Twin Rotor Aerodynamic System Research Articles

Robust residual generator design for sensor fault detection in twin rotor aerodynamic system

The twin rotor aerodynamic system (TRAS) reflects the dynamics of vertical take-off rotor systems. TRAS considers the coupling effect and gyroscopic disturbance torque as unwanted signals. For safe and reliable TRAS operation, proper control input is vital, along with fast fault indication. This paper addresses the output sensor fault detection problem in the linear model of TRAS subjected to l2-norm bounded disturbance. A robust design of an observer is formulated as H-/H∞ optimization problem to maximize the sensitivity/robustness criterion. The approach minimizes the disturbance effect on the residual signal, which leads to successful fault detection. Furthermore, a linear quadratic regulator-based state feedback controller is proposed to meet the system's desired transient response requirement. The incorporation of an observer-based residual generator for fault detection along with the state-feedback controller differs the current work from the existing work. Successful fault detection in the output sensor of TRAS depicts the good performance of the proposed observer.

Robust point‐to‐point iterative learning control for constrained systems: A minimum energy approach

AbstractIterative learning control (ILC) is a high performance control scenario that is widely applied to systems that repeat a given task or operation defined over a finite duration, and has been introduced to point‐to‐point motion tasks in existing work. However, its design degree of freedom has not been fully utilized to optimize performance beyond tracking accuracy in constrained conditions. The framework of point‐to‐point ILC in this article is extended within discrete linear time‐invariant (LTI) system, so as to take the tracking time instants of desired positions as changing variables. Therefore, it is possible to achieve the objective of minimizing energy while maintaining the required tracking accuracy. The multiobjective optimization problem is divided into two sub‐problems, which are solved with an iterative algorithm composed of norm‐optimal ILC approach as well as the coordinate descend method. Furthermore, the impact of model uncertainty on algorithm performance is also considered, and the iterative algorithm is further extended to capture constrained systems. The algorithm is robust to the model uncertainty and has a certain robustness to output disturbances. Finally, the validity of the proposed algorithm is verified by a twin rotor aerodynamic system (TRAS) model.

μ-Synthesis FO-PID for Twin Rotor Aerodynamic System

μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters values. However, the free parameters available for tuning must be involved only in classical arithmetic operations, which leads to a problem for the fractional-order operator or for its integer-order approximation, exponential operations being involved. The main goal of the current article consists of presenting a possibility to integrate a fixed-structure multiple-input-multiple-output (MIMO) fractional-order proportional-integral-derivative (FO-PID) controller in the μ-synthesis optimization problem. The solution consists in a possibility to find a set of tunable parameters isomorphic with the fractional-order such that the coefficients involved in the approximation of the fractional element, along with the formulation of a fixed-structure mixed-sensitivity loop shaping μ-synthesis control problem. The proposed design procedure is applied to a twin rotor aerodynamic system (TRAS) using both MATLAB numerical simulation and practical experiments on laboratory scale equipment. Moreover, a comparison with the unstructured μ-synthesis is performed, highlighting the advantages of the proposed solution: simpler form and guaranteed robust stability and performance.

Model Predictive Control of Nonlinear MIMO Systems Based on Adaptive Orthogonal Polynomial Networks

This paper considers a new design of model predictive control based on specific models in the form of adaptive orthogonal polynomial networks, built around a specially tailored basis of generalized orthogonal functions. Polynomial model has a single layer structure and a smaller number of model parameters than classical neural networks, usually used for model predictive control design, leading to lower complexity and shorter calculation time. Desired property of adaptability of the model is achieved by using additional variable factors inside the orthogonal basis. The designed controller was applied in control of twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems and compared to the other state-of-the-art control algorithms.

Design of an Adaptive Linear Quadratic Regulator for a Twin Rotor Aerodynamic System

This paper deals with a twin rotor aerodynamic system (TRAS), which is a multi-input multi-output (MIMO) system with high crosscoupling between its two channels. It proposes an adaptive linear quadratic regulator (ALQR) to stabilize this system. The justification for using an adaptation technique is that the conventional LQR—designed by linearizing the TRAS about a certain equilibrium point—can no longer achieve the design specifications when the system operating point deviates significantly from the equilibrium point. To introduce an adaptation mechanism in the system, formulas for determining the operating points of the TRAS in terms of the reference inputs are deduced, and the linearized TRAS model is parameterized in terms of the reference inputs so that when the reference inputs change, a new LQR is designed with respect to these new reference inputs, resulting in an ALQR. To demonstrate the superiority of the ALQR over the LQR, transient response specifications (rise time, settling time, and percentage overshoot) as well as integral square error (ISE), integral absolute error (IAE), integral time squared error (ITSE), and integral time absolute error (ITAE) are calculated for both systems. The main contribution of this paper is that it identifies the operating range by its width and its position with respect to the equilibrium point (width, position), and it investigates the effect of these two attributes on the performance of the closed-loop system by considering five cases with different width and position. Simulation results (carried out by MATLAB) show that the ALQR outperforms the LQR and the PID controller in all cases, and its superiority becomes more significant for cases that are characterized by a large deviation from the equilibrium point.

Designing optimal models of nonlinear MIMO systems based on orthogonal polynomial neural networks

ABSTRACT This paper presents a new method for modelling of dynamic systems by using specially designed orthogonal polynomial neural networks. These networks utilize the feature that the basis made of orthogonal functions can be used for approximation of arbitrary function, while their property of orthogonality enables optimal performances in the sense of both convergence time and approximation error. In this regard, generalized quasi-orthogonal polynomials, specifically tailored for the application in the modelling of complex dynamic systems with time-varying behaviour, are considered. Adaptivity of the designed model is achieved by using variable factors inside the orthogonal basis. The designed orthogonal neural network is applied in modelling of laboratory twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems. Detailed comparative analysis is performed for a different number of polynomials in expansion with the purpose of finding the optimal model in the sense of trade-off between model accuracy and complexity.

A Hybrid H∞ Control Based ILC Design Approach for Trajectory Tracking of a Twin Rotor Aerodynamic System

This paper investigates the trajectory tracking problem for a Multi-Input Multi-Output (MIMO) Twin Rotor Aerodynamic System (TRAS) using a hybrid architecture based on an H∞∞∞∞ controller and Iterative Learning Control (ILC). TRAS is a fast, nonlinear coupled system and therefore it is a challenging task to design a control system that ensures the tracking for fast changing trajectories. The controllers proposed in the literature for the TRAS through linear approaches tend to have a large control effort, while the ones designed using the nonlinear approaches track only for smooth input trajectories. Both issues are important from control point of view. In this paper, these issues are addressed by designing a feedback H∞∞∞∞ control that stabilizes the system and a feedforward ILC which reduces the control effort. The H∞∞∞∞ controller achieves the tracking for input trajectories with sharp edges, but the control effort required for tracking is large. With the proposed hybrid approach, tracking is achieved by the H∞∞∞∞ controller whereas the required control effort is reduced in each subsequent iteration by ILC. After a few iterations, accurate tracking at a minimized control effort is achieved. The simulations have been performed using MATLAB software and the controller designed through the proposed approach has been validated on nonlinear model of the system. The results of the proposed technique, compared with the flatness-based and back-stepping control strategies, show that the proposed controller ensures accurate tracking at the reduced control effort.

Design of a PID-Lead Compensator for a Twin Rotor Aerodynamic System (TRAS)

This paper deals with a Twin Rotor Aerodynamic System (TRAS). It is a Multi-Input Multi-Output (MIMO) system with high crosscoupling between its two channels. It proposes a hybrid design procedure that combines frequency response and root locus approaches. The proposed controller is designated as PID-Lead Compensator (PIDLC); the PID controller was designed in previous work using frequency response design specifications, while the lead compensator is proposed in this paper and is designed using the root locus method. A general explicit formula for angle computations in any of the four quadrants is also given. The lead compensator is designed by shifting the dominant closed-loop poles slightly to the left in the s-plane. This has the effect of enhancing the relative stability of the closed-loop system by eliminating the oscillation in its transient part but at the expense of greater rise time. However, for some applications, long rise time may be an allowable price to get rid of undesired oscillation. To demonstrate the proposed hybrid controller's performance numerically, a new performance index, designated by Integral Reciprocal Time Absolute Error (IRTAE), is defined as a figure to measure the oscillation of the response in its transient part. The proposed controller enhances this performance index by 0.6771%. Although the relative enhancement of the performance index is small, it contributes to eliminating the oscillation of the response in its transient part. Simulation results are performed on the MATLAB/Simulink environment.

Design of a PID-Lead Compensator for a Twin Rotor Aerodynamic System (TRAS)

This paper deals with a Twin Rotor Aerodynamic System (TRAS). It is a Multi-Input Multi-Output (MIMO) system with high crosscoupling between its two channels. It proposes a hybrid design procedure that combines frequency response and root locus approaches. The proposed controller is designated as PID-Lead Compensator (PIDLC); the PID controller was designed in previous work using frequency response design specifications, while the lead compensator is proposed in this paper and is designed using the root locus method. A general explicit formula for angle computations in any of the four quadrants is also given. The lead compensator is designed by shifting the dominant closed-loop poles slightly to the left in the s-plane. This has the effect of enhancing the relative stability of the closed-loop system by eliminating the oscillation in its transient part but at the expense of greater rise time. However, for some applications, long rise time may be an allowable price to get rid of undesired oscillation. To demonstrate the proposed hybrid controller's performance numerically, a new performance index, designated by Integral Reciprocal Time Absolute Error (IRTAE), is defined as a figure to measure the oscillation of the response in its transient part. The proposed controller enhances this performance index by 0.6771%. Although the relative enhancement of the performance index is small, it contributes to eliminating the oscillation of the response in its transient part. Simulation results are performed on the MATLAB/Simulink environment.

Disturbance observer based control of twin rotor aerodynamic system

Twin rotor aerodynamic system (TRAS) approximates the dynamics of helicopters and other vertical take off rotor crafts. The nonlinear nature with significant cross-coupling between the inputs and outputs of the main and tail rotors make the control of such system for either stabilization or reference tracking a challenging task. In this paper, the problem of disturbance rejection for TRAS is addressed by designing disturbance observers through $H_{\infty}$ based approach. The system is decoupled into main and tail rotors subsystems. For each subsystem, an inner loop disturbance observer is synthesized that provides disturbance rejection, whereas to ensure stability and performance an outer loop baseline feedback controller is designed. Two different cases are considered. In first case 2 proportional-integral-derivative controllers are designed to use as outer loop baseline feedback controllers with disturbance observers whereas in the second case linear quadratic Gaussian (LQG) controllers are designed. For both cases simulations are performed with nonlinear Matlab Simulink model of TRAS and results are compared to determine which approach delivers better performance. Simulation results show that the 2 conflicting requirements of reference tracking and disturbance rejection can be met simultaneously with the proposed approach increasing the disturbance rejection capability of the closed loop system.

Particle swarm-based and neuro-based FOPID controllers for a Twin Rotor System with improved tracking performance and energy reduction

This paper examines two approaches in tuning fractional order proportional-integral-differential (FOPID) control named as neuro-based FOPID (NNFOPID) and particle swarm-based FOPID (PSOFOPID) for pitch control of a Twin Rotor Aerodynamic System (TRAS). For the neuro-based FOPID control, the innovations are the modification of output equation in the artificial neural network and the implementation of the Rectified Linear Unit (ReLU) activation function. The advantages of the proposed approach are a lighter network and the ability to tune more practical controller parameters without a deep knowledge of the system to achieve a satisfying pitch tracking response. As for the particle swarm-based FOPID control, the application of PSO with spreading factor algorithm is extended for tuning the FOPID controller gains and the innovation here is a new procedure in setting the initial search range. The important advantages of this proposed swarm-based algorithm are the avoidance of being trapped in local optima and reduction of the search area respectively. The performances of the proposed controllers are proven by extensive simulations and experimental verifications based on five standard criteria: square-wave characteristics, reference to disturbance ratio, evaluation time, energy consumption of the control signal and tracking performance. The performances of the proposed controllers are compared against an optimised PID control in three system conditions, namely Case I) without coupling effect and wind disturbance, Case II) with coupling effect only and Case III) with wind disturbance only. Together, this study finds that NNFOPID control offers an accurate system positioning by a 34% reduction in steady-state error with the lowest energy consumption and minimum evaluation time in Case II. In terms of the tracking performance and robustness for Case II, the superiority of PSOFOPID control is confirmed by a 27% reduction in the tracking error and the lowest oscillation value. The experimental results also validate the robustness and energy consumption of both controllers in Case III. It is envisaged that the proposed control designs can be very useful in tuning FOPID controller gains for high performance, low energy, and robust aerodynamics systems.

Sliding mode control assisted by GPI observers for tracking tasks of a nonlinear multivariable Twin-Rotor aerodynamical system

This paper explores the techniques based on Generalized Proportional Integral Observers (GPI), under the approach of active disturbance rejection, applied to the control of multivariable nonlinear systems with the same number of inputs and outputs (square). As a central axis, a sliding mode control scheme assisted by GPI observers is proposed. These observers are responsible for estimating the disturbances associated with the dynamics of the sliding surfaces produced by non-linearities, not modeled elements, parameter uncertainty and external disturbances. This process allows the creation of sliding regimes under the point of view of decoupled control. As a case study, the position control of a small-scale 2-DOF helicopter affected by adverse operating conditions, such as unknown external disturbances and actuator faults, is considered. Finally, experimental results that validate the proposed control strategy and a comparison with a linear GPI observer-based active disturbance rejection control scheme are presented.

Linearized Modelling and Control for a Twin Rotor System

The focus of this paper is on the control design and simulation of twin rotor aero-dynamical system (TRAS). The challenges for control design in these systems lie in their nonlinearity and the inherent cross coupling between motion in the vertical and horizontal directions. Working from a highly nonlinear, dynamically coupled, mathematical model, controller design is presented for the angular position/velocity in vertical and horizontal planes of motion. Three linear control methods were developed and optimized to control the TRAS, namely full state feedback (FSF), linear quadratic regulator (LQR), and PID control. Simulation and experimental results show trade-off between these control methods. Although better performance was achieved with LQR, more effort was needed. The PID control has always proved to be a simple approach that works well with linear models. However, in this study case the performance was strongly affected by the coupling effect as demonstrated by simulation and experimental results

Second Order Intelligent Proportional-Integral Fuzzy Control of Twin Rotor Aerodynamic Systems

This paper proposes a hybrid controller that consists of a second order data–driven Model–Free Control (MFC), also known as intelligent proportional–integral (iPI), and a Takagi-Sugeno Fuzzy (TSF) logic controller for nonlinear Multi Input–Multi Output (MIMO) twin rotor aerodynamic systems (TRASs). The pitch position control is carried out using a single input–single output control system structure. The hybrid controller (the second order MFC algorithm and the TSF logic controller) is referred to as second order MFC–TSF controller. The performance of the control system structure (CSS) with the new second order MFC–TSF controller is compared with the performance of a CSS with the second order MFC controller, which is optimally tuned in a model-based manner by a Grey Wolf Optimizer algorithm. Experimental validation results on a nonlinear TRAS laboratory equipment are included.

Simultaneous estimation of multiple sensor and process faults for non-linear discrete-time systems

The paper deals with the problem of simultaneous estimation of sensor and process faults. For that purpose, a novel scheme is proposed and its complete design procedure is described. The approach results in a robust estimation strategy with guaranteed convergence. In particular, apart from simultaneous estimation ability the proposed approach makes it possible to attenuate the exogenous disturbances up to the predefined level. Finally, the design procedure boils down to solving a set of linear matrix inequalities. The last part of the paper shows an illustrative example with the application dedicated to the laboratory twin-rotor aero-dynamical MIMO system.

A New Method to Tune a Fractional-Order PID Controller for a Twin Rotor Aerodynamic System

This paper proposes a new method to tune a fractional-order Proportional–Integral–Derivative controller (also called \(\mathrm {P}\mathrm {I}^{\uplambda }\mathrm {D}^{\upmu }\) ) for a Twin Rotor Aerodynamic System, which is a nonlinear highly coupled Multi-Input–Multi-Output system. The five parameters of the controller are tuned using optimization to minimize a performance index which is a weighted sum of absolute values of four frequency domain specifications: gain crossover frequency, phase margin, ISO damping property (to be robust against process gain variation), and magnitude peak value at the resonant frequency, where the latter is the new control design specification that is suggested by this paper. The performance of the proposed controller is compared with that of an integer-order Proportional–Integral–Derivative (PID) controller. Simulation results shows that the fractional-order controller outperforms its integer-order counterpart in minimizing the performance index, which results in satisfying the required design specification more accurately. This is demonstrated by first testing the performance of the of the closed-loop system where the fractional-order controller gives better performance than the integer-order controller and second by testing the robustness of the system by changing one of the process parameters, where the fractional-order controller is much more robust, unlike the integer-order controller where the closed-loop system becomes unstable.

Model-free sliding mode control of nonlinear systems: Algorithms and experiments

This paper proposes two model-free sliding mode control system (MFSMCS) structures. The new structures are compared with a model-free intelligent proportional-integral (iPI) control system structure. Two simple design approaches for the MFSMCS structures are suggested. The control system structures and the design approaches are validated by a set of real-time experimental results on a nonlinear laboratory twin rotor aerodynamic system (TRAS). The MFSMCS structures are considered in the framework of a Multi Input-Multi Output TRAS control system, where the azimuth and pitch positions are controlled using separate Single Input-Single Output control system structures for each control channel (azimuth and pitch). The experimental validation is carried out by two scenarios that illustrate and allow the assessment of the MFSMCS structures performance and the comparison versus a model-free iPI control system structure as well.

Fractional Order Modeling and Control of Twin Rotor Aero Dynamical System using Nelder Mead Optimization

This paper presents an application of fractional order controller for the control of multi input multi output twin rotor aerodynamic system. Dynamics of the considered system are highly nonlinear and there exists a significant cross-coupling between the horizontal and vertical axes (pitch & yaw). In this paper, a fractional order model of twin rotor aerodynamic system is identified using input output data from nonlinear system. Based upon identified fractional order model, a fractional order PID controller is designed to control the angular position of level bar of twin rotor aerodynamic system. The parameters of controller are tuned using Nelder-Mead optimization and compared with particle swarm optimization techniques. Simulation results on the nonlinear model show a significant improvement in the performance of fractional order PID controller as compared to a classical PID controller.

Guest Editorial

Guest Editorial

Multi‐input–multi‐output system experimental validation of model‐free control and virtual reference feedback tuning techniques

This study proposes data-driven model-free adaptive control (MFAC), model-free control (MFC) and virtual reference feedback tuning (VRFT) techniques applied to the control of a representative non-linear multi-input-multi-output (MIMO) system represented by the twin rotor aerodynamic system (TRAS). These data-driven techniques are implemented for both a single MIMO controller and two separately designed single-input-single-output controllers running in parallel for azimuth and pitch control. The three techniques are implemented as MFAC and MFC algorithms and as linear controllers tuned by VRFT. The performance of the three data-driven MIMO control system structures is compared systematically on the basis of the experimental results in terms of the values of the sum of mean squared control errors measured on TRAS equipment.