Terminal Sliding Mode Control of a Twin Rotor Multiple-Input Multiple-Output System
TL;DR: A terminal sliding mode control law is obtained for the linearized model of the TRMS system by transforming it to the Brunovsky canonical form and is shown to be stable to disturbances in pitch and yaw.
Abstract: This paper deals with the finite time stabilization of a twin rotor multiple-input multiple-output (TRMS) system. A terminal sliding mode control law is obtained for the linearized model of the system by transforming it to the Brunovsky canonical form. Through experiment, the resulting control law is shown to be stable to disturbances in pitch and yaw.
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TL;DR: In this paper, an observer-based robust controller is proposed to attenuate the chattering effect of the sliding mode control in a two-rotor mimo system, and exponential stability is guaranteed by using the Lyapunov method.
Abstract: Control of the helicopter includes nonlinearities, coupling and external perturbations. This paper presents a control strategy for TRMS (twin rotor mimo system), based on the coupling of the fuzzy logic control with the so-called sliding mode control to make its beam track accurately a reference signal, or reach desired positions in 2 DOF (degree of freedom). Only yaw and pitch angles are considered available for measurement. A non linear observer is used to estimate the unmeasured states. The proposed control scheme can be attenuating the chattering effect of the sliding mode control. Exponential stability is guaranteed by using the Lyapunov method. To show the effectiveness of the proposed observer-based robust controller is illustrated by simulation and experimental results. The real time implementation has been effectuated to the real TRMS system using MATLAB real-time tool box and Advantech PCI1711 card.
25 citations
TL;DR: In this paper, the authors proposed a new method to tune a fractional-order Proportional-Integral-Derivative controller for a twin rotor aerodynamic system, which is a nonlinear highly coupled MIMO system.
Abstract: 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.
21 citations
13 citations
19 Oct 2016
9 citations
TL;DR: The interval type-2 fuzzy logic is used to minimize the major problem of sliding mode and employed in the stability analysis and the obtained simulation and experiment results confirm the effectiveness of the proposed method.
Abstract: Received: 13 November 2018 Accepted: 21 January 2019 The work has done in this paper concern a strategy of control based on real time implementation of backstepping sliding mode using the interval type-2 fuzzy logic and their application to the Twin Rotor MIMO System (TRMS), the backstepping sliding mode controller are the problem of the chattering phenomenon, this can damage the actuators and disrupt the operation and performance of the system, so to reduce this problem we combine the fuzzy logic type 2. The proposed techniques were applied to the TRMS, where the real time implementation of type-2 fuzzy backstepping sliding mode controller (T2FBSMC) were proposed for control system in the presence of external distrubances. The interval type-2 fuzzy logic is used to minimize the major problem of sliding mode and employed in the stability analysis. The obtained simulation and experiment results confirm the effectiveness of the proposed method.
8 citations
Cites methods from "Terminal Sliding Mode Control of a ..."
...The sliding mode control, is a robust control in the presence of parametric variations, characterized by its robustness against nonlinearity and its efficiency in the rejection of disturbances, [6, 7], in [8] sliding mode control is designed for a linearized model of the TRMS system....
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References
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Book•
01 Jan 1985
TL;DR: In this paper, a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems is presented, which is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft.
Abstract: : The principal goal of this three years research effort was to enhance the research base which would support efforts to systematically control, or take advantage of, dominant nonlinear or distributed parameter effects in the evolution of complex dynamical systems. Such an enhancement is intended to support the development of flight controllers for increasing the high angle of attack or high agility capabilities of existing and future generations of aircraft and missiles. The principal investigating team has succeeded in the development of a systematic methodology for designing feedback control laws solving the problems of asymptotic tracking and disturbance rejection for nonlinear systems with unknown, or uncertain, real parameters. Another successful research project was the development of a systematic feedback design theory for solving the problems of asymptotic tracking and disturbance rejection for linear distributed parameter systems. The technical details which needed to be overcome are discussed more fully in this final report.
8,525 citations
"Terminal Sliding Mode Control of a ..." refers background or methods in this paper
...The notion of relative degree, as defined in Isidori (1995), is helpful in understanding the zero dynamics of a system....
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...Since the TRMS is a MIMO system, we consider the vector relative degree, also defined in Isidori (1995)....
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...The notion of relative degree, as defined in Isidori (1995), is helpful in understanding the zero dynamics of a system. Since the TRMS is a MIMO system, we consider the vector relative degree, also defined in Isidori (1995). The term, vector relative degree relates to the number of times the outputs are to be differentiated to explicitly obtain the inputs....
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Journal Article•
4,138 citations
TL;DR: In this article, it is shown that stability of zero dynamics should be taken into account when the regular form consists of blocks of second-order equations, and new theoretical methods are developed in the context of these studies: sliding made nonlinear observers, observers with binary measurements, parameter estimation in systems with sliding mode control.
Abstract: The first sliding mode control application may be found in the papers back in the 1930s in Russia. With its versatile yet simple design procedure the methodology is proven to be one of the most powerful solutions for many practical control designs. For the sake of demonstration this paper is oriented towards application aspects of sliding mode control methodology. First the design approach based on the regularization is generalized for mechanical systems. It is shown that stability of zero dynamics should be taken into account when the regular form consists of blocks of second-order equations. Majority of applications in the paper are related to control and estimation methods of automotive industry. New theoretical methods are developed in the context of these studies: sliding made nonlinear observers, observers with binary
measurements, parameter estimation in systems with sliding mode control.
1,061 citations
Book•
22 Apr 1999TL;DR: The design approach based on the regularization is generalized for mechanical systems and it is shown that stability of zero dynamics should be taken into account when the regular form consists of blocks of second-order equations.
Abstract: Introduction Examples of Dynamic Systems with Sliding Modes Sliding Modes in Relay and Variable Structure Systems Multidimensional Sliding Modes Outline of Sliding Mode Control Methodology Mathematical Background Problem Statement Regularization Equivalent Control Method Physical Meaning of Equivalent Control Existence Conditions Design Concepts Introductory Example Decoupling Regular Form Invariance Unit Control Second-Order Sliding Mode Control Sliding Mode Control of Pendulum Systems Design Methodology Cart Pendulum Rotational Inverted Pendulum (Model) Rotational Inverted Pendulum (Control) Simulation and Experiment Results for Rotational Inverted Pendulum Control of Linear Systems Eigenvalue Placement Invariant Systems Sliding Mode Dynamic Compensators Ackermanns Formula Output Feedback Sliding Mode Control Control of Time-Varying Systems Sliding Mode Observers Linear Asymptotic Observers Observers for Linear Time-Invariant Systems Observers for Linear Time-Varying Systems Observer for Linear Systems with Binary Output Integral Sliding Mode Motivation Problem Statement Design Principles Perturbation and Uncertainty Estimation Examples Summary The Chattering Problem Problem Analysis Boundary Layer Solution Observer-Based Solution Regular Form Solution Disturbance Rejection Solution State-Dependent Gain Method Equivalent Control-Dependent Gain Method Multiphase Chattering Suppression Comparing the Different Solutions Discrete-Time and Delay Systems Introduction to Discrete-Time Systems Discrete-Time Sliding Mode Concept Linear Discrete-Time Systems with Known Parameters Linear Discrete-Time Systems with Unknown Parameters Introduction to Systems with Delays and Distributed Systems Linear Systems with Delays Distributed Systems Summary Electric Drives DC Motors Permanent-Magnet Synchronous Motors Induction Motors Summary Power Converters DC/DC Converters Boost-Type AC/DC Converters DC/AC Converter Summary Advanced Robotics Dynamic Modeling Trajectory Tracking Control Gradient Tracking Control Application Examples Automotive Applications Air/Fuel Ratio Control Camless Combustion Engine Observer for Automotive Alternator
904 citations
"Terminal Sliding Mode Control of a ..." refers methods in this paper
...It has been applied to several nonholonomic mechanical systems in the works of Edwards and Spurgeon (1998); Riachy et al. (2008); Utkin et al. (2009); Yang and Kim (1999)....
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01 Jun 1999
TL;DR: A novel sliding mode control law is proposed for asymptotically stabilizing the mobile robot to a desired trajectory and it is shown that the proposed scheme is robust to bounded external disturbances.
Abstract: Nonholonomic mobile robots have constraints imposed on the motion that are not integrable, i.e., the constraints cannot be written as time derivatives of some function of the generalized coordinates. The position control of nonholonomic mobile robots has been an important class of control problems. In this paper, we propose a robust tracking control of nonholonomic wheeled mobile robots using sliding mode. The posture of a mobile robot is represented by polar coordinates and the dynamic equation of the robot is feedback-linearized by the computed-torque method. A novel sliding mode control law is proposed for asymptotically stabilizing the mobile robot to a desired trajectory. It is shown that the proposed scheme is robust to bounded external disturbances. Experimental results demonstrate the effectiveness of accurate tracking capability and the robust performance of the proposed scheme.
607 citations
"Terminal Sliding Mode Control of a ..." refers methods in this paper
...An adaptive control approach based on the backstepping concept is presented in Yang and Kim (1999) to stabilize the TRMS....
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...It has been applied to several nonholonomic mechanical systems in the works of Edwards and Spurgeon (1998); Riachy et al. (2008); Utkin et al. (2009); Yang and Kim (1999)....
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