RESUMEN
In this paper, a feedback controller based on the extended state observer is proposed for fully actuated systems. First, a generalized proportional-integral observer is designed to estimate states and disturbances simultaneously. Using the linear parameter varying approach and the convexity principle, a linear matrix inequality condition is given to obtain the observer gains. Second, on the basis of the full-actuation property and the estimated states, a feedback controller, utilizing estimated disturbances to compensate for system disturbances, is designed to make all the states of the closed-loop system uniformly ultimately bounded. In addition, if disturbances are constant or slow time-varying, the observation errors and the states of closed-loop system are all exponentially convergent. Two illustrations are provided to show the validity and practicality of the proposed approach. Simulation results show that the estimated disturbances can follow the true values with relatively small errors, so compensating the system disturbances with estimated values can effectively reduce the ultimate bounds of states of the closed-loop system.
RESUMEN
Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method.
RESUMEN
This paper introduces a novel approach to the comprehensive reconstruction and predictive control (PC) of the quadrotor UAV for information-gathering missions, employing fully actuated system (FAS) approaches. Unlike conventional PC methods applied to a quadrotor UAV with hybrid constraints, our work integrates reconstructions of the system model, hybrid constraints, and the receding horizon performance index into to an integrated tracking control scheme within the FAS-PC framework. Specifically, the under-actuated quadrotor UAV model is reconstructed into a full-actuated model to inject full-actuation properties. And the implicit hybrid constraints that arise from the model reconstruction are explicitly transformed and decoupled. Simultaneously, the cascaded predictive algorithm is established that the new time-varying input constraints are solved in each predictive horizon, and then the nonlinear optimization problem is decoupled into four linear convex optimization problems subject to the corresponding decoupled linear constraints and the pre-addressed input constraints. Within this framework, the intrinsic complexities, nonlinearities, and interdependencies of the quadrotor UAV system model, along with hybrid constraints and the optimization dilemma, are considerably diminished. This reduction significantly eases computational demands, enabling satisfactory real-time performance. Furthermore, the selection of predictive parameters guarantees the stability of the resultant tracking error closed-loop system. Finally, the efficacy of the proposed method is validated through two sets of flight missions, conducted via simulation and practical experimentation, respectively.
RESUMEN
This paper investigates the adaptive guaranteed cost stabilization (AGCS) problems for two classes of high-order nonlinear systems with unknown parameters (vector) and time delays. Firstly, based on the high-order fully actuated (HOFA) system approaches, the Lyapunov-Krasovskii functional (LKF) and the guaranteed cost control (GCC), a new AGCS strategy is proposed for HOFA nonlinear system with unknown parameter vector and time delays. Then, based on the above result, another AGCS controller for a class of strict-feedback systems (SFSs) with unknown parameters and time delays is obtained. Two designed controllers ensure that all of the states of two closed-loop systems are global boundedness, and preset arbitrarily the upper bound of cost functions (UBCFs) characterizing the output performance. More importantly, the UBCFs are independent of system initial values, unknown parameters (vector), and even time delays, which is difficult to achieve by using existing control methods. To do this, this paper introduces a local smooth nonlinear function (LSNF), and gives its corresponding lemma, which provide an important mathematical tool. Finally, three simulation examples, including an application in the electromechanical system, are given to prove the effectiveness and the practicability of our proposed control method.