Showing papers by "Hassan K. Khalil published in 2019"

Estimation of the Region of Attraction of Underactuated Systems and Its Enlargement Using Impulsive Inputs

Abstract: Stabilization of an equilibrium point is an important control problem for underactuated systems. For a given control design, the ability of the system to remain stable in the presence of disturbances depends on the size of the region of attraction of the stabilized equilibrium. The sum of squares and trajectory reversing methods are combined together to generate a large estimate of the region of attraction. Then, this estimate is effectively enlarged by applying the impulse manifold method, which can stabilize equilibria from points lying outside the estimated region of attraction. In this paper, the generality of the approach is demonstrated using simulations of a three-link underactuated system. Experimental validation using the pendubot is provided to demonstrate the feasibility of practical implementation.

Regulation of Nonminimum-Phase Nonlinear Systems Using Slow Integrators and High-Gain Feedback

Abstract: This paper investigates the regulation problem for nonminimum-phase nonlinear systems via slow integrators and high-gain feedback. The developed methodology involves four steps: in the first step, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in [18] . In the second step, we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input–output map, a slow integrator is added that enforces the objective of regulation. In the last step, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The design procedure is first presented for the linear model for the clarity of the proposed methodology. The effectiveness of such methodology is demonstrated on the nontrivial translational oscillator rotating actuator example. At last, the design for minimum-phase nonlinear systems is also provided. In this case, the performance recovery of the closed-loop auxiliary system by output feedback is verified.

Stabilization of Homoclinic Orbits of Two Degree-of-Freedom Underactuated Systems

Abstract: A hybrid controller for stabilization of homoclinic orbits of two degree-of-freedom (DOF) underactuated systems is proposed. The controller is comprised of continuous-time inputs, impulsive brakings, and virtual impulsive inputs for resetting of the passive coordinate. Impulsive brakings of the active coordinate result in instantaneous negative changes in the mechanical energy of the system. An impulsive dynamical system framework is adopted for modeling the hybrid dynamics and a Lyapunov function is defined for stabilization of the orbit. Sufficient conditions for stabilization are presented such that the Lyapunov function decreases monotonically under the action of the continuous inputs and undergoes negative jumps due to impulsive brakings. The control design is implemented on an inverted pendulum on a cart example. Simulation results indicate fast convergence of system trajectories to the homoclinic orbit corresponding to the upright equilibrium configuration.

Inversion-free Control of Hysteresis Nonlinearity Using An Adaptive Conditional Servomechanism

Abstract: Smart material-based systems, such as piezoelectric nanopositioning stages, exhibit pronounced hysteresis nonlinearity that poses significant control challenges. Much of the existing work employs an inverse hysteresis operator to approximately cancel out the hysteresis nonlinearity. In this paper we propose an inversion-free approach to the control of systems with hysteresis, removing the computational complexity in constructing an inverse compensator. The hysteresis nonlinearity is modeled as a Modified Prandtl-Ishlinskii (MPI) operator. We utilize the properties of the MPI hysteresis model to transform the system into a semi-affine form, where one term has the control input appearing linearly and the other term represents the hysteretic perturbation. The proposed controller is designed based on an adaptive conditional servocompensator approach, which is a continuously-implemented sliding mode control law powered with an adaptive servocompensator. An analytical bound on the hysteretic perturbation is derived and used in the design of the sliding mode control law. A low-pass filter is augmented with the control law, to avoid solving a complicated equation involved. Our stability analysis shows that, under reasonable assumptions, the boundedness of the closed-loop system trajectories is ensured. Experiments conducted on a commercially available nanopositioner confirms the effectiveness of the proposed method as compared to the case when an inverse model is implemented; indeed, the tracking error is reduced by approximately 50% for sinusoidal references under the proposed controller.

Sensorless Speed Control of PMSM Using Extended High-Gain Observers

Abstract: In this paper, we regulate the speed of a surface mount Permanent Magnet Synchronous Motor (PMSM) with only using current sensors. We use a back-Electromotive Force (back-EMF) based sensorless speed control technique. We reduce the α-β model of the PMSM using singular perturbation theory, which reveals two algebraic expressions for the estimation of the back-EMF signals. We use these expressions to drive a Quadrature Phase Locked Loop (Q-PLL) that estimates rotor position and speed and also estimates the disturbance. The rotor position estimate is used for Park transformation while the speed and disturbance estimates are used in a feedback linearization law to regulate the speed. Our development of the controller only assumes knowledge of the nominal parameters of the PMSM. In addition, we assume the external load to be time-varying and bounded but otherwise unknown. Finally, results from simulation and experiment are shown to confirm robustness, and high performance of the output feedback system.