Robust Model Reference Adaptive Control Research Articles

Decentralized Model Reference Adaptive Control for Systems With Time Delays and Dead Zones

The decentralized robust model reference adaptive control (MRAC) problem is studied for a class of large-scale systems with unknown plant parameters, unknown time-varying delayed interconnections, and unknown dead-zone inputs. Two robust adaptive control schemes are proposed for the cases of symmetric dead-zone input and asymmetric dead-zone input under the assumption of moderate time-delay nonlinearity and the matching conditions of the plant model and the reference model matrix, respectively. The control gain function is explicitly expressed, and its useful properties are established. The Lyapunov-Krasovskii functional with two integral functions is constructed. It is shown that all signals in the closed-loop system are bounded and the state tracking error converges exponentially to a tunable region. The effectiveness and feasibility of the proposed design approach is illustrated by a simulation example.

Design and Cascade PI Controller-Based Robust Model Reference Adaptive Control of DC-DC Boost Converter

In this paper, Cascade PI Controller-Based Robust Model Reference Adaptive Control (MRAC) of a DC-DC boost converter is presented. Non-minimum phase behaviour of the boost converter due to right half plane zero constitutes a challenge and its non-linear dynamics complicate the control process while operating in continuous conduction mode (CCM). The proposed control scheme efficiently resolved complications and challenges by using features of cascade PI control loop in combination with properties of MRAC. The accuracy of the proposed control system’s ability to track the desired signals and regulate the plant process variables in the most beneficial and optimised way without delay and overshoot is verified using MATLAB/Simulink by applying comparative analysis with single PI and cascade PI controllers. Moreover, performance of the proposed control scheme is validated experimentally with the implementation of MATLAB/Simulink/Stateflow on dSPACE Real-time-interface (RTI) 1007 processor, DS2004 High-Speed A/D and CP4002 Timing and Digital I/O boards. The experimental results and analysis reveal that the proposed control strategy enhanced the tracking speed two times with considerably improved disturbance rejection.

Lyapunov stability analysis of discrete-time robust adaptive super-twisting sliding mode controller

This paper presents a discrete-time Robust Adaptive Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The control law is composed by two different control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main advantage of the control structure is its robust performance and high adaptability in face of unmodelled dynamics, presenting a fast reference tracking without chattering, since it uses a second-order Sliding Mode action into adaptive control structure. The stability and robustness analysis of the control structure are presented in discrete time, considering the overall plant, that is, in presence of matched and unmatched dynamics. In addition, the control structure performance is corroborated with simulation results, considering a non-minimum phase unstable plant. Moreover, the presented results are compared with an adaptive first-order SM control-based RMRAC, which can be clearly seen that proposed controller has better performance, mainly by means of chattering mitigation.

A PERFORMANCE COMPARISON OF DISCRETE-TIME LEAST SQUARES-BASED ROBUST MODEL REFERENCE ADAPTIVE CONTROL APPROACHES APPLIED ON GRID-SIDE CURRENT CONTROL OF GRID-TIED POWER CONVERTERS BY LCL FILTER

In this work, two Robust Model Reference Adaptive Control (RMRAC) for grid-side current control of a static 3-wire converter with LCL filter are implemented and compared. The adaptation law used to adjust gains online is a modified Least Square (LS) algorithm. In both methods there is no need using resonant controllers to reject exogenous disturbance. Thereby, it is presented, step-by-step, how to implement both strategies, pointing out benefits and drawbacks of each technique and comparing their performance to track model reference output and robustness to deal with parametric variation of grid conditions. The performance comparison parameters considered are: THD (Total Harmonics Distortion), mean of absolute tracking error and maximum overshoot. Simulation results are presented to support the discussion.

Design of Robust Model Reference Adaptive Controller for a Wider Class of Nonlinear Systems

Design of Robust Model Reference Adaptive Controller for a Wider Class of Nonlinear Systems

Robust model reference adaptive backstepping sliding-mode control for quadrotor attitude with disturbance observer

Purpose The purpose of this research paper is to design a disturbance observer-based control based on the robust model reference adaptive backstepping sliding-mode control for attitude quadrotor model subject to uncertainties and disturbances. Design/methodology/approach To estimate and reject the disturbance, a disturbance observer is designed for the exogenous disturbances with perturbation while a control criterion is developed for the tracking of desired output. To achieve the control performance, backstepping and sliding-mode control techniques are patched together to obtain robust chattering-free controller. Furthermore, a model reference adaptive control criterion is also combined with the design of robust control for the estimation and rejection of uncertainties and unmodeled dynamics of the attitude quadrotor. Findings The findings of this research work includes the design of a disturbance observer-based control for uncertain attitude quadrotor system with the ability of achieving tracking control objective in the presence of nonlinear exogenous disturbance with and without perturbation. Practical implications In practice, the quadrotor flight is opposed by different kinds of the disturbances. In addition, being an underactuated system, it is difficult to obtain an accurate mathematical model of quadrotor for the control design. Thus, a quadrotor model with uncertainties and disturbances is inevitable. Hence, it is necessary to design a control system with the ability to achieve the control objectives in the presence of uncertainties and disturbances. Originality/value Designing the control methods for quadrotor control without uncertainties and disturbances is a common practice. However, investigating the uncertain quadrotor plant in the presence of nonlinear disturbances is rarely taken into consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the uncertainties and disturbances as well as investigate a control algorithm to achieve tracking performance.

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.

A Robust Nonlinear Model Reference Adaptive Control for Disturbed Linear Systems: An LMI Approach

In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC.

Robust model reference adaptive PI controller based sliding mode control for three-phase grid connected photovoltaic inverter

In this paper, the design of a new robust model reference adaptive PI (MRAC-PI) current controller is proposed for a two-stage grid connected photovoltaic (PV) inverter. Perturb & observe (P&O) algorithm is implemented in the boost part in order to extract the maximum power from the PV array. Firstly, the current dynamics with considering the system uncertainties are written in dq frame and are simplified by employing a decoupling system. Then, the MRAC-PI controller is designed based on a sliding mode control (SMC) to improve the robustness of the controller under system uncertainties. The parameters of PI controller are tuned based on SMC laws to track the desired reference model and provides fast and desirable dynamic response. The stability of the robust MRAC-PI is proven by using Lyapunov's theory and Barbalet's lemma. Finally, the performance of the proposed current controller and the conventional PI based voltage oriented control (VOC) during variations in filter inductance and solar irradiance are compared through simulation results. These results show the effectiveness of the proposed controller.

Event-Triggered Robust Control for Output Consensus of Unknown Discrete-Time Multiagent Systems With Unmodeled Dynamics.

This article investigates the event-triggered output consensus problem for a class of unknown heterogeneous discrete-time linear multiagent systems in the presence of unmodeled dynamics. The agents have individual nominal dynamics with unknown parameters, and the unmodeled dynamics are in the form of multiplicative perturbations. A novel design framework is developed based on an event-triggered internal reference model and a distributed model reference adaptive controller. To deal with the heterogeneity of the multiagent system, the event-triggered internal reference model is designed to generate a virtual reference signal for each agent with a dynamic event-triggering mechanism being adopted to reduce the communication burden between neighboring agents. To handle the unknown parameters and unmodeled dynamics, the robust model reference adaptive controller is then designed to follow the generated virtual reference signal. It is shown that if the unmodeled dynamics satisfy certain conditions, then the boundedness of all the signals and variables in the closed-loop system and convergence of consensus errors to a residual set are guaranteed. Moreover, the consensus errors will converge to zero asymptotically in the absence of unmodeled dynamics. Compared with existing related works, the proposed framework is able to deal with the agents with individual unknown nominal dynamics and unmodeled dynamics. Moreover, the proposed framework is fully distributed in the sense that no knowledge of any global information is needed. Finally, the performance of the proposed method is validated by examples.

A Generalization for Model Reference Adaptive Control and Robust Model Reference Adaptive Control Adaptive Laws for a Class of Nonlinear Uncertain Systems with Application to Control of Wing Rock Phenomenon

Lyapunov's direct method is a primary tool for designing Model Reference Adaptive Control (MRAC) and robust MRAC schemes. In general, Lyapunov function candidates contain two categories of quadratic terms. The first category includes the system tracking error quadratic terms or, in some cases, consist of the system state quadratic terms. The second consists of the parameter estimation error quadratic terms. To design MRAC and Robust MRAC systems, researchers have used a limited variety for choosing quadratic terms. In this study, we consider a general form for the tracking error quadratic terms. We consider a strictly increasing function that belongs to the class of c1, which is a function of state tracking error quadratic terms. It yields a general structure for stable adaptive laws for updating controller parameters. For the MRAC scheme, the global asymptotic stability of the closed-loop system and stability and uniform bounded tracking of robust MRAC schemes are guaranteed. To evaluate the performance of the designed controllers, we consider the single DOF wing rock dynamics.

Robust output voltage control of a high gain DC–DC converter under applied load and input voltage uncertainties

In this study, using robust and adaptive approaches, two controllers are designed to compensate for the applied load and input voltage uncertainties of a high voltage gain dc–dc converter. These controllers are designed based on measuring only the output voltage of the converter. The permissible ranges of the uncertainties are calculated using dynamics equations analysis while practical limitations are considered. In the first approach, an input multiplicative uncertainty is considered for the model of the converter by linearisation of non-linear equations as well as using permissible ranges of the uncertainty. Then, a robust H∞ controller is designed. In the second approach, the converter model is considered as a first-order dynamics model with the unknown parameters and an unknown additive term while a direct robust model reference adaptive controller is designed for it. Finally, the non-linear equations of the converter are simulated and the performances of the controllers are compared with each other. The control methods are then implemented on a 200 W prototype of a converter for evaluating the simulations results.

Constrained Robust Model Reference Adaptive Control of a Tilt-Rotor Quadcopter Pulling an Unmodeled Cart

This article presents an innovative control architecture for tilt-rotor quadcopters with H-configuration transporting unknown, sling payloads. This control architecture leverages on a thorough analysis of the aircraft's equation of motion, which reveals gyroscopic effects that were not fully characterized and were disregarded while synthesizing control algorithms in prior publications. Furthermore, the proposed control architecture employs barrier Lyapunov functions and a novel robust model reference adaptive control law to guarantee a priori user-defined constraints on both the trajectory tracking error and the control input, despite poor information on the aircraft's inertial properties and the presence of unknown, unsteady payloads. Flight tests involving a quadcopter pulling an unmodeled cart by means of a thin rope of unknown length, which is slack at the beginning of the mission, verify the effectiveness of the theoretical results.

A Generalized Minimum Phase Property for Finite-Dimensional Continuous-Time MIMO LTI Systems with Additive Disturbances

In this paper, we further generalize the definition of the extended zero dynamics to finite-dimensional continuous-time MIMO LTI systems with additive disturbances; and then introduce the concept of minimum phase for this class of systems. We show that the extended zero dynamics is invariant under the application of dynamic extension to its input, and therefore, a minimum phase system remains minimum phase after a finite number of steps of dynamic extension. We further introduce the extended zero dynamics canonical form for square MIMO LTI systems with uniform vector relative degree. We prove that a system is minimum phase according to our definition if its zero dynamics is asymptotically stable. The converse of the statement holds if the system is stabilizable from the control input.The objective of this research is to solve the model reference robust adaptive control problem for finite-dimensional continuous-time square MIMO LTI systems that is minimum phase according to the generalized definition using an appropriately vectorized version of Pan and Başar (2000), and results here constitute important building blocks. In a subsequent paper, Başar and Pan (2019), we further connect the dots: starting with a square MIMO LTI system that is minimum phase with respect to admissible initial conditions and admissible disturbance waveforms, we must obtain a true system representation that admits both the extended zero dynamics canonical form representation and the strict observer canonical form representation. Toward this end, we need to be able to extend the given system to one with uniform vector relative degree and with uniform observability indices without changing its minimum phase property, and this has been done in Başar and Pan (2019), fully resolving this issue.

Robust Adaptive Control of a Multirotor with an Unknown Suspended Payload

Abstract This paper addresses the problem of a multirotor carrying an unknown suspended payload, allowed to swing in one axis. The payload is unknown in the sense that its parameters, such as the payload mass and cable length, are unknown and its state, the swing angles, are not available for measurement. The suspended payload alters the flight dynamics of the vehicle considerably and the flight controllers need to minimize this effect. A robust model reference adaptive control technique is designed and implemented to minimize the effect of the suspended payload on the vehicle while allowing the controller to adapt to account for the unknown payload. The controller is modified to reject external disturbances and to be robust in the presence of sensor noise and drift. In simulation, this technique proves to dampen the oscillations caused by the payload. A quadrotor was built to practically demonstrate the effectiveness of the controller. The PX4 flight control stack is considered for the firmware of the vehicle. The model reference adaptive controller was implemented and succeeded to dampen the oscillations caused by the payload in a practical flight.

Fractional-order robust model reference adaptive control of piezo-actuated active vibration isolation systems using output feedback and multi-objective optimization algorithm

Improving the control performance of active vibration isolation systems is crucial to provide an ultra-quiet environment for precision instruments. This paper presents a new fractional-order robust model reference adaptive controller for the piezo-actuated active vibration isolation systems with a relative-degree-one model. One advantage of the proposed controller lies in that its controller parameters are adjusted online by fractional proportional–integral-type adaptive laws, which not only speeds up the convergence of the closed-loop system, but also improves the control energy efficiency. Moreover, the proposed controller only uses the measurable input and output of the plant as feedback signals, which is convenient for controller implementation. The stability of the closed-loop system is proved based on the Lyapunov theory in detail. The optimal values of the fractional order and adaptive gains for adaptive laws are determined using the multi-objective genetic algorithm through off-line simulation. Comparative experiments on the piezo-actuated active vibration isolation systems are conducted to verify the effectiveness of the proposed controller. Results show that the proposed controller achieves satisfactory isolation performance in a wider frequency band of 20–500 Hz, and simultaneously reduces the control effort compared with the traditional MRAC methods.

MRAC-Based Voltage Controller for Three-Phase CVCF Inverters to Attenuate Parameter Uncertainties Under Critical Load Conditions

This paper investigates a robust model reference adaptive control (MRAC) method for a three-phase constant-voltage constant-frequency (CVCF) inverter with an output LC filter. The proposed MRAC method is designed to stabilize the error dynamics of the system by a feedback control term in the steady state and attenuate the parameter uncertainties of the system by an updated MRAC term. Unlike the conventional proportional–derivative control (PDC) scheme, the proposed MRAC scheme ensures the fast convergence of the output errors to the exponential trajectories predefined by the reference models. Furthermore, the adaptive state-feedback mechanism can guarantee the fast dynamic response in the transient state without using load current sensors or observers. The asymptotic stability is mathematically proven by a Lyapunov theory. The feasibility of the proposed controller is confirmed through extensive experimental studies on a prototype three-phase CVCF inverter with a TI TMS320LF28335 DSP. Finally, comparative experimental results of three control methods (i.e., conventional PDC, feedback linearization control, and proposed MRAC) are provided to validate the superior performance of the proposed method such as fast transient response, low total harmonic distortion, and robustness to parameter uncertainties under critical load conditions (i.e., abrupt load changes, unbalanced loads, and distorted nonlinear loads).

A Novel Robust Model Reference Adaptive Impedance Control Scheme for an Active Transtibial Prosthesis

SummaryIn this paper, a novel robust model reference adaptive impedance control (RMRAIC) scheme is presented for an active transtibial ankle prosthesis. The controller makes the closed loop dynamics of the prosthesis similar to a reference impedance model and provides asymptotic tracking of the response trajectory of this impedance model. The interactions between human and prosthesis are taken into account by designing a second-order reference impedance model. The proposed controller is robust against parametric uncertainties in the nonlinear dynamic model of the prosthesis. Also, the controller has robustness against bounded uncertainties due to unavailable ground reaction forces and unmeasurable feedbacks of accelerations at the socket place. Moreover, an appropriate Series Elastic Actuator (SEA) mechanism for the prosthetic ankle is included in this work and its effects are discussed. Tracking performance and stability of the closed-loop system are proven via the Lyapunov stability analysis. Using simulations on an overall amputee prosthetic foot system, the effectiveness of the proposed RMRAIC controller is investigated for the task of level ground walking.

Constrained dynamical systems, robust model reference adaptive control, and unreliable reference signals

ABSTRACTIn this paper, we address the robust control design problem for nonlinear dynamical systems tracking unreliable reference signals. Specifically, we present robust model reference adaptive control laws that guarantee uniform ultimate boundedness of the trajectory tracking error for nonlinear plants that are affected by matched, unmatched, and parametric uncertainties, and are subject to constraints on the state space and the measured output. These control laws guarantee satisfactory results even in case the reference trajectory or the reference output signal do not verify the given constraints and hence, may draw the plant's trajectory or measured output outside their constraint sets. A numerical example involving the attitude control of a spacecraft illustrates the feasibility of the theoretical results presented.

Model Reference Robust Adaptive Control for Electro-hydraulic Servo System with State Constraints

Model Reference Robust Adaptive Control for Electro-hydraulic Servo System with State Constraints