Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched perturbations. While TSM manifold allows for different forms of the sliding variable, which are satisfying the $q/p$ power ratio of the measurable output state, we demonstrate that $q/p=0.5$ is the optimal one for the second-order Newton's motion dynamics with a bounded control action. The paper analyzes the time-optimal sliding surface and, based thereupon, claims the optimal TSM control for the second-order motion systems. It is stressed that the optimal TSM control is fully inline with the Fuller's problem of optimal switching which minimizes the settling time, i.e. with time-optimal control of an unperturbed double-integrator. Is is also shown that for the given plant characteristics, i.e. the overall inertia and control bound, there is no need for additional control parameters. The single surface design parameter might (but not necessarily need to) be used for driving system on the boundary layer of the twisting mode, or for forcing it to the robust terminal sliding mode. Additional insight is given into the finite-time convergence of TSM and robustness against the bounded perturbations. Numerical examples with different upper-bounded perturbations are demonstrated.
This paper proposes a distributed secondary voltage control method based on extended state Kalman-Bucy filter (ESKBF) and fast terminal sliding mode (FTSM) control for the resilient operation of an islanded microgrid (MG) with inverter-based distributed generations (DGs). To tackle the co-existence of multiple uncertainties, a unified modelling framework is proposed to represent the set of different types of disturbances, including parameter perturbation, measurement noise, and immeasurably external variables, by an extended state method. Kalman-Bucy filter is then applied to accurately estima…
In this paper, we present a new terminal sliding mode control to achieve predefined-time stability of robot manipulators. The proposed control is developed based on a novel predefined-time terminal sliding mode (PTSM) surface, on which the states are forced to reach the origin in a predefined time, i.e., the settling time is independent to the initial condition and can be explicitly user-defined via adjusting some specific parameters called the predefined-time parameters. It is also demonstrated that the proposed control can provide satisfactory steady-state performance in the case of both ext…
In this paper, adaptive prescribed finite time stabilization of uncertain single-input and single-output nonlinear systems is considered in the presence of unknown states, unknown parameters, external load disturbance, and non-symmetric input saturation. A prescribed finite time disturbance observer is designed to approximate the unmeasured external disturbance. Also, a nonsingular prescribed finite time terminal sliding mode control is proposed for the closed-loop control of the system with the non-symmetric input saturation. Extended Kalman filter algorithm is employed for the real-time esti…
In this paper the problem of guidance formulation for autonomous soft landing of unmanned aerial vehicles on stationary, moving, or accelerating / maneuvering ground vehicles at desired approach angles in both azimuth and elevation is considered. Nonlinear engagement kinematics have been used. While integrated nonlinear controllers have been developed in the literature for this purpose, in practical implementations the controller inputs often need modification of the existing autopilot structure, which is challenging. In order to avoid that a higher-level guidance algorithm is designed in this…
Harbin Institute of Technology（哈尔滨工业大学）；University of California, Berkeley（加州大学伯克利分校）
The precise motion control of a multi-degree of freedom~(DOF) robot manipulator is always challenging due to its nonlinear dynamics, disturbances, and uncertainties. Because most manipulators are controlled by digital signals, a novel higher-order sliding mode controller in the discrete-time form with time delay estimation is proposed in this paper. The dynamic model of the manipulator used in the design allows proper handling of nonlinearities, uncertainties and disturbances involved in the problem. Specifically, parametric uncertainties and disturbances are handled by the time delay estimati…
This paper proposes a practical implementation of sliding mode control (SMC) that utilizes partial modeling compensation. Sliding mode control is well known for its effectiveness as a model free control approach, however, its effectiveness is degraded if there is a constraint on the control gain or limitation on the switching frequency in digital implementation. This is especially the case with systems that involve static friction. This approach aims to enhance the effectiveness of SMC by partial model compensation. Rigorous stability proofs are presented to validate the approach. In addition,…
Lipschitz continuous sliding-mode controllers (LCSMC) are developed as the integral of discontinuous SMC, producing control signals of finite slope. Nevertheless, LCSMC still generate chattering in the presence of fast parasitic dynamics. In this paper, an analysis of chattering in systems driven by LCSMC is performed using the Harmonic Balance (HB) approach. Two kinds of LCSMC are considered: the first one is based on a linear sliding variable (LSV) and the second one on a terminal switching variable (TSV). Predictions of the amplitude and frequency of self-excited oscillations allowed to com…
This paper proposes a global iterative sliding mode control approach for high-precision contouring tasks of a flexure-linked biaxial gantry system. For such high-precision contouring tasks, it is the typical situation that the involved multi-axis cooperation is one of the most challenging problems. As also would be inevitably encountered, various factors render the multi-axis cooperation rather difficult; such as the strong coupling (which naturally brings nonlinearity) between different axes due to its mechanical structure, the backlash and deadzone caused by the friction, and the difficultie…
The problem of motion planning for affine control systems consists of designing control inputs that drive a system from a well-defined initial to final states in a desired amount of time. For control systems with drift, however, understanding which final states are reachable in a given time, or reciprocally the amount of time needed to reach a final state, is often the most difficult part of the problem. We address this issue in this paper and introduce a new method to solve motion planning problems for affine control systems, where the motion desired can have indefinite boundary conditions an…
Estimation of interactive forces, which are mostly unavailable for direct measurement on the interface between a system and its environment, is an essential task in various motion control applications. This paper proposes an interactive force estimation method, based on the well-known equivalent output injection of the second-order sliding mode. The equivalent output injection is used to obtain a frequency-unshaped quantity that appears as a matched external disturbance and encompasses the interactive forces. Afterwards, a universal lead-lag shaper, depending on dynamics of the motion control …
Within the framework of Sliding Mode Control, safety critical control looks at two problems of theoretical significance: construct a sliding manifold that does not intersect a given unsafe set of the state space, and design a robust controller that safely takes the system trajectory to the manifold during the reaching phase and enforces the sliding motion. In this technical note, we address both problems. We introduce the notion of Safe Sliding Manifold (SSM) of relative degree one, and show that it is possible to construct it from the gradient of a class of Lyapunov-like energy functions, pre…
Time-delay Control Using a New Nonlinear Adaptive Law for Cable-Driven Robots
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Donghai Laboratory（东海实验室）；China Academy of Machinery Beijing Research Institute of Mechanical and Electrical Technology Co., Ltd.（中国机械工业北京机电技术研究院有限公司）
Ultrasonic motors (USMs) are commonly used in aerospace, robotics, and medical devices, where fast and precise motion is needed. Remarkably, sliding mode controller (SMC) is an effective controller to achieve precision motion control of the USMs. To improve the tracking accuracy and lower the chattering in the SMC, the fractional-order calculus is introduced in the design of an adaptive SMC in this paper, namely, adaptive fractional-order SMC (AFOSMC), in which the bound of the uncertainty existing in the USMs is estimated by a designed adaptive law. Additionally, a short memory principle is e…
This paper studies an attitude control system design based on modified Rodrigues parameters feedback. It employs a linear continuous sliding mode controller. The sliding mode controller is able to bring the existence of the sliding motion asymptotically. Besides, the attitude control system equilibrium point is proved to have an asymptotic stability guarantee through further analysis. This stability analysis is conducted since the sliding mode existence on the designed sliding surface does not imply the stability guarantee of the system's equilibrium. This paper ends with some numerical exampl…
The conceptual design and flight controller of a novel kind of quadcopter are presented. This design is capable of morphing the shape of the UAV during flight to achieve position and attitude control. We consider a dynamic center of gravity (CoG) which causes continuous variation in a moment of inertia (MoI) parameters of the UAV in this design. These dynamic structural parameters play a vital role in the stability and control of the system. The length of quadcopter arms is a variable parameter, and it is actuated using attitude feedback-based control law. The MoI parameters are computed in re…
This paper introduces a new technique for learning probabilistic models of mass and friction distributions of unknown objects, and performing robust sliding actions by using the learned models. The proposed method is executed in two consecutive phases. In the exploration phase, a table-top object is poked by a robot from different angles. The observed motions of the object are compared against simulated motions with various hypothesized mass and friction models. The simulation-to-reality gap is then differentiated with respect to the unknown mass and friction parameters, and the analytically c…
