In this paper, the control problem of continuous stirred tank reactors (CSTR) is studied. The considered CSTR are required to contain unknown functions and unknown dead zone input. An adaptive controller that uses the neural networks (NNs) is provided to solve the unknown terms. The proposed approach overcomes the effect of the dead zone input. The dead zone input in the systems is compensated for by introducing a new Lyapunov form and Young's inequality. The backstepping procedure is exploited to implement controller design with adaptation laws. The stability is analyzed using Lyapunov method. The performance is examined for CSTR to confirm the effectiveness of the proposed approach based on computer simulation. 相似文献
We note that some existing algorithms are based on the normalized least-mean square (NLMS) algorithm and aim to reduce the computational complexity of NLMS all inherited from the solution of the same optimization problem, but with different constraints. A new constraint is analyzed to substitute an extra searching technique in the set-membership partial-update NLMS algorithm (SM-PU-NLMS) which aims to get a variable number of updating coefficients for a further reduction of computational complexity. We get a closed form expression of the new constraint without extra searching technique to generate a novel set-membership variable-partial-update NLMS (SM-VPU-NLMS) algorithm. Note that tile SM-VPU-NLMS algorithm obtains a faster convergence and a smaller mean-squared error (MSE) than the existing SM-PU-NLMS. It is pointed out that the closed form expression can also be applied to the conventional variable-step-size partial-update NLMS (VSS-PU-NLMS) algorithm. The novel variable-step-size variable-partial-update NLMS (VSS-VPU-NLMS) algorithm is also verified to get a further computational complexity reduction. Simulation results verify that our analysis is reasonable and effective. 相似文献
For compensating backlash phenomenon in servo systems, the authors propose an observer method in this paper to estimate both system states and vibration torque before controller design. First, a systematic scheme is given to obtain plant parameters, which is very important in observing system states. This is a parameter estimation principle that gives a crude estimation and computes the differences between the crude and true values. As a result, the precise value of the parameters is obtained by adding together the crude value and the difference. Then, based on the precise estimated parameters, an extended state observer (ESO) is designed to obtain feedback and feedforward signals. Consequently, robust compensation control is achieved by designing an output feedback controller, consisting of a feedback term and a feedforward term. Finally, in order to validate the proposed approach, extensive experiments are performed on a practical servo system with backlash nonlinearity. 相似文献
In this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results. 相似文献
Due to the complexity of the machine tool structure and the cutting process, the dynamics of machining processes are still not completely understood. This is especially true due to the demand of high-speed machining to increase productivity. In order to model and control these complex processes, new approaches, which can represent complex phenomenon combined with learning ability, are needed. The combined neural–fuzzy approach appears to be ideally suited for this purpose. In this paper, the recently developed fuzzy adaptive network (FAN) is used to model surface roughness in turning operations. The FAN network has both the learning ability of neural network and linguistic representation of complex, not well-understood, vague phenomenon. Furthermore, it can continuously improve the initially obtained rough model based on the daily operating data. To illustrate this approach, a model representing the influences of machining parameters on surface roughness is established and then the model is verified by the use of the results of pilot experiments. Finally, a comparison with the results based on statistical regression is provided. 相似文献