Order Adaptive Control Research Articles

Adaptive control with lower-order dynamics for nonlinear systems with unknown control coefficients

While adaptive control has been extensively studied for a variety of uncertain nonlinear systems, overparametrization still exists in many works. By overparametrization, it means that the order of the adaptive controller is (much) higher than the number of unknown parameters of the system, which is a defect from a theoretical perspective and indicates high cost in controller's implementation. This paper investigates adaptive control with lower-order dynamics for nonlinear systems with unknown control coefficients, managing to significantly reduce or eliminate overparametrization and showing the differences in controllers' dynamic orders of different control strategies. The uncertain nonlinear system in question has n unknown control coefficients and a p-dimension unknown vector in the system nonlinearities. We consider two cases of unknown control coefficients: case (a): their signs are known; case (b): their signs are unknown, i.e. unknown control directions. For case (a), first by compensating for unknown control coefficients and their reciprocals, as well as the unknown vector, we design an adaptive controller with ( 2 n + p − 1 ) -order dynamics, where no inequality estimate is used to avoid conservatism of the controller. Second, for case (a), via bounding the system uncertainties by a single unknown constant, we design an adaptive controller with only 1-order dynamics, where inequality estimates are used and hence the controller suffers conservatism. For case (b), by adopting multiple Nussbaum functions, we design a ( 2 n + p − 1 ) -order adaptive controller, where n-order dynamic compensation is employed to overcome n non-identical unknown control directions. As in case (a), because no inequality estimate is used, conservatism of the controller is avoided. Regardless of conservatism, for case (b), by bounding the uncertainties in the destabilizing terms, we design n-order adaptive controller, where, of course, inequality estimates have to be used.

State Space Model Reference Adaptive Control for a Class of Second-Degree Fractional Order Systems with Different Eigenvalues

This study proposes an adaptive control synthesis for a class of second-degree fractional order systems with different eigenvalues in the state-space domain. The proposed fractional order adaptive controller is a generalization of the MRAC controller for the class of scalar fractional order systems. In order to control the fractional order plant, an adaptive state space feedback controller is applied based on the error between the system output and a chosen reference model using a fractional adaptation law to make the fractional order plant track the fractional order reference model. We show that the resulting adaptive regulator is able to stabilize the fractional order second degree system with a satisfying performance. A simulation example illustrating these performance properties is provided along with a comparison with a fractional order sliding mode control (FOSMC) to demonstrate the superiority of the proposed control scheme.

Reinforcement learning robust nonlinear control of a microgrid with hybrid energy storage systems

The parameter variations in the microgrid models including internal and external faults, modelling uncertainties, unexpected changes in load or disturbances and harmonic currents are unavoidable in a microgrid. Here, a hybrid energy generation system consisting of Proton-Exchange Membrane Fuel Cells)PEMFC(/PhotoVoltiaic)PV (/Battery Energy Storage System)BESS(is considered. A new Backstepping Fractional order Adaptive Terminal Sliding Mode Control (BFATSMC) based on Reinforcement Learning (RL) is designed to soar robustness and disturbance rejection for an autonomous microgrid. To verify the performance of the BFATSMC a comparative study is investigated and the proposed method is applied to an islanded microgrid. In the presence of nonlinear and unbalanced loads with harmonic, unmodeled dynamics, and parametric uncertainties, the proposed method has successfully controlled the voltage.

Performances Improvement of Fractional order Systems using the Fractional Order Adaptive PID Controller

Performances Improvement of Fractional order Systems using the Fractional Order Adaptive PID Controller

Performance Improvement of Aircraft pitch angle using the Fractional Order Adaptive PID Controller

Performance Improvement of Aircraft pitch angle using the Fractional Order Adaptive PID Controller

Pitch Angle Control of an Airplane Using Fractional Order Direct Model Reference Adaptive Controllers

This paper deals with the longitudinal movement control of an airplane (pitch angle) using fractional order adaptive controllers (FOACs). It shows the improvements achieved in the plane’s behavior, in terms of the minimization of a given performance index. At the same time, less control effort is needed to accomplish the control objectives compared with the classic integer order adaptive controllers (IOACs). In this study, fractional order direct model reference adaptive control (FO-DMRAC) is implemented at the simulation level, and exhibits a better performance compared with the classic integer order (IO) version of the DMRAC (IO-DMRAC). It is also shown that the proposed control strategy for FO-DMRAC reduces the resultant system control structure down to a relative degree 2 system, for which the control implementation is simpler and avoids oscillations during the transient period. Moreover, it is interesting to note that this is the first time that an FOAC with fractional adaptive laws is applied to the longitudinal control of an airplane. A suitable model for the longitudinal movement of the airplane related to the pitch angle θ as the output variable with the lifter angle (δe) as the control variable, is first analyzed and discussed to obtain a reliable mathematical model of the plane. All of the other input variables acting on the plane are considered as perturbations. For certain operating conditions defined by the flight conditions, an FO-DMRAC is designed, simulated, and analyzed. Furthermore, a comparison with the implementation of the classical adaptive general direct control (relative degree ≥ 2) is presented. The boundedness and convergence of all of the signals are theoretically proven based on the new Lemma 3, assuring the boundedness of all internal signals ω(t).

Fractional order adaptive MRAC controller design for high-accuracy position control of an industrial robot arm

Most of conventional feedback controllers become inefficient in hard industrial environments like in steel industry, because of uncertainties in the plant model, or process dynamics variation due to nonlinear actuators, and changes in the character of the disturbances. This paper proposes an adaptive control design based on fractional order model reference adaptive control (FOMRAC) strategy in order to deal with an uncertain horizontal positioning control of an unloading machine in a rotary hearth furnace for hot rolling operation. The proposed FOMRAC scheme uses the MIT rule as an adaptive mechanism with two main modifications comparatively to the conventional MRAC: the reference model is an adequate fractional order system and the parameter adjustment rule contains a fractional order integrator. Stability analysis of the proposed control scheme is performed using the Lyapunov stability theorem. Numerical simulations are presented to show the effectiveness of the proposed fractional adaptive schemes applied to an industrial robot arm loading round steel blocks from inside a rotary hearth furnace. After comparison with the conventional MRAC, it is shown that the performances of FOMRAC are superior to classical control schemes.

Novel Robust Control Using a Fractional Adaptive PID Regulator for an unstable system

Recent advances in fractional order calculus led to the improvement of control theory and resulted in potential use of fractional adaptive PID controller in advanced academic and industrial applications as compared to the conventional adaptive PID controller. Basically, a fractional order adaptive PID controller is an improved version of classical integer order adaptive PID controller that outperformed its classical counterpart. In case of a closed loop system, a minute change would result in instability of the overall system. An efficient PID controller can be used to control the response of such system. Among various parameters of an instable system, speed of the system is an important parameter to be controlled efficiently. The current research work presents the speed controlling mechanism for an uncertain instable system by using fractional order adaptive PID controller.To validate the arguments, effectiveness and robustness of the proposed fractional order adaptive PID controller have been studied in comparison to the classical adaptive PID controller using The Criterion of quadratic error. Simulation findings and comparisons demonstrated that the proposed controller has superior control performance and outstanding robustness in terms of percentage overshoot, settling time, rising time, and disturbance rejection.

Optimal MPPT and BES Control for Grid-Tied DFIG-Based Wind Energy Conversion System

As the wind energy is progressively pursued to supplement conventional power generation, the stochastic wind behavior considerably deteriorates power quality (PQ) and stability of the connected grid. This article is attributed to the comprehensive control design of the grid-integrated doubly fed induction generator (DFIG) wind energy system that aims to address encountered wind variability and PQ intricacies. Battery energy storage with bidirectional dc–dc converter control is assimilated at the dc-link of the DFIG that regulates the dc-link voltage to mitigate the wind power fluctuations in specified grid power modes. A higher order adaptive control for grid-interfaced converter accurately computes desired weights of various components to exercise accurate power balance and PQ control. Moreover, a novel Jaya particle swarm optimization algorithm is adopted for the optimal tuning of wind maximum power point tracking and the dc-link voltage PI controller parameters that significantly improves steady-state and dynamic responses of both the controllers. The rotor speed converges faster with precise reference tracking that leads to almost zero steady-state error using optimized PI controller gains. Along with the attenuated initial overshoot and fast settling time during sudden large step wind speed change, the dc-link voltage also characterizes superior response with optimal tuning during load unbalance and abnormal grid voltage conditions. The presented control strategy analyzes the capability of DFIG system under variable wind-speed changes, specified grid power modes, load changes, and other grid disturbances. The satisfactory system response is endorsed through experimental results conducted on a laboratory prototype.

Fractional order robust adaptive control design for actuator failure compensation in dual ball-beam system

This paper is to proposes a fractional order adaptive control scheme design for actuator failure compensation in order to balance of a ball-beam system with redundant actuators. The proposed controller is based on a fractional order sliding surface from which an adaptive actuator failure compensation control scheme is obtained. In order to control the dual ball-beam system with redundant motors, a linearized model is derived, which is subjected to actuator failures. A set of numerical simulation tests representing few selected types of actuator failures scenarios are carried out to assess the output tracking performance of the proposed controller design when dealing with such failures

Sensorless vector control of doubly fed induction generator based wind turbine using fuzzy fractional order adaptive disturbance rejection control

ABSTRACT This paper represents a novel sensorless method for the vector control of doubly fed induction generator (DFIG) in a wind turbine system. The proposed method is based on the fuzzy fractional order adaptive disturbance rejection control (FFOADRC) estimating the rotor velocity. In this new method, there is no need to calculate the coupling terms and eliminate them by feed-forward compensation. In addition, all disturbances (internal and external) are estimated by a fractional order extended state observer (FESO). The effects of these disturbances are then neutralized by generating a suitable control command. The operation of the proposed system has been simulated in Matlab/Simulink environment. The comparisons were made between FFOADRC, adaptive disturbance rejection control (ADRC), fuzzy ADRC (FADRC), and proportional-integral (PI) controller under different operating conditions. The results show that: (1) After DFIG starts and under similar conditions, using FFOADRC, FADRC, and ADRC, the velocity reaches the steady state with the overshoot values of 0%, 3.64%, and 8.03%, respectively. (2) In the steady state after wind velocity variation, the %THD values of the stator current using FFOADRC, FADRC, and ADRC are, respectively, 1.47, 1.54, and 2.79. In this case, utilizing the PI controller, the control circuit has a slower performance than three other controllers. (3) The comparison between the aforementioned controllers during DFIG velocity control shows that using FFOADRC, the values of settling time, rise time, peak time, and delay time are smaller, and we have better performance that indicates the superiority of FFOADRC over ADRC, FADRC, and PI controller. Therefore, FFOADRC improves the wind turbine performance in different conditions

Fractional order adaptive sliding-mode finite time control for cable-suspended parallel robots with unknown dynamics

Fractional order adaptive sliding-mode finite time control for cable-suspended parallel robots with unknown dynamics

Design of a Fuzzy Fractional Order Adaptive Impedance Controller with Integer Order Approximation for Stable Robotic Contact Force Tracking in Uncertain Environment

Abstract Current research in robot compliance control is unable to take both transient contact force overshoots and steady-state force tracking problems into account. To address this problem, we propose a fuzzy fractional order (FO) adaptive impedance controller to avoid the force overshoots in the contact stage while keeping force error in the dynamic tracking stage, where traditional control algorithms are not competent. A percentage gain is adopted to map FO parameters to integer order (IO) parameters by their natural properties, and a fuzzy logical controller is introduced to improve the system stability. The simulation results indicate that the proposed controller can be made more stable than and superior to the general impedance controller, and the force tracking results also have been compared with the previous control methods.

Fractional order adaptive MRAC controller design for high-accuracy position control of an industrial robot arm

Fractional order adaptive MRAC controller design for high-accuracy position control of an industrial robot arm

RETRACTED: Fractional order adaptive robust formation control of multiple quad-rotor UAVs with parametric uncertainties and wind disturbances

In recent times, multiple Unmanned Aerial Vehicles (UAVs) are being widely utilized in several areas of applications such as agriculture, surveillance, disaster management, search and rescue operations. Degree of robustness of applied control schemes determines how accurate a swarm of UAVs accomplish group tasks. Formation and trajectory tracking controllers are required for the swarm of multiple UAVs. Factors like external environmental effects, parametric uncertainties and wind gusts make the controller design process as a challenging task. This article proposes fractional order formation and trajectory tacking controllers for multiple quad-rotors using Super Twisting Sliding Mode Control (STSMC) technique. To compensate the effects of the disturbances due to parametric uncertainties and wind gusts, Lyapunov function based adaptive controllers are formulated. Moreover, Lyapunov theorem is used to guarantee the stability of the proposed controllers. Three types of controllers, namely fixed gain STSMC and fractional order Adaptive Super Twisting Sliding Mode Control (ASTSMC) methods are tested for the swarm of UAVs by performing the numerical simulations in MATLAB/Simulink environment. From the presented results, it is verified that in presence of wind disturbances and parametric uncertainties, the proposed fractional order ASTSMC technique showed improved robustness as compared to the fixed gain STSMC and integer order ASTSMC.

Fractional Order Adaptive Fast Super-Twisting Sliding Mode Control for Steer-by-Wire Vehicles with Time-Delay Estimation

It is difficult to model and determine the parameters of the steer-by-wire (SBW) system accurately, and the perturbation is variable with complex and changeable tire–road conditions. In order to improve the control performance of the vehicle SBW system, an adaptive fast super-twisting sliding mode control (AFST-SMC) scheme with time-delay estimation (TDE) is proposed. The proposed scheme uses TDE to acquire the lumped dynamics in a simple way and establishes a practical model-free structure. Then, a fractional order (FO) sliding mode surface and a fast super-twisting sliding mode control structure were designed on the basic super-twisting sliding mode to ensure fast convergence and high control accuracy. Since the uncertain boundary information of the actual system is unknown, a novel adaptive algorithm is proposed to regulate the control gain based on the control errors. Theoretical analysis concerning system stability is given based on the Lyapunov theory. Finally, the effectiveness of the method is verified through comparative experiments. The results show that the proposed TDE-AFST-FOSMC control scheme has the advantages of model-free, fast response and high accuracy.

Estimating the ultimate bounds and synchronization of fractional-order plasma chaotic systems

• The global Mittag–Leffler ultimate bounds and synchronization for fractional order plasma chaotic systems are studied. • Some new ellipsoid and cylindrical domains as well as a rotatory paraboloid of the bounds are derived via generalized Lyapunov function theory. • Linear feedback control tactics with two inputs or one input as well as fractional order adaptive control with one input are proposed. • The boundaries and feedback gain constants are easier to be calculated and the controller structures are simpler. This paper focuses on the Mittag–Leffler ultimate bounds (MLUBs) and synchronization of fractional-order plasma chaotic systems (FOPCSs). For one thing, by choosing some appropriate generalized Lyapunov functions and combining fractional-order differential inequalities, some new estimates on the 3D ellipsoid and cylindrical domains as well as a rotatory paraboloid of the bounds for the FOPCS are acquired according to system parameters, which perfect the previous studies and may infer a few new estimates. For another, linear feedback control tactics with two inputs or one input as well as fractional-order adaptive control with one input and a single variable are presented to realize the synchronization of two FOPCSs. Several new sufficient conditions for synchronization are analytically obtained by using inequality methods. The boundaries and feedback gain constants are easier to be calculated and the controller structures are simpler. Finally, numerical simulations are shown to confirm the correctness of the presented synchronization schemes.

Novel Intelligent Optimization Algorithm Based Fractional Order Adaptive Proportional Integral Derivative Controller for Linear Time Invariant based Biological Systems

Novel Intelligent Optimization Algorithm Based Fractional Order Adaptive Proportional Integral Derivative Controller for Linear Time Invariant based Biological Systems

Fractional adaptive SMC fault tolerant control against actuator failures for wing rock supervision

This article presents a new fractional order adaptive control scheme design based on sliding mode configuration for actuator failure compensation applied to a wing rock system with redundant actuators. The main objective of this work is to establish an adaptive control law that compensates faulty actuators by taking into account actuator redundancy and introducing fractional calculus. First, a non-integer sliding mode surface is defined. Next, an adaptive scheme is derived from the ideal control law to accommodate for the occurring failures during operation. Then, the stability analysis of the closed loop system is performed using the Lyapunov theory under certain assumptions on the system and the failures. Finally, simulations were carried out on a wing rock system subjected to various actuator failures scenarios in order to illustrate the effectiveness of the proposed control law.

A Discrete-Time Robust Adaptive PI Controller for Grid-Connected Voltage Source Converter with LCL Filter

In this work, it is presented a new direct discrete-time robust adaptive PI (Proportional Integral) Controller for grid-injected current control loop of a voltage source converter with LCL filter. The mathematical background is based on Robust Model Reference Adaptive Control theory. However, the proposed controller is straightforward, it does not need a reference model and has capability to track directly currents reference. This approach simplifies significantly controller design, resulting in a reformulation of parameters vector used for adaptation of adjustable gains. It turns the controller robust to unmodelled dynamics, while avoid the complexity inherent to the conventional high order adaptive controllers for grid-connected power systems. Besides, it is highlighted that proposed controller does not need resonant controllers for grid disturbance rejection, or require any knowledge of grid parameters, lines impedance or load power demand. Also, due to its simple structure, it is easily implemented and does not require a high processing capacity. Furthermore, the effectiveness of the control strategy in terms of reference tracking, harmonics content and robustness to the grid impedance variation is corroborated through experiments.