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Modern turbojet engines are controlled using digital controllers. First of all, the micro turbojet engine discrete model is identified. System identification technique utilized real data obtained from jet cat P200sx engine running experiments. Digital PID controllers are mostly used for controlling these engines. The tuning techniques for digital PID controller parameters are of a great interest. Two tuning techniques are used in this paper to tune the PID controller parameters for the discrete model obtained. In the first, model based local optimal control technique is used to tune the PID controller parameters around certain operating points along the whole range. This technique is used for the first time with the concerned engine. The gain scheduling is used to manage the controller parameters around these operating points. In the second technique, genetic algorithms are used at different operating points along the whole range of operation. Also, the gain scheduling is used to manage the controller parameters around these operating points. The two tuning techniques are compared in Matlab simulation environment. The comparison is based on each controller robustness against noise effect and disturbance rejection. The simulated results are discussed and show better behavior for the digital PID controller tuned using model based local optimal control.

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.

A real-time and calibration-free lane departure warning system algorithm is proposed. The pre-processing stage of the lane departure algorithm is carried out using Gaussian pyramid to smooth the image and reduce its dimensions, which decrease the unnecessary details in the image. A lane detection stage is then developed based on Edge Drawing Lines (EDLines) algorithm that is a real-time line segment detector, which has false detection control. The reference-counting technique is used to track the lane boundaries and predict the missing ones. Experimental results show that the proposed algorithm has accuracy of 99.36% and average processing time of 80 fps (frame per second). The proposed algorithm is efficient to be used in the self-driving systems in the Original Equipment Manufacturers (OEMs) cars.

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).

Integrated framework to simulate electronic system (including digital and analog devices) with the mechanical parts of a heterogeneous automotive system is presented. The electronic system, consisting of many Electronic Control Units (ECUs), is modeled to simulate the mechatronic system functionality. The recently developed Functional Mock-up standard approach is used to have a model for a complex cyber-physical automotive system. The framework simulates real system including the Hardware (HW) and the Software (SW) to run on the ECUs. It allows Co-development of the automotive system SW and HW while the mechanical system is in the loop. Hardware and Software debugging is demonstrated using the developed methodology. The development cycle for the automotive mechatronic system could be greatly shortened using the proposed framework.

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.

We consider the problem of output feedback tracking of flexible joint manipulators where the link angle is the output to be controlled and the motor angle is the measured output. We allow the use of any globally stabilizing full state feedback control. We show recovery of the stability and trajectory performance of the state feedback by using a high gain observer-based output feedback control. Finally, we demonstrate the effectiveness of the proposed scheme in the single link case, where the zero dynamics are not asymptotically stable.

A sliding mode controller is proposed for a class of systems comprising a hysteresis operator preceding an kth-order linear plant without zero dynamics. The hysteresis operator is modeled with piecewise linear characteristics with uncertainties, and a nominal inverse operator is included to mitigate the hysteresis effect. A bound on the inversion error is used in the design of the sliding mode controller. The stability of the closed-loop system is established, and singular perturbation is exploited to analyze the system behavior within the boundary layer. In particular, analytical insight is gained on the frequency-scaling behavior of the tracking error under a periodic reference. Simulation and experimental results on a piezoelectric actuator-based nanopositioner are presented to illustrate the design and analysis, where the hysteresis nonlinearity is represented by a Prandtal-Ishlinskii operator.

The objective of the research is to develop new methods or indicators regarding cyclostationarity (CS) that could clearly point out and differentiate between walking disorder signals. Normal human locomotion is the rather grand term given to the description of walking by individuals who fall within the range considered as “normal”, and is seen as a sequence of cyclic and repeated gestures. It is a highly individual and variable activity influenced by many various factors. Analysis and treatment of such sequences, are demonstrated, and have proved that such processes are cyclostationary. This article suggests that “Kurtosis” provides a strong indicator of CS, and shows empirically the existence of a relationship between the “Kurtosis” and the known indicator of CS; specifically “the degree of cyclostationarity (DCS)”. An empirical study on the biomechanics of locomotion is performed with the objective of using it as supportive evidence of that relationship.

In this paper, we present analysis on the stabilization and regulation of the tracking error for an n-dimensional dynamic system with zero dynamics, which is preceded by a Prandtl-Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. We treat this problem from the perspective of switched systems, where the state of the hysteresis operator defines the switching surfaces. The common Lyapunov function theorem is utilized together with an LMI condition to show that, under suitable conditions, the tracking error of the system goes to zero exponentially fast when a constant reference is considered. A key feature of this LMI condition is that it does not require the hysteresis effect to be small, meaning that hysteresis inversion is not required. We use this condition together with a periodicity assumption to prove that a servocompensator-based controller can stabilize a system with hysteresis without using hysteresis inversion. Finally, we conduct experiments using a servocompensator-based controller, where we verify the stability of the system and achieve a mean tracking error of 0.5% at 200 Hz using a sinusoidal reference.

In this paper we utilize dynamic inversion together with high-gain observers to stabilize an inverted pendulum on a cart. Dynamic inversion is used to invert the nonlinear map involving the control input and the high-gain observers are used to estimate the states and terms related to acceleration variables. Through numerical simulations and experiments, it is shown that it is possible to stabilize the inverted pendulum on a cart and recover the performance of state feedback control.

We solve the problem of semi-global output feedback stabilization of a class of non-minimum phase nonlinear systems using a full order Extended Kalman Filter-Extended High Gain Observer proposed in [1]. We allow for any globally stabilizing full state feedback control scheme to be used as long as it satisfies a particular ISS condition. The proposed output feedback control system strategy is constructive and simple. Finally, we provide an example that illustrates the procedure and efficacy of the control design.

The stability of systems with hysteresis, driven by developments in smart material applications, has been an important topic of research over the past two decades. Most results provide sufficient conditions for boundedness of the system states, but do not further investigate the steady state solutions. In this paper, we present an example of a system with hysteresis that possesses self-excited limit cycles. In particular, we consider an integral-controlled system with backlash (also known as play operator). A Newton-Raphson algorithm is formulated to calculate the limit cycles in the system. We then prove that the amplitude and period of these limit cycles have linear relationships to parameters within the system. These results are then confirmed in simulation, where we demonstrate our ability to predict and modify the properties of the limit cycles.

Piezoelectric actuators are commonly modelled by a hysteresis operator preceding fast, stable linear dynamics. This motivates our work to analyze systems with these characteristics when a popular control architecture involving both hysteresis inversion and feedback is adopted. In particular, we are interested in the frequency-scaling behavior of the tracking error for such systems, which is of practical interest but has received little attention in the literature. The hysteresis nonlinearity in our analysis is represented by piecewise linear segments, which is applicable to many hysteresis operators. To fix ideas, we consider a proportional integral controller for the feedback component, as well as the case where a constant-gain feedforward component is added to the feedback term. This work is a continuation of our previous work where we only examined the system behavior for a given hysteresis segment. Here we use singular perturbation techniques to separate the slow variables of the controller from the fast variables of the plant dynamics, and derive the solution of the closed-loop system and the tracking error at the steady state under a sinusoidal reference. The analysis incorporates the effect of uncertainty in the hysteresis model, and offers insight into how the tracking error scales with the reference frequency. The analysis is confirmed with experimental and simulation results for the control of a piezo-actuated nanopositioner.

In this paper we propose a new method for the design of an output feedback controller for a minimum-phase, uncertain, input-nonaffine, nonlinear system. By combining dynamic inversion control together with extended high-gain observer, our output feedback controller is able to bring the trajectories of the closed-loop system arbitrarily close to that of a given target system. Stability analysis of the closed-loop system is presented along with simulation results of trajectory tracking.

In this paper we propose a conditional integrator for solving the regulation problem of a class of nonlinear systems that probably possess unstable zero dynamics. The control scheme mainly takes advantage of the auxiliary controller proposed in [3] and a slow integrator. We present that the solution of the regulation problem can be cast as two auxiliary problems. Furthermore it is shown that the design of the conditional integrator requires the design of a feedback control that solves two stabilization problems simultaneously, one inside the boundary layer of a continuously-implemented sliding model control, and one outside it. Hence the design of the auxiliary controller can be independent of the internal model. We approach this issue by using a two-time-scale method. The effectiveness of the controller is illustrated through a linear example.

In this paper we propose a robust control scheme for a piezo-actuated nanopositioner to track arbitrary references. The positioner is represented as a linear system preceded by hysteresis, which is modeled with a Prandtl-Ishlinskii (PI) operator. In order to reduce the hysteresis effect, an approximate operator is used as a feedforward compensator. A sliding mode controller is then used to mitigate the effect of inversion error. In existing work on sliding mode control of piezo-actuated systems, the coefficient of the switching component of the control is typically chosen by trial and error. In contrast, in this work we analytically derive an upper bound on the inversion error using the hysteresis model. This bound is a function of the state and time, which is much less conservative than constant bounds. The stability of the closed-loop system is established by Lyapnuov analysis. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed method.

The problem of stabilizing steady gliding is very critical for an underwater glider, which is subject to many non-negligible disturbances from the aquatic environment. Traditional control methods like PID control, LQR control or torque control, can not provide simultaneously easy controller implementation and fast convergence speed for stabilization. In paper we propose a new nonlinear, passivity-based controller for the stablization problem. The controller is designed based on an approximation of a reduced model that is obtained through singular perturbation analysis, and consequently, it does not require full state feedback and is thus easy to implement. The local stability of the closed-loop full system is established through linearization. Simulation results are provided to demonstrate that the proposed controller achieves rapid convergence in stabilization.

For underactuated mechanical systems the use of disturbance estimators has been limited. For fully actuated mechanical systems, disturbance cancellation techniques have been studied and used to reduce the effect of disturbances on system performance. Particularly, the extended high gain observer has shown promising results in performance recovery. However, using the extended high gain observer to estimate and cancel the disturbance in one link of an underactuated system results in adding that disturbance to other links. This paper explores the effects of applying the extended high gain observer to an underactuated mechanical system. We show that the extended high gain observer can be used to reduce the effect of disturbances in a rotary pendulum system.

In this work, we address the tracking problem for an unknown reference comprised of two sinusoids. We propose an adaptive servocompensator based on a pair of frequency estimators. Slow adaptation is used to create three time scales within the closed-loop system, corresponding to the controller and plant dynamics, fast frequency estimate, and slow frequency estimate. Stability of the boundary-layer system, comprised of the servocompensator and plant dynamics, is achieved with a stabilizing controller. Novel nonlinear analysis is then performed on the average system to show global asymptotic stability. The algorithm's performance is verified by experiments conducted on a commercial nanopositioner, and its performance is shown to be comparable to that of iterative learning control.

In this paper, we address the regulation problem for a linear plant driven by a neutrally stable exosystem. It is assumed that the plant is subjected to an exogenous disturbance, and that this signal is formed of known harmonics of a sinusoidal reference signal whose frequency is unknown. Such an exosystem is motivated by the case where the system possesses an input nonlinearity like hysteresis. We propose an adaptive servocompensator requiring estimation of only the primary frequency. Using two-time-scale analysis, we establish the semi-global convergence of the parameter error to an arbitrarily small neighborhood of zero, when the adaptation gain is small enough and when the disturbance is sufficiently small comparing to the reference signal. The proposed control scheme involves far fewer adaptation variables than existing methods, and its performance is verified in both simulation and experiments conducted on a nanopositioning stage.

One of the fundamental objectives in systems neuroscience is to precisely control the spatiotemporal firing of cortical neurons to elicit a desired pattern of activity. In this work, we study the effects of intracortical micro-stimulation on the dynamics of a basal ganglia microcircuit model, and explore the feasibility of controlling the spatiotemporal firing patterns of the population in the presence of unobserved inputs. Results from the simulation study suggest that properly designed Multiple-Input-Multiple-Output (MIMO) feedback controller can force a subpopulation of output neurons to follow a prescribed spatiotemporal firing pattern despite the presence of unobserved inputs. The accuracy of the spike timing of the controlled neural firing with respect to the reference spike trains is in the order of tens of milliseconds. Even a simplified circuit model of Hammerstein-Wiener type can help in prescreening potential stimulation sites and analyzing the nominal stability of the closed-loop system.

Scanning probe microscopes, used in a diverse range of fields, are commonly actuated by piezoelectric nanopositioners. Because of coupling between hysteresis and fast dynamics, precise control of piezo-actuated systems is a difficult task. To solve this problem, we propose the use of an adaptive servocompensator. First, we present an adaptive law augmented with parameter projection, and establish its robustness to matched disturbances. Next, we show that with well designed hysteresis inversion, there exists an asymptoticly stable periodic solution to the closed-loop system. This facilitates the treatment of the error in hysteresis inversion as an exogenous periodic disturbance. Using adaptation, we can modify the parameters of the servocompensator to track the reference signal and reduce the effect of hysteresis on the tracking error. We confirm our theoretical results through experimentation on a commercial nanopositioner, in which we test tracking and adaptation performance for different input signals. Tracking performance of the proposed adaptive servocompensator is comparable to that of an iterative control algorithm, yet without requiring any knowledge about the spectrum or period of the reference. In addition, we demonstrate robustness of the controller to varying loading conditions.

This paper proves a new property of the nonlinear regulators of [4] and [7]. In both papers the steady-state control is immersed into a linear internal model. In general, the model produces the sinusoidal signals generated by an exosystem, as well as a number of their harmonics, which are induced by the system's nonlinearities. When the internal model does not account for all harmonics, there will be an error between the steady-state control needed to achieve zero steady-state regulation error and the steady-state control produced by the internal model. If the norm of this error is bounded by a constant δ, it is shown in [4] and [7] that the steady-state regulation error will be of the order O(δ). In this paper we prove a shaper result where the steady-state regulation error is shown to be of the order O(μδ), where μ is a design parameter of the continuously-implemented sliding mode controller of [4] and [7]. Therefore, the regulation error can be reduced by decreasing μ. This result allows us to tradeoff the dimension of the internal model versus the value of μ as means of reducing the regulation error.

Partly motivated by the nanopositioning application in AFM and SPM systems, we consider the problem of tracking periodic signals for a class of systems consisting of linear dynamics preceded by a hysteresis operator, where uncertainties exist in both the dynamics and the hysteresis. A servocompensator is proposed, in combination with an approximate hysteresis inverse, to achieve high-precision tracking. The servocompensator accommodates the internal model of the reference signal and a finite number of harmonic terms. It is shown that, with a Prandtl-Ishlinskii (PI) hysteresis operator, the closed-loop system admits a unique, asymptotically stable, periodic solution, which justifies treating the inversion error as an exogenous periodic disturbance. Consequently, the asymptotic tracking error can be made arbitrarily small when the servocompensator accommodates a sufficient number of harmonic terms. Robustness with respect to uncertainties in the dynamics is also established. Simulation and experimental results are presented to validate the approach and evaluate the role of hysteresis inversion. In particular, experiments on a nanopositioner show that, with the proposed method, tracking can be achieved for a 200 Hz reference signal with 0.6% mean error and 2.3% peak error for a travel range of 20 µm.

In this paper, we present an output feedback regulator for nonlinear systems that could potentially include unstable zero dynamics. The regulation scheme adopted herein incorporates continuously-implemented sliding mode control and an extended high gain observer to estimate the derivatives of the output and one of the unknown functions. The result is illustrated using a simulation.

In the paper [1], Serrani and Isidori design an output feedback controller that achieves semiglobal output regulation for a class of minimum phase nonlinear systems. The controller has three basic components: an internal model to ensure asymptotic regulation, a high-gain partial state feedback controller to stabilize the augmented system of the plant and the internal model, and a high-gain observer to implement the partial state feedback. In this paper we show a property of the transient performance of the controller of [1]. We consider an alternate controller that shares with the controller of [1] the structure of high-gain partial state feedback and high-gain observer, but without internal model. Such controller can only achieve practical regulation. We show that when the controller and observer gains are high enough, the trajectories under the two controllers will be close to each other. This property shows that the transient performance of the controller of [1] is not degraded by the inclusion of the internal model.

This paper studies the design of a full-order, high-gain observer for a class of minimum-phase nonlinear systems. The dynamic state feedback design is modified to include the observer for the internal dynamics. It is shown that the performance of such a dynamic partial-state feedback control can be recovered by the output feedback control using a sufficiently fast high-gain observer, in the presence of model uncertainty.

The design of advanced components for space and terrestrial telecommunications requires both sophisticated design methodologies and manufacturing technologies for improving current component performances. In particular, determining the optimal shape and size of a component is a problem of primary importance for microwave engineers. In order to improve the classical microwave filters, shape and topology optimization methods can be utilized together with numerical modeling methods. Topology gradient and level set methods are coupled here with the finite element method for optimizing the shape of dielectric resonators included in microwave filters.

High-gain observers are commonly utilized to estimate the states used in constructing the output feedback control, when such states are derivatives of the output. In the presence of measurement noise, the estimation error can be noticeably compromised if the observer gain is chosen too large. However, the effect of measurement noise on the tracking error is less significant. This phenomenon is demonstrated with a nonlinear motivating example, and further explored in the context of linear systems from a transfer function perspective.

Motivated by the adaptive control problem for systems with hysteresis, a two-time-scale averaging framework is presented in this paper for systems involving operators, by extending the work of Teel and co-workers. The developed averaging theory is applied to the analysis of a model reference adaptive inverse control scheme for a system consisting of linear dynamics preceded by a Prandtl-Ishlinkskii (PI) hysteresis operator. The fast component of the closed-loop system involves the coupling of an ordinary differential equation and a hysteresis operator derived from the PI operator and its inverse, while the slow component is the parameter update rule. The stability of the boundary-layer system and that of the average system are established under suitable conditions, which implies practical regulation of the parameter error and tracking error under the adaptive scheme.

A design technique based on a shape optimization strategy (topology gradient algorithm) and a 3D ceramic stereolithography process are described in this paper. Our goals are to propose innovative components in terms of electric performances and topologies, by using these two approaches together. Several components have been designed, manufactured and tested with success. An example is given for the design of microwave filters including dielectric resonators.

This paper studies the output regulation of nonlinear systems using conditional servocompensators. Previous work introduced the conditional servocompensator that acts as a traditional servocompensator in a neighborhood of the zero-error manifold, while acting as a stable system outside a boundary layer, leading to improvement in the transient response while achieving zero steady-state tracking error in the presence of time-varying exogenous signals. The conditional servocompensator tool was introduced for sliding-mode feedback controllers. This paper extends the technique to more general feedback controllers by using Lyapunov redesign and saturated high-gain feedback.