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- Gradient descent (2)
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- Approximate differentiation (1)
- Centroid defuzzification triangular membership (1)
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- Disturbance observer (1)
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Articles 1 - 6 of 6
Full-Text Articles in Engineering
Training Fuzzy Systems With The Extended Kalman Filter, Daniel J. Simon
Training Fuzzy Systems With The Extended Kalman Filter, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
The generation of membership functions for fuzzy systems is a challenging problem. We show that for Mamdani-type fuzzy systems with correlation-product inference, centroid defuzzification, and triangular membership functions, optimizing the membership functions can be viewed as an identification problem for a nonlinear dynamic system. This identification problem can be solved with an extended Kalman filter. We describe the algorithm and compare it with gradient descent and with adaptive neuro-fuzzy inference system (ANFIS) based optimization of fuzzy membership functions. The methods discussed in this paper are illustrated on a fuzzy filter for motor winding current estimation, and are compared with Butterworth …
Training Radial Basis Neural Networks With The Extended Kalman Filter, Daniel J. Simon
Training Radial Basis Neural Networks With The Extended Kalman Filter, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Radial basis function (RBF) neural networks provide attractive possibilities for solving signal processing and pattern classification problems. Several algorithms have been proposed for choosing the RBF prototypes and training the network. The selection of the RBF prototypes and the network weights can be viewed as a system identification problem. As such, this paper proposes the use of the extended Kalman filter for the learning procedure. After the user chooses how many prototypes to include in the network, the Kalman filter simultaneously solves for the prototype vectors and the weight matrix. A decoupled extended Kalman filter is then proposed in order …
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Sum Normal Optimization Of Fuzzy Membership Functions, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This …
From Linear To Nonlinear Control Means: A Practical Progression, Zhiqiang Gao
From Linear To Nonlinear Control Means: A Practical Progression, Zhiqiang Gao
Electrical and Computer Engineering Faculty Publications
With the rapid advance of digital control hardware, it is time to take the simple but effective proportional-integral-derivative (PID) control technology to the next level of performance and robustness. For this purpose, a nonlinear PID and active disturbance rejection framework are introduced in this paper. It complements the existing theory in that (1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; (2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. Stability analysis, as well as …
A Stable Self-Tuning Fuzzy Logic Control System For Industrial Temperature Regulation, Zhiqiang Gao, Thomas A. Trautzsch, James G. Dawson
A Stable Self-Tuning Fuzzy Logic Control System For Industrial Temperature Regulation, Zhiqiang Gao, Thomas A. Trautzsch, James G. Dawson
Electrical and Computer Engineering Faculty Publications
A closed-loop control system incorporating fuzzy logic has been developed for a class of industrial temperature control problems. A unique fuzzy logic controller (FLC) structure with an efficient realization and a small rule base that can be easily implemented in existing industrial controllers was proposed. The potential of FLC in both software simulation and hardware test in an industrial setting was demonstrated. This includes compensating for thermo mass changes in the system, dealing with unknown and variable delays, operating at very different temperature set points without retuning, etc. It is achieved by implementing, in the FLC, a classical control strategy …
Kalman Filtering With State Equality Constraints, Daniel J. Simon, Tien Li Chia
Kalman Filtering With State Equality Constraints, Daniel J. Simon, Tien Li Chia
Electrical and Computer Engineering Faculty Publications
Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state …