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This paper presents an output feedback model predictive control for a class of nonlinear systems in a multirate scheme, where the control sampling period is larger than the estimation sampling period. With a small sampling period, the observer is designed to be faster than the dynamics of the closed-loop system under state feedback. Stabilization is achieved by a separation approach in which the control is designed first using state feedback and practical stabilization is achieved by output feedback.

In this paper, we consider the frequency synchronization problem in a network of lossless, connected and network-reduced power system. Frequency synchronization is an important problem in power systems as frequency deviation can lead to degraded power quality, tripping of generators, etc. We present a load-estimator-based consensus algorithm that achieves practical frequency synchronization in the presence of unknown time-varying power demand. It is shown that the synchronization error can be made arbitrarily small by tuning a controller parameter. Finally, simulations are performed to show the efficacy of the proposed controller.

We propose a scalable second-order consensus algorithm where by tuning the controller parameter, the convergence rate of the consensus protocol is almost invariant with respect to the size of the network. This is beneficial when the algebraic connectivity of the graph Laplacian decreases towards zero, with an increase in the network size, which leads to degraded closed-loop performance. We realize the controller using a high-gain observer and it is shown that for sufficiently small observer parameter, the convergence rate under output feedback approaches the one under state feedback. We also study the controller performance under stochastic disturbances by first defining a performance output and then calculating the ℋ 2 norm from the disturbance input to the performance output. We show that the ℋ 2 norm for the state feedback controller is scalable as the network size increases. Moreover, we also show that for sufficiently small observer parameter, the ℋ 2 norm under output feedback approaches the one under state feedback.

We study a trajectory tracking problem for a multi-rotor in the presence of modeling error and external disturbances. The desired trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume that only position and orientation measurements for the multi-rotor and position measurements for the reference system can be accessed. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the feed-forward term required for trajectory tracking, the multi-rotor states, as well as modeling error and external disturbances. We design an output feedback controller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. We rigorously analyze the proposed controller and establish its stability properties. Finally, we numerically illustrate our theoretical results using the example of a multi-rotor landing on a ground vehicle.

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.

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.

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.

Ahstract- The synchronization problem for identical linear systems is well studied in the literature. However one of the major assumptions in the design of the distributed controller requires the knowledge about the second smallest eigenvalue of the graph Laplacian. The dynamic controller designed by Scardovi and Sepulchre [1] for time-varying graphs does not require this assumption but it requires the agents knowledge of its own output and involves more information exchange among the distributed controllers. This paper is based on a simple observation on specializing the controller of [1] to time-invariant graphs, which removes the agents requirement of the knowledge about its own output and also reduces the amount of information exchange required by the dynamic controller of [1].

This paper focuses on the regulation problem for non-minimum-phase nonlinear systems with slow integrators, high-gain feedback and high-gain observer. The developed methodology involves four steps: At first, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in [11]. Then 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. At last, 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 effectiveness of such methodology is demonstrated on the linearized inverted pendulum on a cart model (LIPC-model).

The swing-up control problem of the inertia wheel pendulum is revisited in this paper. As different from existing methods, purely impulsive control inputs are used for swing-up. A mathematical formulation of the problem indicates that swing-up can be achieved using impulsive inputs applied at two discrete time instants. Two different swing-up schemes are presented and validated using numerical simulations where the impulsive inputs are approximated by high-gain feedback. The results of numerical simulations establish a direct link between high wheel velocities during swing-up and control strategies that take the pendulum directly to the upright configuration. They also indicate that the time required for swing-up is much less than that reported in the literature.

In this paper, we propose the design of an adaptive conditional servocompensator along with approximate hysteresis inversion for a piezoelectric nanopositioner to track desired periodic trajectories. The nanopositioner is modeled with a linear system proceeded by a hysteresis operator, which is represented by a Modified Prandtl-Ishlinskii (MPI) operator. The adaptive law, which is equipped with smooth parameter projection for robustness against matched disturbances, is initiated only when the trajectory driven by a continuously-implemented sliding mode control (SMC) enters a boundary layer around the sliding manifold. To reduce the conservativeness of the SMC law, we analytically derive the bound on the hysteresis inversion error. It is shown that, under appropriate conditions, the closed-loop system is well-posed and the tracking error converges exponentially to a periodic solution in the neighborhood of the origin. Experiments conducted on a commercial nanopositioner confirm the theoretical analysis, and demonstrate the efficacy of the proposed controller in comparison with a continuously-implemented SMC without the adaptive internal model. In particular, for a 100 Hz reference trajectory, the mean tracking error is found to be less than 0.015 %, compared to 0.15 % for the case when the adaptive internal model is not used.

Trajectory reversing is a method commonly used for estimating the region of attraction of stabilized equilibria. Using a discrete set of points obtained by trajectory reversing, this paper presents an algorithm for estimation and mathematical representation of the region of attraction using convex hulls. Several two-dimensional examples are presented to illustrate the usefulness of the algorithm. The method provides larger estimates compared to that obtained by existing algorithms but its main advantage lies in its applicability to higher-order systems. The mathematical representation of the region of attraction is useful in applying the Impulse Manifold Method, which was developed for stabilization of equilibria of underacuated systems from configurations lying outside their region of attraction. The region of attraction of the pendubot upright equilibrium is estimated to demonstrate the applicability of our algorithm to higher-order systems and illustrate the usefulness of the Impulse Manifold Method through simulations.

We propose a new algorithm for controlling the transient behavior of the tracking error for higher relative degree systems. When considering problems of tracking, controlling the transient behavior of the error is more important when compared to its derivatives. We introduce a concept of virtual output, which converts an arbitrary relative degree system into a relative degree one system. The virtual output is chosen in such a way that the tracking error approaches it from the initial time and the difference between the virtual output and the tracking error can be made arbitrarily small. Assuming that the state derivatives are not available for feedback we use a high-gain observer to estimate the derivatives and construct the virtual output. By designing a performance funnel for the virtual output we are able to make the error evolve within the funnel.

The paper addresses the high-gain observer design for nonlinear systems in the presence of sensor nonlinearities. It is shown that the properties of high-gain observers with linear outputs will hold with nonlinear outputs, provided the nonlinear output function is incrementally inside the sector [β, ∞] for some β > 0 and the observer eigenvalues are chosen to be real.

This paper presents an algorithm to enlarge the estimate of the Region of Attraction of stable equilibria of underactuated systems. To achieve this, we use a combination of the Sum of Squares (SOS) method and the Impulse Manifold Method (IMM). Initially, the SOS method is used to optimize the control input u(x) in order to obtain an enlarged Region of Attraction. The IMM is then applied on enlarged Region of Attraction obtained using SOS to further enlarge it. The IMM is implemented using high gain feedback and to demonstrate the efficacy of our algorithm, we present simulation results where an initial configuration of an acrobot lying outside the true region of attraction is stabilized.

High-gain observers proved to be a useful tool in the design of output feedback control of nonlinear systems. However, the observer faces a numerical challenge when its dimension is high. For an observer of dimension ρ and a high-gain parameter k, the observer gain is of the order of kρ and the observer variables could be of the order of kρ−1 during the transient period. This paper presents a new high-gain observer that is based on cascading lower-dimensional observers with saturation functions in between them. In the new observer, the gains and variables are of the order of k. It is shown that the cascade observer has properties similar to the standard one.

It is shown that a nonlinear output feedback stabilizing controller, which combines a globally bounded state feedback controller with a high-gain observer, is robust with respect to input and output time-delays in the plant. The time delay needs to be sufficiently small, but the upper bound on the delay is independent of how fast the observer is.

In this paper, feedback linearization is used to control the speed of a surface mount Permanent Magnet Synchronous Motor (PMSM). An extended high-gain observer is also used to estimate both the speed of the motor and the disturbance present in the system to recover the performance of feedback linearization. The disturbance is assumed to be unknown, and time-varying but bounded. Stability of the output feedback system is shown. Finally, simulation and experimental results confirm stability, robustness, and performance of the system.

In this paper, we propose a new method for implementation of a High-Gain Observer (HGO) to cope with measurement noise through Stochastic Approximation (SA). Most approaches have been using a trade-off between a speed of regeneration of states in the presence of uncertainties and the effect of measurement noise. Through SA, we are able to reserve authentic properties of the HGO i.e., a fast reconstruction of system states and robustness to uncertainties, while dealing with the effect of measurement noise both in practical and analytical manners. Regularity conditions are verified to analyze the stability by the associated Ordinary Differential Equation (ODE), i.e., the ODE method. Stability analysis of the full system is conducted. Numerical simulation results demonstrate the validity of the proposed design method.