Date of Award
Doctor of Philosophy (PhD)
Aeronautics and Astronautics
Committee Member 1
Committee Member 2
Committee Member 3
The simultaneous presence of factors such as uncertain plant parameters (e.g., inertia variations, change of damping coefficient), time-varying disturbances (e.g., imprecise mathematical models, uncertain nonlinearities), input delay (e.g., due to transport phenomenon, computation latencies, communication lags), and inaccessibility of the plant states of an nth− order dynamical system present a challenge to the formal control design and to its closed loop stability and performance guarantees. It is well-known that input delays can cause negative phase shifts, limiting the control bandwidth which when coupled with system uncertainties can potentially shift the system into an unstable region of operation. This is especially critical for unstable systems with faster dynamics (like flying objects and linear motor systems). This effect is only compounded if full information on the states is not available for tracking purposes and makes the control of these dynamic systems very challenging.
This research develops a control framework, referred to as prediction-based adaptive robust control (PARC), for high performance tracking control of input delayed uncertain nth− order LTI single input full state feedback / SISO feedback systems to simultaneously handle the effects of above factors with theoretical guarantees of stability and performance of the closed loop system. The proposed PARC design effectively combines the design techniques of prediction-based control, adaptive control, and deterministic robust control, while smoothly addressing the conflict of assumptions with the individual control strategies, to simultaneously compensate for the above complexities. The proposed framework retains many of the advantages of the underlying control schemes while extracting additional benefits from their integration. Our framework systematically addresses several challenges associated with the above problem -1) how to robustify the standard finite spectrum assignment (FSA) prediction scheme, typically used to handle input delays, that could become inaccurate due to parameter and disturbance uncertainties; 2) how to effectively handle the emergent unmatched disturbance phenomenon that result from such standard prediction scheme; 3) how to design a stabilizing tracking control framework with transient and steady-state performance guarantees to simultaneously handle the above factors without inducing potentially destabilizing oscillations due to uncertain prediction; and 4) how to design a globally exponentially converging state estimator in the presence of both parameter uncertainties and time-varying disturbances.
By systematically exploiting the information structure of an uncertain time-delayed dynamical system and under some reasonable technical conditions, the proposed PARC framework attempts to yield good performances without requiring ad hoc delay compensation strategies or time-consuming and expensive off-line identification of system parameters and disturbance model. Using the system measurements, estimates of the states and that of the tracking error are constructed using an adaptive robust observer that satisfies certain technical conditions to guarantee its existence. These estimates are then used: 1) with the prediction-based adaptive model compensation and the prediction-based projection type adaptation laws to reduce the structured portion of the cumulative uncertainties in a stable manner and 2) with a prediction-based robust filter to attenuate the cumulative uncertainties due to uncertain prediction to guarantee semi-global exponential convergence for the tracking error with an uniform ultimate bound that depends on the delay, uncertainty bounds, and controller gain. Further, a robust prediction scheme is discussed that implicitly factors in the system uncertainties in its prediction and helps to decompose the unmatched uncertainties into a larger matched portion and a smaller unmatched portion, leading to less conservative results. The proof relies on Lyapunov-based analysis with mathematical induction arguments to guarantee the stability and performance for the tracking error, while the boundedness of the control law is shown by recasting the delayed input integral equation into a series convergence problem using the Picard iteration. It is further noted that if no time-delay acts on the system, then the proposed controller can guarantee global stability and performance for the tracking error. Further, if no disturbance acts on the system after some finite time, then we retrieve the results of the standard Model Reference Adaptive Control (MRAC) design. The design is simple and amenable to implementation. The effectiveness of the analytical findings is validated with illustrative examples such as a longitudinal flight control of a jet transport aircraft and motion control of linear motor drives.
Additionally, when the human (pilot) interacts with the machine (automation), emergent problems referred to as mode confusion or automation surprise arise as investigated by the NTSB in the Asiana-214 SFO crash on July 6, 2013 among other aviation incidents/accidents as reported in the NASA Aviation Safety Reporting System. Mode confusion typically happens due to a mismatch between the actual aircraft state and the state the pilot expects. Detecting such problems using formal verification and validation (V & V) methods such as model checking are important topics for safety of the aviation. This problem is challenging because the underlying hybrid nature of the pilot-automation system leads to the state space explosion problem for the model checkers, and neglecting such dynamics leads to limited applicability. This research proposes a scalable formal V & V framework to qualitatively and quantitatively detect the mode confusion problems in the flight deck. The approach develops a hybrid model for the automation and a discrete event system for the pilot to capture the effects of mode confusion. To efficiently infer the expectations or intents of the automation and the pilot, predicate-based abstraction is discussed by partitioning the state space along the vertical, speed, and lateral dimensions. The effectiveness of the formal mode confusion detection method is validated with well-documented incidents/accidents such as Boeing 777’s kill-the-capture incident and Airbus 312’s speed protection accident.
Finally, we discuss potential avenues of future research that can build upon this work to further enhance the applicability of the framework.
Nandiganahalli, Jayaprakash “Suraj”, "Towards Predictor Adaptive Robust Control and Inference of Cyber-Physical Systems with Applications to Aerospace Systems" (2018). Open Access Dissertations. 2080.