Elbrous M. Jafarov

A new variable structure PID-controller design for robot manipulators

In this brief, a new variable structure proportional-integral-derivative (PID) controller design approach is considered for the tracking stabilization of robot motion. The work corroborates the utility of a certain PID sliding mode controller with PID sliding surface for tracking control of a robotic manipulator. Different from the general approach, the conventional equivalent control term is not used in this controller because that needs to use the matching conditions and exact full robot dynamics knowledge, which involves unavailable parameter uncertainties. Though the sliding surface includes also the integral error term, which makes the robot tracking control problem complicated, the existence of a sliding mode and gain selection guideline are clearly investigated. Moreover, different from uniformly ultimately boundedness, the global asymptotic stability of the robot system with proposed controller is analyzed. The sliding and global stability conditions are formulated in terms of Lyapunov full quadratic form and upper and lower matrix norm inequalities. Reduced design is also discussed. The proposed control algorithm is applied to a two-link direct drive robot arm through simulations. The simulation results indicate that the control performance of the robot system is satisfactory. The chattering phenomenon is handled by the use of a saturation function replaced with a pure signum function in the control law. The saturation function results in a smooth transient performance. The proposed approach is compared with the existing alternative sliding mode controllers for robot manipulators in terms of advantages and control performances. A comparative analysis with a plenty of simulation results soundly confirmed that the performance of developed variable structure PID controller is better under than those of both classical PID controller and an existing variable structure controller with PID-sliding surface.

Robust sliding-mode control for the uncertain MIMO aircraft model F-18

Robust flight control laws based on variable structure control (VSC) theory and Lyapunov V-function method are designed for a simplified aircraft model F-18. A min-max control (MMC) and VSC laws are derived, for multi-input multi-output (MIMO) systems with plant uncertainties and input disturbance. Two types of robust feedback controllers MMC and VSC for uncertain MIMO systems are considered. For both cases the existence conditions of a stable sliding mode and the robust asymptotic stability in uncertain MIMO systems by MMC and VSC are investigated. For the design of an MMC and VSC, measurable states and sliding surface are chosen so that the zero dynamics of the system are stable. An application of tracking and positioning of VSC of longitudinal dynamics is presented. Finally, simulation results are presented to show the effectiveness of the design methods.

Robust sliding mode controllers design techniques for stabilization of multivariable time-delay systems with parameter perturbations and external disturbances

In this paper, robust delay-independent stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances are considered. To achieve this goal, two types of robust sliding mode controllers design techniques are advanced. The first is an integral sliding mode controller design modification to Shyu and Yan type controller design. The mismatching sliding conditions are parametrically obtained by using the Lyapunov-Razumikhin-Hale method and formulated in terms of some matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations is advanced by using the Lyapunov-Krasovskii V-functional method. The sliding, global stability and delay-dependent β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. A sliding mode controller design example for AV-8A Harrier VTOL aircraft with lateral unstable dynamic model parameters is considered to illustrate the controller design method. Design procedures and simulation results show that our advanced method is useful, and unstable lateral dynamics is successfully stabilized by using the combined controller.In this paper, robust delay-independent stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances are considered. To achieve this goal, two types of robust sliding mode controllers design techniques are advanced. The first is an integral sliding mode controller design modification to Shyu and Yan type controller design. The mismatching sliding conditions are parametrically obtained by using the Lyapunov-Razumikhin-Hale method and formulated in terms of some matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations is advanced by using the Lyapunov-Krasovskii V-functional method. The sliding, global stability and delay-dependent β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. A sliding mode controller design e...

Design of robust autopilot‐output integral sliding mode controllers for guided missile systems with parameter perturbations

The guided missile system is considered as SISO plant with parameter perturbations. The structure of the missile system is not suitable for the use of classical linear controllers. On the other hand, the missile system should be capable of good performances, such as zero steady state error, less settling time etc. Standard VSC control laws fail to control the steady state error due to the structure of the system matrices. For this reason we have proposed two new robust output integral sliding mode controllers and design procedures. An integrator is included in the sliding function, which results in the reduction and removal of the output error. The total control consists of two parts: equivalent control which compensates the nominal regime of the missile system; and VSC which compensates the parameter perturbations (changes in Mach number, altitude and mass of the vehicle, etc.) of the missile system. We have derived new constructive sliding and stability conditions for both cases by using Lyapunov’s direct method. Computer simulations indicate that this approach yields a satisfactory control performance.

Robust reduced-order sliding mode observer design

In this article, a triple state and output variable transformation-based method combined with linear matrix inequality (LMI) techniques to design a new robust reduced-order sliding mode observer for perturbed linear multiple-input and multiple-output systems is developed. The state and output variables of the original system are triple transformed into suitable canonical form coordinates to facilitate the design of a reduced-order observer. The existing transformations are summarised in this study and presented systematically. A new combined observer configuration is proposed and compared with another type of observers. Global asymptotical stability LMI and sliding mode existence conditions for the coupled observer error system are derived using Lyapunov full quadratic form. Reaching and sliding modes of motion of decoupled observer error system are discussed as well. Two numerical and simulation examples are given to illustrate the usefulness of the proposed design techniques.

Design of sliding mode control for multi-input systems with multiple state delays

The design problem of a sliding mode controller for multi-input systems with several delays is investigated. A new control law is proposed. The sufficient conditions for the existence of a sliding mode are derived. The results are given in terms of matrix norm inequalities. We have developed some constructive delay-independent conditions for the asymptotic stability of multivariable systems with multiple state delays based on a Lyapunov-Krasovskii functional combined with linear matrix inequalities techniques. Under these conditions we have successfully designed a sliding mode control law for the stabilization of a multi-input system with several delays. The sliding and stability conditions are less conservative than existing conditions.

Robust sliding mode speed hold control system design for full nonlinear aircraft model with parameter uncertainties: A step beyond

In this paper, an aircraft speed hold flight control problem is addressed only in one loop via sliding mode control with parameter uncertainties in flight speed and altitude without any reconfiguration of control parameters. Complete nonlinear longitudinal flight dynamics model is built for a conventional aircraft for speed hold problem. Control commands are assumed to be elevator angle deflection and trust input of jet-engine/propeller. Actuator limits are calculated to determine violation limits. A design example is given to illustrate effectiveness of proposed control system with compared simulations for three different flight conditions.

Robust stabilization of input‐delayed systems with design example for rocket motor control

Purpose – This paper aims to use a new design approach based on a Lagrange mean value theorem for the stabilization of multivariable input‐delayed system by linear controller.Design/methodology/approach – The delay‐dependent asymptotical stability conditions are derived by using augmented Lyapunov‐Krasovskii functionals and formulated in terms of conventional Lyapunov matrix equations and some simple matrix inequalities. Proposed design approach is extended to robust stabilization of multi‐variable input‐delayed systems with unmatched parameter uncertainties. The maximum upper bound of delay size is computed by using a simple optimization algorithm.Findings – A liquid monopropellant rocket motor with a pressure feeding system is considered as a numerical design example. Design example shows the effectiveness of the proposed design approach.Research limitations/implications – The proposed approach can be used in the analysis and design of the uncertain multivariable time‐delay systems.Originality/value – T...

A NEW VARIABLE STRUCTURE PID-CONTROLLER FOR ROBOT MANIPULATORS WITH PARAMETER PERTURBATIONS: AN AUGMENTED SLIDING SURFACE APPROACH

Abstract In this paper a new variable structure PID-controller is designed for stabilization of robot manipulator systems with parameter perturbations. The sufficient conditions for the existence of a sliding mode is considered. The techniques of matrix norm inequalities are used to cope with robustness issues. Some effective parameter-independent conditions are developed in a concise manner for the global asymptotic stability of the multivariable system using LMIs techniques and principle of Rayleighs min/max matrix eigenvalue inequality. The stability conditions are derived by using the Lyapunov full quadratic form for the first time. The parameter perturbations of the robot motion are evaluated by introducing Frobenius norm. Simulation results have shown that the control performance of the robot system is satisfactory.

Time-varying sliding mode in rigid body motion controlled by magnetic torque

In this work, the problem of rigid body attitude control by magnetic torqueing is considered. The aim of the work is to derive an asymptotically stable solution to this problem, which is known to have two challenging properties: instantaneous underactuation due to the structure of the magnetic torque production law; time-variance due to the dependence of that law on the time-varying local geomagnetic field vector. To ensure an asymptotically stable motion towards the reference state in inertial space, a time-varying sliding manifold is proposed in this paper. The manifold has two parts. The first part is a linear function of states and is well-known in literature to be specific to the problem of rigid body attitude control by momentum exchange- or reaction-based torqueing. The second part consists of two integral terms with respect to time, whose integrands are respectively the angular orientation of the body in inertial space and the component of the control vector along the local geomagnetic field. These designed time-integral terms enable the application of the equivalent control method to the considered problem and make the state vector converge to the reference state in sliding mode. With their inclusion in the sliding vector, there exists a time-varying sliding mode in nonlinear rigid body motion controlled by magnetic torque, which is proven by the satisfaction of the reaching condition for the general reaching law. The presented exemplary results of simulation studies, which are carried out under both ideality assumption and non-ideal conditions that are modelled with high-fidelity, verify the mathematical results.