Yuri Orlov

Discontinuous unit feedback control of uncertain infinite-dimensional systems

Control systems, driven by a discontinuous unit feedback in a Hilbert space, are studied. The equation which describes a system motion, taking place in the discontinuity manifold and further referred to as a sliding mode, is derived by means of a special regularization technique. Based on the sliding mode equation, the procedure of synthesis of a discontinuous unit control signal is developed. Restricted to a class of infinite-dimensional systems with finite-dimensional unstable part, this procedure generates the control law which ensures desired dynamic properties as well as robustness of the closed-loop system with respect to matched disturbances. As an illustration of the capabilities of the procedure proposed, a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators.

Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor

This paper develops discontinuous control methods for minimum-phase semilinear infinite-dimensional systems driven in a Hilbert space. The control algorithms presented ensure asymptotic stability, global or local accordingly, as state feedback or output feedback is available, as well as robustness of the closed-loop system against external disturbances with the a priori known norm bounds. The theory is applied to stabilization of chemical processes around prespecified steady-state temperature and concentration profiles corresponding to a desired coolant temperature. Two specific cases, a plug flow reactor and an axial dispersion reactor, governed by hyperbolic and parabolic partial differential equations of first and second order, respectively, are under consideration. To achieve a regional temperature feedback stabilization around the desired profiles, with the region of attraction, containing a prescribed set of interest, a component concentration observer is constructed and included into the closed-loop system so that there is no need for measuring the process component concentration which is normally unavailable in practice. Performance issues of the discontinuous feedback design are illustrated in a simulation study of the plug flow reactor.

Exact linearization and sliding mode observer for a quadrotor unmanned aerial vehicle

In this paper, a feedback linearization-based controller with a sliding mode observer running parallel is applied to a quadrotor unmanned aerial vehicle. An adaptive estimator is added to the overall system to estimate the effect of external disturbances such as wind. The whole observer-estimator-control law constitutes an original approach to vehicle regulation with minimal number of sensors. Performance issues of the controller are illustrated in a simulation study that takes into account parameter uncertainties and external disturbances as well as measurement noise.

Hybrid Sliding-Mode-Based Control of Underactuated Systems With Dry Friction

In this paper, hybrid control synthesis is proposed for a class of 2-degrees-of-freedom (DOF) underactuated mechanical systems with Coulomb friction in the joints. The control objective is to regulate both actuated and unactuated joints to desired positions. The proposed synthesis combines second-order sliding-mode (SOSM) control methods and a pure technical solution of imposing a relatively stronger dry friction on the unactuated joint as compared to that of the actuated joint. This design feature allows us to decouple the hybrid synthesis procedure into two steps. At the first step, a SOSM control algorithm is utilized to drive the unactuated link to the desired position in finite time. Once this task is achieved, the control input is switched to another SOSM algorithm which drives the actuated link to its desired position. As the amplitude of the controller used at the second step is smaller than the Coulomb friction level in the unactuated link, but it is greater than that in the actuated link, the unactuated link remains at rest, whereas the actuated link is regulated to the endpoint of interest. Performance issues of the developed synthesis, including robustness features of the closed-loop system, are illustrated in an experimental study made for a laboratory horizontal 2-DOF pendulum.

Extended invariance principle for nonautonomous switched systems

Stability analysis is developed for nonlinear nonautonomous switched systems, trajectories of which admit, generally speaking, a nonunique continuation on the right. For these systems Krasovskii-LaSalles invariance principle is extended in such a manner to remain true even in the nonautonomous case. In addition to a nonsmooth Lyapunov function with negative-semidefinite time derivatives along the system trajectories, the extended invariance principle involves a coupled indefinite function to guarantee asymptotic stability of the system in question. As an illustration of the capabilities of this principle, a switched regulator of a fully-actuated manipulator with frictional joints is constructed.

Brief Proportional derivative and strain (PDS) boundary feedback control of a flexible space structure with a closed-loop chain mechanism

A simple space truss structure, a rigid connection of two flexible beams, is modeled as a distributed parameter system subject to holonomic constraints. Boundary feedback control synthesis is developed for this structure. The synthesis is carried out in the infinite-dimensional setting, mathematical features of which give rise to a stabilizing PDS control algorithm. Due to simplicity of the implementation, the algorithm becomes extremely attractive under limitations on the computer power in the space. The effectiveness of the control strategy proposed is supported by experimental tests.

Nonlinear H ∞ control of a Quadrotor (UAV), using high order sliding mode disturbance estimator

A nonlinear H ∞ output feedback controller is proposed and coupled to a high-order sliding mode estimator to regulate an UAV in the presence of the unmatched perturbations. The plant to be controlled is a Quadrotor helicopter described by nonlinear dynamics with plant uncertainties due to the variations of inertia moments and payload operation. A robust state estimation is considered under model uncertainties as well as external/measurement disturbances. Performance issues of the controller are illustrated in a simulation study made for an UAV prototype.

Model Orbit Robust Stabilization (MORS) of Pendubot with Application to Swing up Control

Orbital stabilization of a simple underactuted manipulator, namely, two-link pendulum robot (Pendubot) is under study. Since underactuated systems cannot be stabilized by means of smooth feedback, the solution to the stabilization problem is sought within switched control methods. The quasi-homogeneous control synthesis is utilized to design a switched controller that drives the Pendubot to its zero dynamics in finite time and maintains it there in sliding mode. The constructed controller is such that the Pendubot zero dynamics is generated by a modified Van der Pol oscillator, being viewed as a reference model. The closed-loop system is thus capable of moving from one orbit to another by simply changing the parameters of the proposed modification of the Van der Pol oscillator. Performance issues of the controller constructed are illustrated in a simulation study of the swing up control problem of moving the Pendubot from its stable downward position to the unstable inverted position and stabilizing it about the vertical.

Nonlinear H ∞ -control of time-varying systems

Nonlinear H/sub /spl infin//-controller synthesis is developed for time-varying systems via measurement feedback. Both global and local solutions of the problem are derived. The global solution is based on a solution to appropriate strict Hamilton-Jacobi-Isaacs inequalities, whereas the local solution is derived by means of a certain perturbation of the Riccati equations used in solving the linear H/sub /spl infin//-control problem for the linearized system.

Finite Time Stability and Quasihomogeneous Control Synthesis of Uncertain Switched Systems with Application to Underactuated Manipulators

Switched control synthesis is developed for underactuated mechanical systems. In order to locally stabilize an underactuated system around an unstable equilibrium, its output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Once such an output has been chosen, the desired stability property of the closed-loop system is provided by applying a quasihomogeneous switched controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits an infinite number of switches on a finite time interval, it does not rely on the generation of sliding modes, while providing robustness features similar to those possessed by their sliding mode counterparts. Theoretical results are supported by an application to drive systems with backlash.