L. Dorcak, I. Petras, I. Kostial, J. Terpak
In this paper we will present a mathematical description and analysis of a fractional-order regulated system in the state space and the state-space controller design based on placing the closed-loop poles on the complex plane. Presented are the results of simulations and stability investigation of this system.
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In this paper we present the mathematical description and analysis of a fractional-order regulated system in the state space. A little historical background of our results in the analysis and synthesis of the fractional-order dynamical regulated systems is given. The methods and results of simulations of the fractional-order system described by a state space equation equivalent to three-member fractional-order differential equation with a fractional-order $PD^δ$ regulator are then presented. The possibility of investigating the stability of such systems is also considered.
This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems and fractional-order controllers. In the next section we describe how to apply the fractional controller on control systems.
Novel closed-loop controllers for fractional linear quadratic tracking systems
本文提出了一种新颖的闭环控制器方法，用于解决分数线性二次跟踪系统的最优控制问题，并通过示例验证了其有效性。
This paper deals with the fractional-order controllers and their possible hardware realization based on PIC microprocessor and numerical algorithm coded in PIC Basic. The mathematical description of the digital fractional -order controllers and approximation in the discrete domain are presented. An example of realization of the particular case of digital fractional-order PID controller is shown and described.
This paper is concerned with model reference adaptive controller design for a class of nonlinear fractional order systems. Recent works on this topic rarely include direct methods and they are mostly based on indirect methods where the frequency distributed model is used to prove the stability of the closed loop system. Since the chain rule cannot be applied in fractional derivations, in order to prove the lyapunov stability here fractional inequalities are used. Finally, by means of a numerical example, the controller performance is demonstrated.
This paper deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractional order linear time invariant (FO-LTI) systems by means of linear matrix inequalities (LMIs). Our purpose is to design a low order controller that stabilizes the fractional-order linear system in the presence of model uncertainties. No limitative constraint on the state space matrices of the uncertain system is assumed in the design procedure. Furthermore, adopting the most complete model of linear controller, with direct feedthrough parameter, does not disturb the LMI-based approach …
A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PIλDμ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equiva…
This paper proposes the application of fractional-order PID (FOPID) controller for output voltage control of boost converters. For this purpose, parameters of the FOPID controller are calculated such that the Integral Absolute Error (IAE) of the variations of the output voltage is minimized. Since the search space is very large in dealing with such an optimization problem, the Artificial Bee Colony (ABC) algorithm is used for optimal tuning the parameters of the FOPID controller. Simulations, which are performed by using the complete non-minimum phase model of the boost converter, confirm the …
The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index…
This paper presents a fractional-order framework for control of blood pressure. A new perspective is explored to control the blood pressure in lieu of the conventional control framework. A multi-variable scenario is adopted to control two outputs: Mean Arterial Blood Pressure (MABP) and Cardiac Output (CO) simultaneously.
This paper is concerned with a linear fractional representation approach to the synthesis of linear coherent quantum controllers for a given linear quantum plant. The plant and controller represent open quantum harmonic oscillators and are modelled by linear quantum stochastic differential equations. The feedback interconnections between the plant and the controller are assumed to be established through quantum bosonic fields. In this framework, conditions for the stabilization of a given linear quantum plant via linear coherent quantum feedback are addressed using a stable factorization appro…
Whale Optimization Algorithms based fractional order fuzzy PID controller for Depth of Anesthesia
针对麻醉深度控制中的非线性与患者生理参数不确定性，提出用WOA优化参数的FOFPID与FOPID，并基于8例患者的药效动力学和药代动力学模型验证FOFPID性能更优。
Performance Comparison of Optimal Fractional Order Hybrid Fuzzy PID Controllers for Handling Oscillatory Fractional Order Processes with Dead Time
本文研究了基于模糊逻辑的PID控制器，通过不同形式的模糊推理组合设计了分数阶混合模糊PID控制器，用于处理具有死区的分数阶过程，比较了不同控制器结构的性能。
Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PIλDμ Controllers to Handle a Class of Fractional Order Systems
本文提出基于LQR技术的分数阶PID或PIλDμ控制器时间域最优整定方法，用于处理具有单非整数阶元件的分数阶系统，通过优化权值矩阵提升系统响应性能。
The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parametrization of all robustly regulating controllers. The main results are formulated with minimal assumptions and without using coprime factorizations, thus guaranteeing their applicability with a very general class of systems. In addition to theoretical results, the design of robust controllers is addressed. The results are il…
This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm design for low-order controller based on direct Lyapunov approach is proposed. In the presented algorithm the conditions containing the bilinear variables are decoupled into separate conditions without imposing equality constraints or considering an iterative search of the controller parameters. There is no any limiting constraint on the state space matrices and…
The internal model principle states that all robustly regulating controllers must contain a suitably reduplicated internal model of the signal to be regulated. Using frequency domain methods, we show that the number of the copies may be reduced if the class of perturbations in the problem is restricted. We present a two stage design procedure for a simple controller containing a reduced order internal model achieving robust regulation. The results are illustrated with an example of a five tank laboratory process where a restricted class of perturbations arises naturally.
Discrete-Time Fractional-Order PID Controller: Definition, Tuning, Digital Realization and Experimental Results
本文提出离散时间分数阶PID控制器，讨论其特性与应用，开发两种调参方法，展示其在复杂控制问题中的高性能表现。
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A practical example for modelling the fractional-order control loop is shown and obtained results are discussed in conclusion.
In this paper, a fractional Lotka-Volterra mathematical model for a bioreactor is proposed and used to fit the data provided by a bioprocess known as continuous fermentation of Zymomonas mobilis. The model contemplates a time-delay $τ$ due to the dead-time in obtaining the measurement of biomass $x(t)$. A Hopf bifurcation analysis is performed to characterize the inherent self oscillatory experimental bioprocess response. As consequence, stability conditions for the equilibrium point together with conditions for limit cycles using the delay $τ$ as bifurcation parameter are obtained. Under the …
Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization
本文提出一种基于混沌多目标优化的分数阶PID控制器设计方法，用于AVR系统，通过改进的NSGA-II算法优化控制器参数，保证系统稳定性和鲁棒性。
This paper addresses the consensus of a class of uncertain nonlinear fractional-order multi-agent systems (FOMAS). First a fractional non-fragile dynamic output feedback controller is put forward via the output measurements of neighboring agents, then appropriate state transformation reduced the consensus problem to a stability one. A sufficient condition based on direct Lyapunov approach, for the robust asymptotic stability of the transformed system and subsequently for the consensus of the main system is presented. Additionally, utilizing S-procedure and Schur complement, the systematic stab…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways for modelling of fractional-order systems are illustrated with a numerical example and obtained results are discussed in conclusion.
The paper investigates a new hybrid synchronization called modified hybrid synchronization (MHS) via the active control technique. Using the active control technique, stable controllers which enable the realization of the coexistence of complete synchronization, anti-synchronization and project synchronization in four identical fractional order chaotic systems were derived. Numerical simulations were presented to confirm the effectiveness of the analytical technique.
A class of non-linear fractional-order system stabilisation via fixed-order dynamic output feedback controller
本文研究了一类非线性分数阶系统的鲁棒稳定化问题，采用线性矩阵不等式（LMIs）方法设计了基于直接Lyapunov方法的低阶控制器系统稳定化算法。该算法将包含双线性变量的条件分解为独立条件，无需施加等式约束或考虑控制器参数的迭代搜索。没有对状态空间矩阵施加任何限制，并假设了最完整的输出反馈控制器。仿真结果证明了所提设计的有效性和简便性。
This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of dynamic properties in fractional- and integer-order systems with a controller, designed for an integer-order system as the best approximation to given fractional-order system. Other open questions are pointed out, which should be answered in this area of research.
This paper addresses the design of finite-dimensional feedback control laws for linear discrete-time fractional-order systems with additive state disturbance. A set of sufficient conditions are provided to guarantee convergence of the state trajectories to an ultimate bound around the origin with size increasing with the magnitude of the disturbances. Performing a suitable change of coordinates, the latter result can be used to design a controller that is able to track reference trajectories that are solutions of the unperturbed fractional-order system. To overcome the challenges associated wi…
Control Strategy for Anaesthetic Drug Dosage with Interaction Among Human Physiological Organs Using Optimal Fractional Order PID Controller
本文提出利用最优分数阶PID控制器优化麻醉药物输注模型，通过粒子群优化算法确定控制器参数，实现更高效的药物输注控制，减少药物用量并提高系统鲁棒性。
For a partially unknown linear systems, we present a systematic control design approach based on generated data from measurements of closed-loop experiments with suitable test controllers. These experiments are used to improve the achieved performance and to reduce the uncertainty about the unknown parts of the system. This is achieved through a parametrization of auspicious controllers with convex relaxation techniques from robust control, which guarantees that their implementation on the unknown plant is safe. This approach permits to systematically incorporate available prior knowledge abou…
Robust Stabilization of Fractional-order Interval Systems via Dynamic Output Feedback: An LMI Approach
本文研究了分数阶线性时不变区间系统的鲁棒动态输出稳定化问题，提出基于LMI的设计方法，通过设计鲁棒动态输出反馈控制器实现系统渐近稳定，并通过数值实例验证了方法的有效性。
This paper is concerned with mismatched disturbance rejection control for the second-order discrete-time systems.Different from previous work, the controllability of the system is applied to design the disturbance compensation gain, which does not require any coordinate transformations. Via this new idea, it is shown that disturbance in the regulated output is immediately and directly compensated in the case that the disturbance is known. When the disturbance is unknown, an extra generalized extended state observer is applied to design the controller. Two examples are given to show the effecti…
On the Mixed H2/H-infinity Loop Shaping Trade-offs in Fractional Order Control of the AVR System
本文研究了分数阶PID控制器在AVR系统中的频域设计，通过系统范数结合多目标优化算法，分析了设定点跟踪、负载扰动和噪声抑制等性能指标的权衡。
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an asymptotically stable equilibrium point of the controlled system. We employ a finite-dimensional approximation of the original infinite-dimensional dynamics for which the approximation error can become arbitrarily small. We use the approximate dynamics to design a tube-based model predictive controller which steers the system state to a neighbourhood of the origin o…
Multi-objective LQR with Optimum Weight Selection to Design FOPID Controllers for Delayed Fractional Order Processes
本文提出基于LQR技术的分数阶PID控制器最优折中设计方法，通过两个冲突的时间域控制目标解决有延迟分数阶系统的控制问题，并通过数值模拟验证了两种延迟处理技术的优劣及负载扰动抑制能力。
As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that such non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of nonminimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and the gain margin without leading to internal…
Kriging based Surrogate Modeling for Fractional Order Control of Microgrids
本文研究了分数阶控制器在微电网中的应用，采用克里格代理建模技术优化分数阶PID参数，通过数值模拟验证了方法的有效性，并与传统进化优化技术进行比较。
Fractional Order Fuzzy Control of Nuclear Reactor Power with Thermal-Hydraulic Effects in the Presence of Random Network Induced Delay and Sensor Noise having Long Range Dependence
本文提出一种分数阶模糊PID控制器，用于在随机网络延迟和长程依赖传感器噪声存在下控制核反应堆功率，通过遗传算法优化实现鲁棒性。
Fractional Order Load-Frequency Control of Interconnected Power Systems Using Chaotic Multi-objective Optimization
本文研究了使用混沌多目标优化设计分数阶PI控制器以提高互联电力系统的负荷频率控制性能，通过比较不同优化算法的解质量和计算时间，验证了FOPID控制器在处理冲突时间域设计目标方面的优势。
Fractional Order AGC for Distributed Energy Resources Using Robust Optimization
本文研究了分数阶自动发电控制在电力系统频率振荡阻尼中的应用，采用分布式能源发电，通过鲁棒优化技术优化控制器参数，提升系统性能。
Fractional Order Fuzzy Control of Hybrid Power System with Renewable Generation Using Chaotic PSO
本文提出一种分数阶模糊控制方案，结合混沌PSO优化，提升混合电力系统在非线性工况下的性能与鲁棒性。
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for asymptotically stabilizing such uncertain fractional-order systems is designed. The derived stabilization conditions are in LMI form. Simulation results of two numerical examples illustrate that the proposed sufficient theoretical results are applicable and effective for tackling robust stabilization problems. Keywords: Fractional-order system, nonlinear unc…
In this paper an offset-free model predictive control scheme is presented for fractional-order systems using the Grünwald-Letnikov derivative. The infinite-history fractional-order system is approximated by a finite-dimensional state-space system and the modeling error is cast as a bounded disturbance term. Using a state observer, it is shown that the unknown disturbance at steady state can be reconstructed and modeling errors and other persistent disturbances can be attenuated. The effectiveness of the proposed controller-observer ensemble is demonstrated in the optimal administration of an a…
A Separation Principle for Discrete-Time Fractional-Order Dynamical Systems and its Implications to Closed-loop Neurotechnology
本文提出了一种适用于离散时间分数阶动力系统的分离原理，该原理允许在闭环设置中独立设计控制器和状态估计器，从而确保有效的估计和控制，并通过神经生理数据验证了该原理的应用。
The dual iteration was introduced in a conference paper in 1997 by Iwasaki as an iterative and heuristic procedure for the challenging and non-convex design of static output-feedback controllers. We recall in detail its essential ingredients and go beyond the work of Iwasaki by demonstrating that the framework of linear fractional representations allows for a seamless extension of the dual iteration to output-feedback designs of practical relevance, such as the design of robust or robust gain-scheduled controllers. In the paper of Iwasaki, the dual iteration is solely based on, and motivated b…
We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the Routh-Hurwitz and the Matignon stability criteria, we analyze the novel chaotic fractional order system and propose a control methodology that is better than the nonlinear counterparts available in the literature, in the sense of simplicity of implementation and analysis. A scalar control input that excites only one of the states is proposed, and sufficient condi…
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization theorem is also included, where sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. Utilizing efficient lemmas, the stability and stabilization theorems are proposed in the form of LMIs, which is more suitable to check due to various existing efficient convex opt…
This paper considers a class of space fractional partial differential equations (FPDEs) that describe gas pressures in fractured media. First, the well-posedness, uniqueness, and the stability in $L_(\infty{R})$of the considered FPDEs are investigated. Then, the reference tracking problem is studied to track the pressure gradient at a downstream location of a channel. This requires manipulation of gas pressure at the downstream location and the use of pressure measurements at an upstream location. To achiever this, the backstepping approach is adapted to the space FPDEs. The key challenge in t…
Multi-objective Active Control Policy Design for Commensurate and Incommensurate Fractional Order Chaotic Financial Systems
本文针对分数阶金融系统设计多目标主动控制策略，通过多目标优化框架选择控制器参数，分析了渐近稳定性和多目标之间的权衡关系，并对比了三种多目标优化算法的性能。
Fractional Calculus in Optimal Control and Game Theory: Theory, Numerics, and Applications -- A Survey
本文综述了分数阶微积分在最优控制与博弈论中的理论、数值方法及应用，探讨了记忆效应系统建模、分析及控制设计方法，并分析了不同计算方法的精度与复杂度权衡。
Performance enhancement of non-minimum phase feedback systems by fractional-order cancellation of non-minimum phase zero on the Riemann surface: New theoretical and experimental results
本文提出通过分数阶预补偿器抵消非最小相位零点，提高系统增益和相位裕度，同时保持开环带宽，从而简化控制问题。
Continuous Order Identification of PHWR Models Under Step-back for the Design of Hyper-damped Power Tracking Controller with Enhanced Reactor Safety
本文针对500 MWe压水堆建立了离散时间高整数阶线性传递函数模型，通过最小二乘估计法在八个不同运行点识别了非线性核反应堆模型，并利用合成频域数据识别了分数阶模型，以设计连续阶PID类补偿器，实现宽范围运行条件下的功率跟踪，提高反应堆安全性。
Robust Attitude Control of Nonlinear UAV Dynamics with LFT Models and $\mathcal{H}_\infty$ Performance
本文研究了在风扰和陀螺噪声下，基于LFT模型和H_∞性能的鲁棒控制器在多旋翼姿态调节中的应用，通过非线性仿真验证了其在恶劣风扰下的优越性能。
Design of a Fractional Order Phase Shaper for Iso-damped Control of a PHWR under Step-back Condition
提出一种分数阶相位整形器结合PID控制器的方法，实现加压重水反应堆在阶跃回退时的等阻尼闭环响应，以优化功率下降的动态性能。
Adaptive backstepping control for FOS with nonsmooth nonlinearities
针对分数阶系统的输入饱和与死区等非光滑非线性问题，提出通过引入中间变量分解控制输入的自适应反步控制方法，实现扰动估计与饱和补偿，保证输出渐近跟踪参考信号。
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