Time-varying high-gain trajectory linearization observer design

Abstract

-In this paper, we extend the previous results on trajectory linearization observer (TLO) for SISO to MIMO nonlinear time-varying (NLTV) systems, and extend the highgain observer theory for linear time-invariant (LTI) observer error dynamics to linear time-varying (LTV) observer error dynamics, using the (time-varying) PD-eigenvalue assignment method. In addition, the time-varying high gain TLO alleviates the slowly varying restriction, and relaxes the restriction of existing time-invariant nonlinear high gain observer to affine nonlinear systems to allow for any linearizable NLTV system.

Trajectory Linearization Control Based Output Tracking Method for Nonlinear Uncertain System Using Linear Extended State Observer

“…Above all, compared with , only three parameters of the proposed method are required to be tuned while preserving excellent performance, such as disturbance rejection and tracking characteristics, in spite of uncertainties and measurement noise, which makes it extremely simple and practical. Particularly, the proposed LESO‐TLC scheme can handle the output tracking problem for a non‐affine nonlinear uncertain system without any extra assumptions or coordinate transformations, which can be viewed as an outstanding feature, compared with other DOBC methods.…”

“…That is to say, when external and internal uncertainties are large enough to surpass the stability domain provided by TLC, the performance of the TLC approach may be degraded. Thus, in order to overcome this drawback, various composite control approaches concerning TLC have been investigated in the past decade . To date, the existing enhanced TLC methods can be summarized as follows: by employing the excellent ability of neutral network (NN) or fuzzy logic in approximating the unknown nonlinear functions, the unknown uncertainties can be estimated and canceled out in the enhanced control law; thus, the nominal performance of the system can be recovered.…”

“… This is the first paper that employs LESO to improve the closed‐loop performance and capability in disturbance rejection for TLC when larger uncertainties are considered. Compared with methods proposed in , the novel controller has a simpler structure and can achieve fast and accurate response via effective compensation for unmodeled errors and disturbances. Unlike the conclusions on stability made by , the stability analysis in this paper not only gives the statement about the convergence of tracking error, but also provides a viable guideline to select the parameters of the controller; hence, the complicated selection of PD‐eigenvalues via PD‐spectrum theorem, which is widely used, can be avoided. Simulations on non‐affine nonlinear uncertain systems are first considered in this paper to demonstrate the comparative advantage over the existing disturbance observer based control (DOBC) methods, including ADRC mentioned in the literature. The issues on sensitivity to noise and the guideline of tuning parameters are first carried out and discussed to exhibit the promising prospects for the proposed control scheme in engineering applications. …”

A Novel Method of Robust Trajectory Linearization Control Based on Disturbance Rejection

“…Thus, with the consideration of limitations of TLC in presence of uncertainties, how to enhance or improve the robustness and performance of TLC is becoming one of the active topics in control community recently [4,[7][8][9][10][11][12][13][14]. So far, the existing approach adopted by researchers can be classified as follows.…”

“…Based on [12,13] proposed a robust adaptive TLC(RATLC) algorithm, wherein only one parameter needs to be adapted on line, but there are too many design parameters to be chosen. Unlike the methods mentioned above, in [14], by using PD-eigenvalue assignment method, trajectory linearization observer is designed to cancel the uncertainties, but the design process seems cumbersome and the results are not satisfactory. Among the literatures mentioned above, one limitation which must be taken into account is that due to the complexity of the theory, it is overwhelmingly difficult to provide a guideline to tune the corresponding parameters, especially those which will influence the system performance greatly.…”