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A sliding mode observer (SMO) design and convergence analysis are presented in this paper, which includes a rigorous treatment to address multiple discontinuities in the resulting estimation error dynamics. In an extension of our previous SMO results, the current work provides a non-trivial reworking of the SMO estimation error system development and stability analysis that incorporates differential inclusions. The specific contributions presented in this paper beyond the previous work include: (1) A differential inclusions-based analysis of the SMO, which incorporates the set-valued definition of the discontinuous signum function; (2) An expanded derivation of the estimation error dynamics, which emphasises advantageous properties particular to our SMO structure; (3) A Lyapunov-based stability analysis of the SMO, that rigorously incorporates the multiple discontinuities in the estimation error dynamics. The Lyapunov-based stability analysis proves that the SMO achieves finite-time estimation of the complete state vector, where the output equation is in a nonstandard mathematical form. To test the performance of the SMO, numerical simulation results are also provided, which demonstrate the capability of the SMO to estimate the state of a fluid flow dynamic system using only a single sensor measurement of the flow field velocity. [ABSTRACT FROM AUTHOR]

Summary: This article presents a nonlinear closed‐loop active flow control (AFC) method, which achieves asymptotic regulation of a fluid flow velocity field in the presence of actuator uncertainty and sensor measurement limitations. To achieve the result, a reduced‐order model of the flow dynamics is derived, which utilizes proper orthogonal decomposition (POD) to express the Navier‐Stokes equations as a set of nonlinear ordinary differential equations. The reduced‐order model formally incorporates the actuation effects of synthetic jet actuators (SJA). Challenges inherent in the resulting POD‐based reduced‐order model include (1) the states are not directly measurable, (2) the measurement equation is in a nonstandard mathematical form, and (3) the SJA model contains parametric uncertainty. To address these challenges, a sliding mode observer (SMO) is designed to estimate the unmeasurable states in the reduced‐order model of the actuated flow field dynamics. A salient feature of the proposed SMO is that it formally compensates for the parametric uncertainty inherent in the SJA model. The SMO is rigorously proven to achieve local finite‐time estimation of the unmeasurable state in the presence of the parametric uncertainty in the SJA. The state estimates are then utilized in a nonlinear control law, which regulates the flow field velocity to a desired state. A Lyapunov‐based stability analysis is provided to prove local asymptotic regulation of the flow field velocity. To illustrate the performance of the proposed estimation and AFC method, comparative numerical simulation results are provided, which demonstrate the improved performance that is achieved by incorporating the uncertainty compensator. [ABSTRACT FROM AUTHOR]

A synthetic jet actuator-based output feedback control method is presented, which achieves asymptotic limit cycle oscillation regulation in small unmanned aerial vehicle wings, where the dynamic model contains uncertainty and unmodeled external disturbances. In addition, the proposed control method compensates for the parametric uncertainty and nonlinearity inherent in the synthetic jet actuator dynamics. Motivated by the limitations characteristic of small unmanned aerial vehicles, the control method is designed to be computationally inexpensive, eliminating the need for time-varying parameter update laws, function approximators, or other computationally heavy techniques. To this end, a computationally minimal robust-inverse control method is utilized, which is proven to compensate for the uncertainties in both the aerial vehicle dynamics and the synthetic jet actuator dynamics. By endowing the robust-inverse control law with a bank of dynamic filters, asymptotic limit cycle oscillation regulation is achieved using only pitching and plunging displacement measurements in the feedback loop. The result is an asymptotic synthetic jet actuator-based limit cycle oscillation regulation control method, which does not require velocity measurements, adaptive laws, or function approximators in the feedback loop. To achieve the result, a detailed mathematical model of the limit cycle oscillation dynamics is utilized, which includes nonlinear stiffness effects, unmodeled external disturbances, and dynamic model uncertainty, in addition to the parametric uncertainty in the synthetic jet actuator dynamic model. A rigorous Lyapunov-based stability analysis is utilized to prove asymptotic regulation of limit cycle oscillations, and numerical simulation results are provided to demonstrate the performance of the proposed control law. [ABSTRACT FROM AUTHOR]

Abstract: In a typical adaptive update law, the rate of adaptation is generally a function of the state feedback error. Ideally, the adaptive update law would also include some feedback of the parameter estimation error. The desire to include some measurable form of the parameter estimation error in the adaptation law resulted in the development of composite adaptive update laws that are functions of a prediction error and the state feedback. In all previous composite adaptive controllers, the formulation of the prediction error is predicated on the critical assumption that the system uncertainty is linear in the uncertain parameters (LP uncertainty). The presence of additive disturbances that are not LP would destroy the prediction error formulation and stability analysis arguments in previous results. In this paper, a new prediction error formulation is constructed through the use of a recently developed Robust Integral of the Sign of the Error (RISE) technique. The contribution of this design and associated stability analysis is that the prediction error can be developed even with disturbances that do not satisfy the LP assumption (e.g., additive bounded disturbances). A composite adaptive controller is developed for a general MIMO Euler–Lagrange system with mixed structured (i.e., LP) and unstructured uncertainties. A Lyapunov-based stability analysis is used to derive sufficient gain conditions under which the proposed controller yields semi-global asymptotic tracking. Experimental results are presented to illustrate the approach. [Copyright &y& Elsevier]

Summary: Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO. [ABSTRACT FROM AUTHOR]

Observer-based sliding mode control of combustion instability in a Rijke-type thermoacoustic system is considered. A commonly used thermoacoustic model with sensors and monopole-like actuators is linearized and formulated in a state-space form. It is assumed that the velocity or pressure sensor locations are chosen to assure the observability of the system. An observer-based sliding mode controller is then implemented to tune the actuators so that the system is asymptotically stable. The effectiveness of the controller is illustrated through a simulation example involving two modes and one sensor. The successful demonstration indicates that the observer-based feedback controller can be applied to a real combustion system with multiple modes. [ABSTRACT FROM AUTHOR]