed approach, simulation and experimental results on a wheeled mobile robot are presented. This article presents a systematic NN‐based finite‐time practical tracking control for disturbed non‐holonomic systems subject to input saturation and state constraints. By dexterously using relay switching, dynamic surface control and finite‐time filters, it leads to a control process that is computationally simple.
Journal Article
Policy iteration for H∞ control of polynomial time‐varying systems
This paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time‐varying H∞ control problem with the ADP approach. Considering the time as an independent variable for sum‐of‐squares (SOS) optimization problems, an SOS‐based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed‐loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H∞ controller with a smaller disturbance attenuation coefficient, a two‐loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples. In this paper, the H∞ control problem is solved for polynomial time‐varying systems. A sum‐of‐squares‐based approximate dynamic programming method is proposed to solve this problem. The convergence and stability properties of the proposed algorithm are stated and proven.
Journal Article
Estimation of shape memory alloy actuator dynamics to design reduced‐order position controller with input saturation
This study focuses on the precise model estimation for a position control problem actuated by a shape memory alloy (SMA) wire. Because the hysteresis characteristic of SMA introduces complexities in system modelling and adds degrees of freedom, a model with reduced order is implemented for controller design. This model is online updated by calculating a complementary term from the measured data to compensate for the SMA actuator dynamics and other parametric uncertainties. The position controller, derived from the formulated reduced‐order model, adapts itself to real conditions and is cost‐effective due to the use of only displacement sensor. The saturation of the control input is modelled within the structure of a constrained optimization problem solved by Karush–Kuhn–Tucker theorem. The boundedness of mean and covariance of tracking error and its derivative is demonstrated by stochastic analysis. The experimental results conducted on a platform incorporating a SMA wire show the efficiency of the proposed system in precisely controlling the position by admissible voltage range. The comparative results with a sliding mode controller indicate higher accuracy for the proposed controller to reduce the effect of uncertainties. This study focuses on the precise model estimation for a position control problem actuated by a shape memory alloy wire made of nickel‐titanium. The position controller, designed from the constructed reduced‐order model, adapts itself to real conditions and is cost‐effective due to the use of only a displacement sensor.
Journal Article
Interval compression‐based model‐free control algorithm for reducing actuator execution frequency
The complexity of real‐world systems poses challenges to model‐based control, sparking significant interest in model‐free control methods. By depending exclusively on the system's input–output data, the proposed method eliminates the need to construct intricate internal system models. The implementation is straightforward, can satisfy bounded control inputs, and allows for arbitrary adjustment of the actuator's execution frequency. The proposed method establishes an iterative mechanism under the constraint of bounded control inputs. It guarantees the algorithm's convergence by ensuring the continuous narrowing of the control interval. Furthermore, the update conditions within the iterative strategy can adapt to extremely low and continuously adjusting actuator execution frequencies. The bounded stability of the control method is proven using the continuity definition of functions. Its effectiveness and feasibility are validated through simulation and experimental verification. This paper presents a novel model‐free control algorithm that relies solely on the system's inputs and outputs. The implementation is straightforward, can satisfy bounded control inputs, and allows for arbitrary adjustment of the actuator's execution frequency.
Journal Article
Disturbance Observer Based Adaptive Control Scheme for Synchronization of Fractional Order Chaotic Systems With Input Delay
In recent years, considerable attention has been attracted to the synchronization of chaotic systems due to their important applications. However, fractional order non‐linear chaotic systems face critical challenges, particularly from input delays and external disturbances in practical applications. In this paper, a robust synchronization method based on state prediction is introduced to address these challenges. First, a novel adaptive disturbance observer for fractional order systems is proposed, ensuring that disturbance estimation is achieved within an arbitrary time. The effects of disturbances are mitigated by this observer, which plays a crucial role in synchronization scheme design. Second, an arbitrary time exponential sliding mode controller that integrates state prediction and the disturbance observer is presented to handle input delay in fractional chaotic systems subjected to external disturbances. Third, a control scheme incorporating state prediction and sliding mode control is developed to address chaos synchronization for fractional systems with time varying input delays and disturbances. Additionally, an upper bound for input delay is established, demonstrating that if the delay remains below this threshold, the synchronization error is constrained. The efficacy and practical applicability of the proposed synchronization scheme are confirmed through simulation studies and experimental validation on a real‐time Speedgoat machine. In this paper, an adaptive arbitrary time controller is proposed for the synchronization of fractional order chaotic systems. An adaptive disturbance observer is presented, capable of exponentially estimating unknown disturbances in arbitrary time. An adaptive predictor based synchronization scheme using a disturbance observer is proposed for synchronizing fractional‐order chaotic systems with input delay.
Journal Article
Hybrid finite‐time fault‐tolerant consensus control of non‐linear fractional order multi‐agent systems based on fault detection and estimation
This paper addresses the problem of achieving finite‐time fault‐tolerant consensus control for a class of non‐linear fractional‐order multi‐agent systems (NFO‐MAS) using finite‐time fault detection and estimation, as well as a finite‐time state observer. To achieve this, a specific lemma is utilized to rewrite the high‐order model of NFO‐MAS as a lower‐order NFO unique system. By employing new identification rules and introducing a fault estimation method, both the state variables and faults of the agents are estimated within a finite time. Subsequently, a finite‐time sliding mode control law is designed based on the estimated fault and the state variables obtained from the proposed finite‐time observer to achieve consensus within a finite time for the fractional‐order non‐linear MAS. The stability of the fault estimation, state observer, and consensus controller is proven using the finite‐time Lyapunov theory. The effectiveness of the proposed approach is demonstrated through numerical simulations. In this paper, the problem of finite time fault detection and estimation along with achieving finite time consensus is investigated for a class of fractional order multi‐agent systems with non‐linear dynamics. The stability proof of the fault estimation, state observer, and consensus controller is presented using the Lyapunov theory.
Journal Article