High Order Differential Feedback Controller Research Articles

Fractional High-Order Differential Feedback Controller Based on Meta-Heuristic Algorithms for Automatic Voltage Regulator

In this study, optimally parameter tuning of fractional high-order differential feedback controller (FHODFC) for an automatic voltage regulator (AVR) system regulating the terminal voltage of the synchronous generator is presented. Recently developed meta-heuristic optimization techniques named honey badger algorithm (HBA) and gorilla troops optimizer (GTO) have been employed for the first time in order to optimally determine ten different parameters of the FHODFC. The performance of the proposed controllers, that is, HBA-FHODFC and GTO-FHODFC, is analyzed in terms of transient and steady state responses, and robustness against uncertainties and external disturbances. In addition, their performance is compared to a FHODFC of which parameters were tuned by using particle swarm optimization algorithm in a previous study. The results indicate that the proposed HBA-FHODFC and GTO-FHODFC controllers provide zero overshoot and better results in terms of settling time and objective function then the PSO tuned FHODFC. Therefore, the proposed controllers can be used as an effective method in the AVR system.

Improved high order differential feedback control of quadrotor UAV based on improved extended state observer

Quadrotor unmanned aerial vehicle (QUAV) system is nonlinear, strongly coupled, and sensitive to unknown disturbances and uncertainties. The uncertainty, disturbance, and even unknown model function are the undesired force acting on the QUAV, so they must be totally estimated online. The ideal control scheme is that the total estimation is feedback in the opposite direction to the controller to compensate the model error or counteract the force caused by the unknown model and disturbance. An improved extended state observer (IESO), also called an improved high-order differentiator (IHOD), is designed to estimate the unknown model and disturbance of the QUAV. It is proved that the IESO is one type higher than the traditional ESO. Consequently, the estimation accuracy of IESO is higher than that of the ESO at the same bandwidth, and is verified through some typical functions. The IESO estimations for 2nd-order derivative of reference input and the total unknown model function are fed back to compensate the undesired force in opposite direction, and then an improved high-order differential feedback controller (IHODFC) is designed with the assigned closed-loop poles. The proof of the stability of the closed-loop system controlled by the IHODFC is given. The performance is verified by the tests using the Pixhawk-based DJI F450 frame experimental verification platform. The IHODFC superiority is demonstrated by comparing the classic model-free controller PID and active disturbance rejection control (ADRC).

Chaos control of small-scale UAV helicopter based on high order differential feedback controller

ABSTRACT The small-scale unmanned aerial vehicle (UAV) helicopter has a complex structure, strong nonlinearity, coupling and open-loop instability, making it shake violently and even produce chaotic oscillation under wind disturbances and improper configuration. The chaotic angular velocity dynamic model of the UAV helicopter is analysed via two cases. The sliding mode controller (SMC) relying on the linearised model, the PID controller, and the high order differential feedback controller (HODFC) not relying on the model are designed. The closed-loop system stability under both SMC and HODFC are analysed. The HODFC with a control filtering can actively reject the disturbance and uncertainty. The control performance of HODFC is superior to SMC and PID controllers. The SMC and HODFC can stabilise the chaotic oscillations of UAV helicopter’s angular velocity, whereas the PID controller fails, and the HODFC control effect is superior to the SMC for disturbance rejection, uncertainty and linearisation bias in steady-state errors.

High-Order Differential Feedback Control for Quadrotor UAV: Theory and Experimentation

A model-independent control strategy called high-order differential feedback control (HODFC) is applied to a quadrotor unmanned aerial vehicle (QUAV) based on a semi-autopilot indoor optical positioning system. The affine system form of the quadrotor model is provided to facilitate the design of the HODFC. A fifth-order high order differentiator (HOD) is introduced to estimate with high precision the derivatives of the reference input and the QUAV system’s states. A filtering signal of the control output is incorporated in the control law to overcome the system model’s unknown part in the HODFC scheme. The stability of both the HODFC and the HOD are proved. The physical and straightforward parameters are provided to make the HODFC scheme for the QUAV easy to operate. The real-time trajectory tracking experiments with varied reference trajectories and disturbances are carried out to illustrate the superior performance of the HODFC versus the proportional-integral-derivative (PID) method, in terms of the mean of absolute error, the integral of absolute error and the integral of the time-weighted absolute error. The results also demonstrate that the HODFC has superiority in static and dynamic trajectory tracking, especially when the system is disturbed.

Application of Non-Model Dependent Hybrid Higher-Order Differential Feedback Controller on Crane System

Shipping of goods from one place to another in industries is commonly achieved with crane system. But such movement of the system results in undesirable sway which degrades the accuracy and safety. In this paper, hybrid control schemes of the model-dependent and non-model dependent filters and controllers are proposed for precise trolley position control and sway suppression of the crane systems. Output based filter (OBF) was designed usingtheoutputofthesystem,soitdoesnotdependonthemodelofthesystemwhiletimedelayfilters(TDF)were designed using the model parameters (i.e. natural frequency and damping ratio), in which Zero Vibration (ZV) and zero vibration derivative (ZVD) were considered. These depend on the model of the system and these filters are for sway suppression of the payload. In addition, proportional integral derivative (PID) controller and higher order differential feedback controller (HODFC) were incorporated with each filter separately for precise trolley position control. Based on the analysis of the simulation results, it was observed that a precise tracking of the payload was achievedwithpercentageoftheswayreductionofthehybridcontrollersasfollows;PID-ZV=76%,PID-ZVD=88%, PID-OBF=96% HODFC-ZV=77%, HODFC-ZVD=79% and HODFC-OBF=95%. The hybrid controllers shown precise tracking and higher sway reduction control. But HODFC-OBF is a model-free control schemes, thus more robust.

Design of an Optimized Fractional High Order Differential Feedback Controller for Load Frequency Control of a Multi-Area Multi-Source Power System With Nonlinearity

Load frequency control (LFC) is one of the essential process in interconnected power systems. To provide high quality, reliable and stable electrical power, designed controller should perform satisfactorily, i.e. suppress area frequency and tie-line power deviations. Within this scope, in this study, a high order differential feedback controller (HODFC) and a developed fractional high order differential feedback controller (FHODFC) are proposed for LFC problem in multi-area power systems for the first time. The gains of the HODFC and FHODFC are optimally tuned by particle swarm optimization (PSO) algorithm aiming to minimize integral of time weighted absolute error (ITAE) performance index. The superiority of the developed FHODFC are verified by comparing reported controller structures in the recent state-of-the-art literature and HODFC for two identical non-reheat thermal power system and two-area multi-source power system consisting of gas, thermal and hydro generation units with/without consideration of HVDC link. To test the robustness of the designed controllers, varying system parameters and loading conditions are investigated. The governor dead band (GDB) and generation rate constraint (GRC) limitations are also considered for the system under study to examine non-linearity handling success of the proposed controllers. Performance results indicate that the developed FHODFC provides better dynamic response and robustness than other published techniques under nonlinearities, random load pattern, and variations in system parameters and loading conditions.

High order differential feedback controller design and implementation for a Stewart platform

Stewart platform or other parallel manipulators with a Stewart structure are commonly used in flight simulators, surgical operations, medical rehabilitation processes, machine tools, industrial applications, etc. Therefore, researchers have paid attention to position control of these manipulators in addition to their design and development process. In this study, a developed Stewart platform and its inverse kinematic analysis are presented first. Then, a model-free control scheme called a high order differential feedback controller scheme is designed for the Stewart platform in order to improve its trajectory tracking performance and robustness against to different reference trajectories. Real-time trajectory tracking experiments with varied reference trajectories are carried out to show the robustness and effectiveness of the high order differential feedback controller scheme compared to the traditional proportional–integral–derivative controller of which the parameters are optimally tuned. The obtained visual trajectory tracking results and numerical performance results based on error-based performance measurement metrics such as integral of absolute error, integral of squared error, and integral of time-weighted absolute error are provided for both the proposed high order differential feedback controller scheme and the optimal tuned proportional–integral–derivative controller. Experimental results show that the proposed high order differential feedback controller scheme is more robust than the proportional–integral–derivative controller. Furthermore, the high order differential feedback controller scheme has superiority in both transient and steady-state responses and even the parameters of the proportional–integral–derivative controller are optimally tuned.

Fractional High-Order Differential Estimator and Feedback Controller Design for a Single-Input–Single-Output Affine Chaotic System

AbstractControl of chaos generally refers to realize a desired behavior of chaotic system output and its states. In this manner, we design a fractional high-order differential feedback controller (FHODFC) to increase tracking performance of a nonlinear system output and its differentials for a desired trajectory signal. The proposed controller is based on fractional calculus and high-order extracted differentials of error signal. The suggested fractional approach is applied to a single-input–single-output affine Duffing-Holmes dynamical system in matlab/simulink environment. Duffing-Holmes system is analyzed for two different problems: estimation and control problems. The simulation results clearly demonstrate superior dynamic behavior of the FHODFC compared to the classical high-order differential feedback controller (HODFC) version for both estimation and control problems.

Design of an optimized fractional high-order differential feedback controller for an AVR system

This paper proposes a high-order differential feedback controller (HODFC) and a fractional high-order differential feedback controller (FHODFC) to improve regulating ability of a commonly used automatic voltage regulator (AVR) system. In controller design process, particle swarm optimization (PSO) algorithm is utilized together with analytic approach. A constrained optimization problem is solved by PSO algorithm considering a specified objective function to obtain a less setting time, percentage overshoot, and regulation error. In order to test the performance of the proposed controllers, optimally tuned (proportional–integral–derivative) PID controllers available in the literature are implemented. The results demonstrate that the proposed FHODFC provides less percentage overshoot, settling time, rise time, and peak time than other proposed controllers, i.e., HODFC. Furthermore, the performance of the several available PID controllers is significantly worse than both of the proposed controllers in terms of transient response characteristics.

Trajectory and Vibration Control of a Single-Link Flexible-Joint Manipulator Using a Distributed Higher-Order Differential Feedback Controller

The trajectory tracking in the flexible-joint manipulator (FJM) system becomes complicated since the flexibility of the joint of the FJM superimposes vibrations and nonminimum phase characteristics. In this paper, a distributed higher-order differential feedback controller (DHODFC) using the link and joint position measurement was developed to reduce joint vibration in step input response and to improve tracking behavior in reference trajectory tracking control. In contrast to the classical higher-order differential (HOD), the dynamics of the joint and link are considered separately in DHODFC. In order to validate the performance of the DHODFC, step input, trajectory tracking, and disturbance rejection experiments are conducted. In order to illustrate the differences between classical HOD and DHODFC, the performance of these controllers is compared based on tracking errors and energy of control signal in the tracking experiments and fundamental dynamic characteristics in the step response experiments. DHODFC produces better tracking errors with almost same control effort in the reference tracking experiments and a faster settling time, less or no overshoot, and higher robustness in the step input experiments. Dynamic behavior of DHODFC is examined in continuous and discontinues inputs. The experimental results showed that the DHODFC is successful in the elimination of the nonminimum phase dynamics, reducing overshoots in the tracking of such discontinuous input trajectories as step and square waveforms and the rapid damping of joint vibrations.

Hyper-chaos encryption using convolutional masking and model free unmasking

In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative.

Higher-order differential feedback control of a flexible-joint manipulator

This paper presents a new control scheme for a flexible-joint manipulator using a higher-order differential feedback controller (HODFC). Two higher-order differential operators were designed and used to perform observations of both the reference input and the output of the manipulator, together with the requisite state derivatives. An error-based state-space model was then derived from the observed states. A pole-placement procedure with filtering was then used to drive the system error to zero. Practical controller implementation was carried out using the dSPACE real-time prototyping system. For the comparative validation of the performance of the HODFC with respect to a classical proportional-integral and proportional-integral-derivative (PID) controller, several experiments were undertaken. In these experiments, the step input, sine waves, kane trajectories, and external disturbances were applied to the controlled flexible-joint manipulator. The results showed that the HODFC controller eliminated disturbances within one second of occurrence, and produced superior kane trajectory tracking. Moreover, based on the root-mean-square tracking error criterion, the HODFC was observed to track both the sine and kane function trajectories with one-fourth the tracking error obtained with classical PID control.

Adaptive high order differential feedback control for affine nonlinear system

In this paper, we present an adaptive high order differential feedback controller (HODFC) which is a kind of model-free control diagram. The proposed HODFC achieves the objective that the system output and its high differentials approximate the given reference input and its high order differentials, respectively. Stability, convergence, and robustness of the closed-loop system are also studied. Moreover, a kind of linearized decoupling control is obtained for MIMO system by a multivariable HODFC.

Model-free control of affine chaotic systems

In practice, there are many chaotic systems whose models are usually unknown or partially unknown. However, the majority of control schemes focus on model-dependent techniques. The model-free controlling problem for affine chaotic systems is investigated in this Letter. An adaptive higher-order differential feedback controller (HODFC), which does not depend on the model of the controlled chaotic system, is presented. The controller utilizes the information of the measured output and the given objective as well as extracted differentials of those via higher-order differentiator (HOD). Stability, convergence and robustness of the closed-loop system are investigated. The presented adaptive HODFC can successfully control the uncertain Lorenz system, the Chen system, the Duffing–Holmes system, the Rössler system, and a new coined 4-dimensional chaotic system, and can drive their trajectories to desired steady states, unstable periodic orbits, or new chaotic states. Importantly, the controller does not use model functions of these systems above. The control scheme is suitable for both chaotic affine systems and ordinary affine systems without knowing their precise models.