UC Merced

Underactuated mechanical system (UMS) is a special class of mechanical systems that play an important role in a wide variety of engineering applications. UMSs typically show a great difficulty in analysis and control design because of complex nonlinearity and loss of capability to configure arbitrary motions in some directions. Flatness-based control and active disturbance rejection control (ADRC) approach has been an active research topic about dealing with control problems of UMSs. Flatness, as a useful property of a class of dynamical systems, called flat systems, guarantees that all the states and inputs of them can be parameterized by a set of differentially independent coordinates, called flat output. The trajectory planning and tracking control of flat systems can be greatly simplified by prescribing the desired references in `flat space' without any other constraints except for necessary initial and final conditions. Despite its merits in control design, flatness is not a universal property of nonlinear dynamical systems and normally is not effortless to be characterized. Additionally, most UMSs are not inherently flat, i.e., not feedback linearizable, either statically or dynamically. The emerging framework that combines flatness of tangent linearization and ADRC has been experimentally proved feasible and robust for a large class of UMSs in recent years. While this approach continues to extend to more engineering applications, data-driven control design based on the flatness and ADRC has drawn attention of us, as fully detailed model information for flat output characterization is expensive and normally unavailable in control design. With few numbers of input-output measurements and little knowledge of the underlying UMSs, a data-driven approach for this framework enables an efficient, without modeling process, and systematic feedback control design for a class of UMSs with similar dynamical structures. Specifically, we first focus on the identification of flat output of nonlinear UMSs' tangent linearization using only input-output data collected. The identified flat outputs are naturally applied to the flatness-based control and ADRC framework, where several issues, such as trajectory planning and identification of state-flat output relations, are discussed and solved when extensive model information is no longer available. Frequency domain algorithms (FOID, MFOID) and time domain algorithm (FOID-Net) are proposed to solve flat output identification (FOID) problem of nonlinear UMSs. FOID and MFOID leverages the estimated transfer function of various flat output candidate in chosen frequency band to identify their relative degrees which is proved closely related to flatness of linearized UMSs. No detailed mathematical model of the system is needed. Flat output candidate is written as a linear combination of measured outputs. An optimal linear combination is identified so that the candidates achieve the highest relative degree. When the relative degree is equal to the order of the system, the output is flat. We have also developed data handling strategies to obtain the best estimate of the relative degree in the presence of measurement noise, high-frequency dynamics and Nyquist digitization effect. MFOID is an extension of FOID to deal with a special case of flat output of MIMO UMSs. The proposed algorithms are validated by numerical examples and an experimental study of a rotary crane system. The FOID-Net is a neural work framework designed to use time series data to estimate flat output out of linearized systems. We introduce the tracking differentiator into training of neural network which generates the time derivatives of flat output candidates and filter the noisy states. The idea of FOID-Net is based on the essential feature of flat systems that all states and inputs can be expressed by linear or nonlinear functions of flat coordinates. The training method, simulations of Furuta pendulum and a fourth-order nonlinear UMSs are discussed. A framework of designing data-driven robust tracking control based on identified flat output and sparse identification is proposed. Reduced linearized model are proposed to show that the number of components of linear flat outputs can be further reduced. Flat outputs can be identified by FOID algorithm or FOID-Net. Technique of sparse regression is applied to identify the relationships between flat output and system states, which reduces the order of the well-known extended state observer (ESO) and thereby make the ESO more effective for both trajectory planning and tracking in terms of the flat output. When FOID-Net is applied, the flat output-state relations can be directly found by weight matrix of well-trained layer. The proposed control scheme is validated by experimental studies of a rotary crane system in which a rest-to-rest tracking control is implemented.