Stability Of Internal Dynamics Research Articles

Output redefinition-based active disturbance rejection control for nonminimum phase hypersonic vehicles

PurposeThis paper aims to propose and verify an improved cascade active disturbance rejection control (ADRC) scheme based on output redefinition for hypersonic vehicles (HSVs) with nonminimum phase characteristic and model uncertainties.Design/methodology/approachTo handle the nonminimum phase characteristic, a tuning factor stabilizing internal dynamics is introduced to redefine the system output states; its effective range is determined by analyzing Byrnes–Isidori normalized form of the redefined system. The extended state observers (ESOs) are used to estimate the uncertainties, which include matched and mismatched items in the system. The controller compensates observations in real time and appends integral terms to improve robustness against the estimation errors of ESOs.FindingsTheoretical and simulation results show that the stability of internal dynamics is guaranteed by the tuning factor and the tracking errors of external commands are globally asymptotically stable.Practical implicationsThe control scheme in this paper is expected to generate a reliable way for dealing with nonminimum phase characteristic and model uncertainties of HSVs.Originality/valueIn the framework of ADRC, a concise form of redefined outputs is proposed, in which the tuning factor performs a decisive role in stabilizing the internal dynamics of HSVs. By introducing an integral term into the cascade ADRC scheme, the compensation accuracy of matched and mismatched disturbances is improved.

Zero-Level Control Design in AC Microgrids: A Robust Multivariable Approach

In this paper, a multi-input multi-output (MIMO) robust proportional-integral (PI) controller is designed for zero-level control of AC microgrids. The study system is a voltage-sourced converter connected to the rest of the microgrid through a distribution line and an AC output filter. The design procedure of the proposed high-gain PI controller is independent from the state matrix of the distributed energy resources. Severe local load changes are considered as the system unknown disturbances. It is proved that the closed-loop system behaves like a first-order system with stable internal dynamics. As the bandwidth of the suggested zero-level control can be systematically adjusted, it can properly operate in both high and medium frequencies without considerable fluctuations and overshoots at the output. It is also shown that circulating currents, which can cause overcurrent conditions in power electronic devices and damage DC-link capacitors, are limited without using any limiters. By considering some realistic scenarios and through time-domain simulations in MATLAB/SIMULINK and a supporting experimental test, it is shown that the proposed strategy can successfully attenuate adverse effects of unknown disturbances on the load voltage of islanded microgrids.

Integrated Autopilot Guidance Based on Zero-Effort-Miss Formulation for Tail-Controlled Missiles

This paper presents a control structure integrating guidance and control loops for tail-controlled missile systems. Motivated by the fact that common tail-controlled missiles involve non-minimum phase dynamics, the proposed controller is designed to prevent the internal dynamics from diverging, as well as achieving homing against the intended target. To minimize the miss distance at the end of homing, we derive a formulation of a zero-effort-miss using engagement kinematics that contain the rotating dynamics of the missile, which is different from existing approaches. Subsequently, to nullify the zero-effort-miss, a nonlinear controller is designed based on the Lyapunov stability theory. Since the derived controller has a similar structure to the conventional three-loop topology that has been utilized for various tail-controlled flight systems, it is expected that the proposed method can be applied to the actual system from a practical point of view. Numerical simulation results also show that the proposed method achieves target interception while possessing stable internal dynamics.

Academic inbreeding in the Spanish public university system: a review of its institutional and context determinants (Endogamia en el sistema universitario público español: una revisión de sus determinantes institucionales y contextuales)

ABSTRACT University systems with a high level of academic inbreeding tend to be closed to attracting (inter)national talent, while instead prioritizing retention of the human factor in the institution and the stabilization and continuity of internal bureaucratic dynamics. The literature suggests that levels of academic inbreeding depend on both institutional and structural factors within the universities themselves, as well as contextual factors in the country and/or region. In this study, we empirically analyse the causal relationship between levels of academic inbreeding at Spanish public universities and the characteristics of the university context and their institutional features. Our results show that the variables that most influence the level of endogamy of Spanish public universities are their age and their specialization by field of knowledge. Furthermore, the academic inbreeding in Spain seems more related to the chair-holding dynamics by which professors gain power than to any other factor.

Adaptive integral-sliding-mode control strategy for maneuvering control of F16 aircraft subject to aerodynamic uncertainty

Aircraft dynamics are highly nonlinear and the traditional linear flight controllers cannot fully utilize the real-time performance ability of aircraft. This paper investigates a nonlinear control approach for high maneuvering fighter aircraft that deployed baseline nonlinear-dynamics-inversion (NDI) control and high-level robust adaptive integral-sliding-mode (ISM) control. The design objective is to maintain the acceptable flight quality at a high angle-of-attack under the influence of unknown disturbance and aerodynamics uncertainties. The nonlinear dynamics of F16 aircraft are divided into two loops by utilizing time-scale separation principle and adaptive ISM/NDI controller is designed for each loop. The aerodynamics coefficients are estimated using the iterative reweighted least square (IRLS) algorithm based on the wind tunnel real-time flight data available at NASA Langlet and Ame Research center. The internal dynamics stability is proven to validate the complete system stability. Simulations are conducted on F16 aircraft and compared the results with the NDI controller and ISM/NDI controller (without adaptive strategy).

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown “control direction” and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).

Representation and stability of internal dynamics

AbstractWe consider nonlinear multibody systems and present a suitable set of coordinates for the internal dynamics. Furthermore, we derive sufficient conditions on the system parameters of the multibody system such that the internal dynamics are bounded‐input, bounded‐output stable.

Adaptive parameter estimation control of nonminimum phase hypersonic flight vehicle

In this study, considering the longitudinal dynamic model of a nonminimum phase hypersonic flight vehicle, output-redefinition-based adaptive parameter estimation control is proposed. Output redefinition is employed to transform unstable internal dynamics to asymptotically stable internal dynamics. Based on the coordinate transformation of the redefined internal dynamics, the pitch angle command is derived and used as the reference command of the input-output subsystem. For the redefined attitude subsystem and the velocity subsystem, the unknown aerodynamic functions are decomposed into the known state vector and the unknown aerodynamic parameter vector, that is the linear parametric form. The adaptive updating laws are constructed to estimate the aerodynamic parameter vectors, and then the dynamic inversion control is designed for the velocity subsystem and the backstepping control is designed for the input-output subsystem. The system stability is analyzed via the Lyapunov stability theorem while simulation studies are conducted to illustrate the effectiveness of the proposed method.

Disturbance observer‐based output feedback control of hydraulic servo system considering mismatched uncertainties and internal pressure dynamics stability

For valve-controlled hydraulic servo system, the suppression of mechanical dynamics uncertainties and the analysis of internal pressure dynamics stability (i.e. the pressure into the two chambers of the actuator) are still the widespread concern issues. This study presents an easy-to-implement observer-based output feedback control scheme for hydraulic valve-controlled single-rod actuator system with addressing mismatched mechanical dynamic uncertainties and proving internal pressure dynamics stability analysis. The singular value perturbation approach is used to simplify the system model, and then a practical output feedback controller augmented with extended-state observer is developed through back-stepping design approach. The main contribution of this study is two-fold. First, a practical reduced-order model-based back-stepping controller is developed. Second, the stability issue of internal pressure dynamics is analysed. Besides giving theoretical analysis, extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. The present method can guarantee prescribed tracking transient performance in the presence of uncertain disturbances. Also, the stability of internal dynamics is proved.

New Adaptive High Starting Torque Scalar Control Scheme for Induction Motors Based on Passivity

A novel adaptive high starting torque (HST) scalar control scheme (SCS) for induction motors (IM) is proposed in this paper. It uses a new adaptive-passivity-based controller (APBC) proposed herein for a class of nonlinear systems, with linear explicit parametric dependence and linear stable internal dynamics, which encompasses the IM dynamical model. The main advantage of the HST-SCS includes the ability to move loads with starting-torque over the nominal torque with a simple and cost-effective implementation without needing a rotor speed sensor, variable observers, or parameter estimators. The proposed APBC is based on a direct control scheme using a normalized fixed gain (FG) to fine-tune the adaptive controller parameters. The basic SCS for induction motors (IM) and the HST-SCS were applied to an IM of 200 HP and tested using a real-time simulator controller OPAL-RT showing the achievement of the proposal goal.

Output Feedback Approximation-Free Prescribed Performance Tracking Control for Uncertain MIMO Nonlinear Systems

We consider the problem of designing a low-complexity, approximation-free, output-feedback controller to achieve output tracking with prescribed transient and steady-state performance for uncertain, high relative degree, multi-input–multi-output (MIMO) nonlinear systems, which are equivalent via a diffeomorphic coordinate transformation to the Byrnes–Isidori canonical form, with uniform-bounded-input-bounded-state (UBIBS) stable internal dynamics and bounded external disturbances. The proposed controller utilizes the prescribed performance control methodology and high-gain observers. To avoid the propagation of the peaking phenomenon, the developed controller is appropriately saturated without compromising the closed-loop system performance attributes. Moreover, the selection of the observer gains is significantly relaxed owing to the fact that the adopted prescribed performance control technique seeks only for boundedness properties to establish the desired transient and steady-state performance specifications. Finally, various simulation studies clarify and verify the approach.

Stability Criteria for Input Filter Design in Converters with CPL: Applications in Sliding Mode Controlled Power Systems

Microgrids are versatile systems for integration of renewable energy sources and non-conventional storage devices. Sliding Mode techniques grant excellent features of robustness controlling power conditioning systems, making them highly suitable for microgrid applications. However, problems may arise when a converter is set to behave as a Constant Power Load (CPL). These issues manifest in the stability of internal dynamics (or Zero Dynamics), which is determined by the input filter of the power module. In this paper, a special Lyapunov analysis is conducted to address the nonlinear internal dynamics of SM controlled power modules with CPL. It takes advantage of a Liérnad-type description, establishing stability conditions and providing a secure operation region. These conditions are translated into conductance and invariant region diagrams, turning them into tools for the design of power module filters.

Experimental verification of a hybrid control scheme with chaotic whale optimization algorithm for nonlinear gantry crane: A comparative study

This paper proposes an experimental verification of a hybrid partial feedback linearization (PFL) and deadbeat (DB) control scheme as in Hamdy et al. (2018) with chaotic whale optimization algorithm (CWOA) for a nonlinear gantry crane (GC) system. The PFL linearizes the nonlinear model to end up with a linear closed-loop system. The DB controller is utilized for the desirable accelerated response without any oscillation or undesirable effects on the internal dynamics stability. The CWOA is used to tune the controller parameters. A sliding-mode observer (SMO) is utilized to estimate the unmeasured states. Using this hybrid scheme, a better payload sway elimination can be obtained. Finally, the experimental results are presented to illustrate the efficiency and the effectiveness of the proposed scheme with a comparative study.

Combined open-loop and funnel control for underactuated multibody systems

We consider tracking control for multibody systems which are modeled using generalized coordinates. Utilizing the two-degree- of-freedom approach to controller design, we combine a feedforward with a feedback controller. The feedforward control input is computed using the method of servo-constraints, which relies on an inverse model of the system. The feedback control input is generated by a dynamic output feedback which consists of the combination of a funnel controller with a funnel pre-compensator. This feedback controller is model free and hence inherently robust. The control design is restricted to multibody systems with relative degree two or three which have input-to-state stable internal dynamics. In the main result, we prove that the proposed controller is able to guarantee prescribed performance of the tracking error even in the presence of uncertainties and disturbances. We illustrate the application of the control design by a mass on car system (single-input, single-output) and a planar robotic manipulator (two-input, two-output). In the case of relative degree two, these systems contain an unknown friction term.

Funnel control for nonlinear systems with higher relative degree

AbstractWe consider tracking control for nonlinear multi‐input, multi‐output systems which have arbitrary strict relative degree and input‐to‐state stable internal dynamics. For a given reference signal, our aim is to design a controller which achieves that the tracking error evolves within a prespecified performance funnel around the reference signal. To this end, we introduce a new controller which involves the first r−1 derivatives of the tracking error, where r is the strict relative degree of the system.

The funnel pre‐compensator

SummaryWe introduce the funnel pre‐compensator as a novel and simple adaptive pre‐compensator of “high‐gain type”. We show that this pre‐compensator is feasible for a large class of signal pairs, which satisfy a certain relationship. We show that the funnel pre‐compensator guarantees prescribed transient behavior of the compensator error, it is of low complexity and inherently robust since its design is model‐free. As an application in adaptive control of nonlinear systems, a cascade of funnel pre‐compensators is exploited to obtain an artificial output with explicitly known derivatives, which tracks the system output with prescribed transient behavior. In some important cases the interconnection of the system with the pre‐compensator cascade is shown to have input‐to‐state stable internal dynamics. This guarantees feasibility of a novel funnel controller that consists of a funnel pre‐compensator cascade in conjunction with a recently developed funnel controller for systems with arbitrary relative degree. We illustrate the application of this interconnection for some mechanical systems.

A hybrid partial feedback linearization and deadbeat control scheme for a nonlinear gantry crane

This paper presents the design of a hybrid partial feedback linearization and deadbeat control scheme for a nonlinear gantry crane with friction to control its position and sway angle. The partial feedback linearization is used to linearize the nonlinear model and to stabilize its internal dynamics. In many crane applications, it's necessary to accelerate the system response. As a result, this will cause oscillation in the position as well as the sway angle. So, the deadbeat controller is added to get the desirable accelerated response without any oscillation or adverse effects on the internal dynamics stability. By using Lyapunov stability method, the proposed scheme is proved to be globally stable, with converging tracking errors to the desired performance. The simulation results are accomplished to evaluate the effectiveness of the proposed scheme and to demonstrate its reliability to control crane systems with comparative results.

SSR Mitigation of Series-Compensated DFIG Wind Farms by a Nonlinear Damping Controller Using Partial Feedback Linearization

A nonlinear damping controller using partial feedback linearization (PFL) technique is designed with an aim to mitigate subsynchronous resonance (SSR) in series-compensated doubly-fed induction generator (DFIG)-based wind farms, which is integrated to simplified Nordic power system. The controller using PFL technique is implementable into a partially linearized form of a system with DFIG wind farm that results in reduced system order and small computational burden. The derivation of control law does not also demand thorough knowledge of nonlinear and ambiguous system dynamics. The proposed controller design approach has four distinguished steps: 1) scrutinizing partial linearizability, 2) performing partial linearization, 3) assessing stability of internal system dynamics, and 4) obtaining control laws. Small-signal stability analysis is performed that includes electrical damping analysis and eigenvalue analysis. The controller is found to demonstrate a superior performance in SSR mitigation. Time-series simulation is carried out to confirm the veracity of the outcomes obtained from the small-signal stability analysis.

Effects of Viscous Damping on Differential Flatness-Based Control for a Class of Under-Actuated Planar Manipulators

For under-actuated manipulators, not all joint trajectories are dynamically feasible and it is difficult to characterize feasible joint trajectories analytically. Differential flatness, if applicable, provides a systematic approach to plan and control feasible trajectories for such systems. Previously, Agrawal and Sangwan (2008) have formulated a methodology to design under-actuated planar manipulators to be differentially flat. This methodology assumed that the joints in the manipulator have no dissipation. In real systems, however, these joints have dissipative effects (viscous damping, coulomb friction etc.). This letter studies effects of viscous damping at unactuated joints on differential flatness-based control for the class of under-actuated manipulators presented by Agrawal and Sangwan in 2008. It is shown that in presence of viscous damping the original flat outputs lose relative degree and a stable internal dynamics is induced. Hence, the original outputs are no longer flat outputs. However, because of the stable internal dynamics induced they are still useful in applications where only output control is needed and full-state control is not desired. It is also shown that although the original set of outputs lose relative degree with viscous damping, the system remains differentially flat with another set of flat outputs. Hence, full-state control can still be performed with a new set of flat outputs in presence of viscous damping. Simulation results for controllers based on the two scenarios mentioned above are presented with a 3-DOF manipulator.

Funnel control for nonlinear systems with known strict relative degree

We consider tracking control for uncertain nonlinear multi-input, multi-output systems which have arbitrary strict relative degree and input-to-state stable internal dynamics. For a given sufficiently smooth reference signal, our aim is to design a low-complexity model-free controller which achieves that the tracking error evolves within a prespecified performance funnel. To this end, we introduce a new controller which involves the first r−1 derivatives of the tracking error, where r is the strict relative degree of the system. We derive an explicit bound for the resulting input and discuss the influence of the controller parameters. We further present some simulations where our funnel controller is applied to a mechanical system with higher relative degree and a two-input, two-output robot manipulator. The controller is also compared with other approaches.