2016 Chinese Control and Decision Conference (CCDC), 2016
This paper shows further results on the output feedback tracking problem for a class of uncertain... more This paper shows further results on the output feedback tracking problem for a class of uncertain nonminimum phase nonlinear systems, where a state-based uncertainty is involved. Through a new additive state decomposition process, this uncertainty is divided into two parts which are assigned to the two decomposed subsystems, respectively. Then the controller is designed and its stability is analyzed by the nonlinear small-gain theorem. Finally, to demonstrate the effectiveness of the proposed method, an illustrative example is given.
An adaptive-control-like method is the leading repetitive control (RC, or repetitive controller, ... more An adaptive-control-like method is the leading repetitive control (RC, or repetitive controller, also RC) method for nonlinear systems. Before using this method, a tracking problem for nonlinear systems needs to be converted into a rejection problem for nonlinear error dynamics subject to periodic disturbance. This conversion reduces the difficulties of the original problem. Furthermore, the periodic disturbance is considered as an unknown parameter that needs to be learned. As discussed in Chap. 4, the stability is enhanced by introducing a low-pass filter in RC for linear systems, resulting in a filtered repetitive controller (FRC, or filtered repetitive control, which is also designated as FRC). Similarly, it is also necessary to introduce a filter into RC for nonlinear systems. However, the theory on FRC proposed in [1] is derived in the frequency domain and can be applied only with difficulty, if at all, to nonlinear systems.
In this paper, a filtered repetitive controller (FRC) is proposed for robot manipulator tracking.... more In this paper, a filtered repetitive controller (FRC) is proposed for robot manipulator tracking. Error dynamics are obtained first, leaving an unknown periodic signal to be compensated. A new model to describe the periodic signal is proposed then. By this model, an FRC is designed to compensate for the unknown periodic signal. The resulting closed-loop error dynamics are analyzed with the help of a Lyapunov-Krasovskii functional. In order to compare stability of the closed-loop error dynamics with the FRC and corresponding repetitive controller, the convergence rate is proposed to measure their stability. It is shown that the resulting closed-loop error dynamics with the FRC is more stable. In comparison with existing repetitive controllers, the proposed controller provides the flexibility to choose parameters to achieve a tradeoff between tracking performance and stability. Numerical simulations demonstrate the effectiveness of the proposed controller.
This paper presents a new control, namely additive-state-decomposition dynamic inversion stabiliz... more This paper presents a new control, namely additive-state-decomposition dynamic inversion stabilized control, that is used to stabilize a class of multi-input multi-output (MIMO) systems subject to nonparametric time-varying uncertainties with respect to both state and input. By additive state decomposition and a new definition of output, the considered uncertain system is transformed into a minimum-phase uncertainty-free system with relative degree one, in which all uncertainties are lumped into a new disturbance at the output. Subsequently, dynamic inversion control is applied to reject the lumped disturbance. Performance analysis of the resulting closed-loop dynamics shows that the stability can be ensured. Finally, to demonstrate its effectiveness, the proposed control is applied to two existing problems by numerical simulation. Furthermore, in order to show its practicability, the proposed control is also performed on a real quadrotor to stabilize its attitude when its inertia m...
This paper presents a novel control, namely additive-state-decomposition-based dynamic inversion ... more This paper presents a novel control, namely additive-state-decomposition-based dynamic inversion stabilized control, that is used to stabilize a class of systems subject to nonparametric time-varying uncertainties with respect to both state and input. By the additive state decomposition and a new definition of output, the uncertain system is transformed into an uncertainty-free system with relative degree one, in which all uncertainties are lumped into a new disturbance at output. Subsequently, dynamic inversion control is applied to reject the lumped disturbance. Performance analysis of the resulting closed-loop dynamics is given that the stability can be ensured if a key parameter is sufficiently small. Finally, this proposed control is applied to a tracking problem for the missile's angle of attack. Numerical simulation demonstrates its effectiveness.
2016 Chinese Control and Decision Conference (CCDC), 2016
This paper shows further results on the output feedback tracking problem for a class of uncertain... more This paper shows further results on the output feedback tracking problem for a class of uncertain nonminimum phase nonlinear systems, where a state-based uncertainty is involved. Through a new additive state decomposition process, this uncertainty is divided into two parts which are assigned to the two decomposed subsystems, respectively. Then the controller is designed and its stability is analyzed by the nonlinear small-gain theorem. Finally, to demonstrate the effectiveness of the proposed method, an illustrative example is given.
An adaptive-control-like method is the leading repetitive control (RC, or repetitive controller, ... more An adaptive-control-like method is the leading repetitive control (RC, or repetitive controller, also RC) method for nonlinear systems. Before using this method, a tracking problem for nonlinear systems needs to be converted into a rejection problem for nonlinear error dynamics subject to periodic disturbance. This conversion reduces the difficulties of the original problem. Furthermore, the periodic disturbance is considered as an unknown parameter that needs to be learned. As discussed in Chap. 4, the stability is enhanced by introducing a low-pass filter in RC for linear systems, resulting in a filtered repetitive controller (FRC, or filtered repetitive control, which is also designated as FRC). Similarly, it is also necessary to introduce a filter into RC for nonlinear systems. However, the theory on FRC proposed in [1] is derived in the frequency domain and can be applied only with difficulty, if at all, to nonlinear systems.
In this paper, a filtered repetitive controller (FRC) is proposed for robot manipulator tracking.... more In this paper, a filtered repetitive controller (FRC) is proposed for robot manipulator tracking. Error dynamics are obtained first, leaving an unknown periodic signal to be compensated. A new model to describe the periodic signal is proposed then. By this model, an FRC is designed to compensate for the unknown periodic signal. The resulting closed-loop error dynamics are analyzed with the help of a Lyapunov-Krasovskii functional. In order to compare stability of the closed-loop error dynamics with the FRC and corresponding repetitive controller, the convergence rate is proposed to measure their stability. It is shown that the resulting closed-loop error dynamics with the FRC is more stable. In comparison with existing repetitive controllers, the proposed controller provides the flexibility to choose parameters to achieve a tradeoff between tracking performance and stability. Numerical simulations demonstrate the effectiveness of the proposed controller.
This paper presents a new control, namely additive-state-decomposition dynamic inversion stabiliz... more This paper presents a new control, namely additive-state-decomposition dynamic inversion stabilized control, that is used to stabilize a class of multi-input multi-output (MIMO) systems subject to nonparametric time-varying uncertainties with respect to both state and input. By additive state decomposition and a new definition of output, the considered uncertain system is transformed into a minimum-phase uncertainty-free system with relative degree one, in which all uncertainties are lumped into a new disturbance at the output. Subsequently, dynamic inversion control is applied to reject the lumped disturbance. Performance analysis of the resulting closed-loop dynamics shows that the stability can be ensured. Finally, to demonstrate its effectiveness, the proposed control is applied to two existing problems by numerical simulation. Furthermore, in order to show its practicability, the proposed control is also performed on a real quadrotor to stabilize its attitude when its inertia m...
This paper presents a novel control, namely additive-state-decomposition-based dynamic inversion ... more This paper presents a novel control, namely additive-state-decomposition-based dynamic inversion stabilized control, that is used to stabilize a class of systems subject to nonparametric time-varying uncertainties with respect to both state and input. By the additive state decomposition and a new definition of output, the uncertain system is transformed into an uncertainty-free system with relative degree one, in which all uncertainties are lumped into a new disturbance at output. Subsequently, dynamic inversion control is applied to reject the lumped disturbance. Performance analysis of the resulting closed-loop dynamics is given that the stability can be ensured if a key parameter is sufficiently small. Finally, this proposed control is applied to a tracking problem for the missile's angle of attack. Numerical simulation demonstrates its effectiveness.
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