Analysis and optimal control of pulse width modulation feedback systems

Abstract

This paper considers the analysis and optimization problems of a class of pulse width modulation (PWM ) feedback systems by using continuous orthogonal functions. Two algorithms only involving algebraic computation are derived to analyse PWM feedback systems and to design both the optimal control gains and the optimal PWM patterns of PWM feedback systems under the criterion of minimizing a quadratic performance index. The illustrated examples show that the proposed algorithms based on continuous orthogonal functions can obtain satisfactory results.

The Bullet Launcher with A Pneumatic System to Detect Objects by Unique Markers

“…The camera has a resolution of 640× 480 pixels, a frame rate of 30 fps, and a capturing angle of 54 o . The image captured by the camera is processed by a computer using the OpenCV library, which contains an image-processing program for recognizing and identifying objects [18][19][20]. In this research, the features developed by OpenCV for recognizing and identifying objects are the Unique Marker Recognizing [17].…”

“…The object is carried out hierarchically based on predefined colors, patterns, and sizes. Then, the coordinates of the target midpoint are detected in the image, and it will be used as feedback on the servo motor [19][20][21]. Moreover, when the object moves, the camera and its propulsion system will follow the object's movement, as shown in Fig.…”

Design of robust-stable and quadratic finite-horizon optimal active vibration controllers with low trajectory sensitivity for the uncertain flexible rotor systems via the orthogonal-functions approach and the hybrid Taguchi-genetic algorithm

“…Besides, the authors of this paper have also shown that, for solving the TS-fuzzy-model-based dynamic differential equations, the shifted Chebyshev function used in the OFA can obtain the better results than the conventional numerical methods (Ho and Chou, 2005b). On the other hand, the comparison between the shifted Chebyshev function and the piecewise orthogonal function such as the Haar wavelet and block-pulse functions has been studied by Hsieh and Chou (2004). It has been shown that the shifted Chebyshev function can obtain the better results than the piecewise orthogonal function.…”

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

“…So, in this paper, by assuming the value of h i ( z ( t )) to be constant within the small time interval kt f ≤ t ≤ ( k + 1) t f , we propose a new numerical optimization approach, which integrates the OFA and the TSBDEA, to design the quadratic optimal controllers of the uncertain TS fuzzy model systems. In addition, the comparison between the OFA and the piecewise orthogonal function approach such as the Haar wavelet and block‐pulse functions has been studied by the second author with his associate . It has been shown that the OFA can obtain the better results than the piecewise orthogonal function approach.…”

“…The parametric uncertainties may destabilize the TS fuzzy model systems . Some researchers (see, for example, and the references therein) have employed the linear matrix inequality‐based (LMI‐based) techniques to investigate the robust stability and stabilization problems of the TS fuzzy model systems with parametric uncertainties.…”