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Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.
The paper presents design and experimental validation of a stable self-tuning PID controller for three degrees of freedom (3-DOF) helicopter. At first, it is proposed a self-tuned proportional-integral-derivative (PID) controller for a class of uncertain second order multiinput multi-output nonlinear dynamic systems to which the 3-DOF helicopter dynamic model belongs. Within this scheme, the PID controller is employed to approximate unknown ideal controller that can achieve control objectives. PID controller gains are the adjustable parameters and they are updated online with a stable adaptation mechanism designed to minimize the error between the unknown ideal controller and the used by PID controller. The stability analysis of the closed-loop system is performed using Lyapunov approach. It is proven that all signals in the closed-loop system are uniformly ultimately bounded. The proposed approach can be regarded as a simple and effective model-free control since the mathematical model of the system is assumed unknown. Experimental results are presented to verify the effectiveness of the proposed controller.
Content available remote Optimization of fuzzy PID controllers using Q-learning algorithm
In this article, we first chose the design settings of the fuzzy PID controllers (FPIDC) so that the FPIDCs mimic the classical PID controllers. The advantage of these controllers is the combination of the simplicity of the classical PID controllers and the interpretability of fuzzy controllers which makes the task of parameters tuning easier. Secondly, we present a method for optimizing the closed-loop system consisting of a FPIDC and an unknown plant using the Q-learning algorithm (QLA). Specifically, QLA minimizes a cost function which quantifies the performance of FPIDC. Without loss of generality the square error sum cost function is used. The QLA, which is a nonmodel-based method, iteratively search of the best parameters so that the output of the cost function is less then satisfaction threshold. Finally, a simulation example is used to prove the effectiveness of the proposed method.
In this paper, we propose a decentralized direct adaptive fuzzy control method for a class interconnected MIMO non linear plant encountered mainly in robotics. The establishment of the control law introduces very simplest assumptions. Indeed, the functions incorporating the plant dynamic must be continuous and the interconnection terms are bounded by unknown bounds. The fuzzy direct adaptive law is designed to compensate for the interconnections effect and to ensure the closed-loop stability, convergence of the controlled outputs and `boundedness' of adaptation parameters. The proposed method is tested by simulation on the robot Puma 560. In this test the robot is controlled in the operational space as that the robot tip follows a prescribed curve on the sphere where the orientation of the last link (sixth) is maintained radial related to the center of this sphere.
Content available remote Stable indirect adaptive fuzzy control for a class of SISO nonlinear systems
his paper proposed an indirect adaptive fuzzy control scheme for a class of unknown continuous-time nonlinear single-input single-output (SISO) dynamic systems. Within this scheme, the fuzzy systems are employed to approximate the unknown system dynamics. Based on these fuzzy approximations and a Lyapunov synthesis approach, suitable control laws and appropriate parameter adaptive algorithms are developed. It is shown that the proposed control scheme avoids the possible controller singularity problem, guarantes the convergence of the tracking error to zero and the global boundedness of all signals in the closed-loop system. Simulation results, performed on an inverted on a inverted pendulum system, are given to point out the good performance of the developed adaptive control approach.
Content available remote Direct stable fuzzy adaptive control of a class of SISO nonlinear systems
For class of unknown nonlinear single-output (SISO) systems a stable direct adaptive controller witch uses standard fuzzy systems is presented. The proposed scheme includes a proportional-integral-type adaptation law. global boundedness of the overall adaptive system and tracking within a desired precision are established with the new adaptive scheme. This adaptive scheme allows for the incorporation of linquistic information from human experts directly into the controller. Simulations performed on two examples illustrate the approach and exhibit its performance.
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