This article presents absolute stability conditions for a particular class of Takagi–Sugeno fuzzy control systems. Initially, a Takagi–Sugeno fuzzy control system is transformed into a multivariable Lur’e type system. A simple algorithm for checking the absolute stability of this system is then proposed. Since the key of the proposed algorithm is to solve algebraic Riccati equations, software packages such as MATLAB provides a simple means to check the conditions. The proposed approach does not limit the methods of fuzzification and defuzzification. This article presents several analytical examples to verify the simplicity and efficiency of the proposed approach.

Chaotic motion is an undesirable phenomenon in many engineering applications since it leads to a significant degradation of the system performance and restricts the feasible operational range. Therefore, the problem of controlling or suppressing chaos has attracted considerable attention in the literature. However, most chaos control schemes utilize a state feedback signal, and are therefore sensitive to measurement noise. Therefore, a requirement exists for filtering systems capable of separating the measurement noise from the chaotic signal in order to improve the performance of the controlled system. However, the chaotic signal and the measurement noise are both broadband signals, and thus the measurement noise can not be filtered using a low-pass filter since this causes a distortion of the chaotic signal. Accordingly, this paper presents a control scheme for chaotic dynamic systems with significant measurement noise featuring an input-state linearization scheme and a filter based upon an independent component analysis algorithm. The feasibility and effectiveness of the proposed approach are demonstrated by way of numerical simulations using a general Lorenz system for illustration purposes.

This study developed a method for designing parallel two-degree-of-freedom proportional-integral-derivative controllers for unstable time-delay processes with unknown dynamic equations. First, a performance index accounting for both transient response performance and disturbance rejection was developed. To obtain useful data even if the output of the system exceeds the allowable range, an effective penalty function was included in the performance index. The N–M simplex method was used to iteratively determine the optimal controller parameters. The proposed approach has the following advantages: (1) it can be used regardless of the stability of the open-loop system; (2) the mathematical model and parameters of the process need not be known in advance; (3) it can be used for processes that include measurement noise; (4) it has good transient response performance and is also robust against external disturbances; and (5) it enables more efficient controller design and reduces costs.

This paper develops an automatic welding control scheme for alternating current shielded metal arc welding (SMAW) system. A mathematical model of the welding control system is derived and the system parameters identified. An adaptive sliding mode controller is designed to estimate the bound of the system uncertainties and to modulate the electrode feed rate in such a way that the desired arc length and arc current are maintained as the electrode melts during the welding process. The proposed control method is suitable for any consumed electrode welding technique. The simulation and experimental results show that the automatic welding control system successfully maintains the magnitude of the arc current at the desired value and preserves the arc stability, thereby obtaining an enhanced SMAW control system performance.

This paper presents an efficient method for designing optimal controllers. First, we established a performance index according to the system characteristics. In order to ensure that this performance index is applicable even when the state/output of the system is not within the allowable range, we added a penalty function. When we use a certain controller, if the state/output of the system remains within the allowable range within the preset time interval, the penalty function value is zero. Conversely, if the system state/output is not within the allowable range before the preset termination time, the experiment/simulation is terminated immediately, and the penalty function value is proportional to the time difference between the preset termination time and the time at which the experiment was terminated. Then, we used the Nelder–Mead simplex method to search for the optimal controller parameters. The proposed method has the following advantages: (1) the dynamic equation of the system need not be known; (2) the method can be used regardless of the stability of the open-loop system; (3) this method can be used in nonlinear systems; (4) this method can be used in systems with measurement noise; and (5) the method can improve design efficiency.