A new optimal sliding mode controller design using scalar sign function.

This paper presents a new optimal sliding mode controller using the scalar sign function method. A smooth, continuous-time scalar sign function is used to replace the discontinuous switching function in the design of a sliding mode controller. The proposed sliding mode controller is designed using an optimal Linear Quadratic Regulator (LQR) approach. The sliding surface of the system is designed using stable eigenvectors and the scalar sign function. Controller simulations are compared with another existing optimal sliding mode controller. To test the effectiveness of the proposed controller, the controller is implemented on an aluminum beam with piezoceramic sensor and actuator for vibration control. This paper includes the control design and stability analysis of the new optimal sliding mode controller, followed by simulation and experimental results. The simulation and experimental results show that the proposed approach is very effective.

Efficient decentralized iterative learning tracker for unknown sampled-data interconnected large-scale state-delay system with closed-loop decoupling property.

In this paper, an efficient decentralized iterative learning tracker is proposed to improve the dynamic performance of the unknown controllable and observable sampled-data interconnected large-scale state-delay system, which consists of N multi-input multi-output (MIMO) subsystems, with the closed-loop decoupling property. The off-line observer/Kalman filter identification (OKID) method is used to obtain the decentralized linear models for subsystems in the interconnected large-scale system. In order to get over the effect of modeling error on the identified linear model of each subsystem, an improved observer with the high-gain property based on the digital redesign approach is developed to replace the observer identified by OKID. Then, the iterative learning control (ILC) scheme is integrated with the high-gain tracker design for the decentralized models. To significantly reduce the iterative learning epochs, a digital-redesign linear quadratic digital tracker with the high-gain property is proposed as the initial control input of ILC. The high-gain property controllers can suppress uncertain errors such as modeling errors, nonlinear perturbations, and external disturbances (Guo et al., 2000) [18]. Thus, the system output can quickly and accurately track the desired reference in one short time interval after all drastically-changing points of the specified reference input with the closed-loop decoupling property.

Iterative learning-based decentralized adaptive tracker for large-scale systems: a digital redesign approach.

In this paper, a digital redesign methodology of the iterative learning-based decentralized adaptive tracker is proposed to improve the dynamic performance of sampled-data linear large-scale control systems consisting of N interconnected multi-input multi-output subsystems, so that the system output will follow any trajectory which may not be presented by the analytic reference model initially. To overcome the interference of each sub-system and simplify the controller design, the proposed model reference decentralized adaptive control scheme constructs a decoupled well-designed reference model first. Then, according to the well-designed model, this paper develops a digital decentralized adaptive tracker based on the optimal analog control and prediction-based digital redesign technique for the sampled-data large-scale coupling system. In order to enhance the tracking performance of the digital tracker at specified sampling instants, we apply the iterative learning control (ILC) to train the control input via continual learning. As a result, the proposed iterative learning-based decentralized adaptive tracker not only has robust closed-loop decoupled property but also possesses good tracking performance at both transient and steady state. Besides, evolutionary programming is applied to search for a good learning gain to speed up the learning process of ILC.

Digital redesign of analog smith predictor for systems with input time delays.

This paper presents a new methodology for digitally redesigning an existing analog Smith predictor control system, such that the cascaded analog controller with input delay can be implemented with a digital controller. A traditional analog Smith predictor system is reformulated into an augmented system, which is then digitally redesigned using the predicted intersampling states. The paper extends the prediction-based digital redesign method from a delay free feedback system to an input time-delay cascaded system. A tuning parameter v is optimally determined online such that in any sampling period, the output response error between the original analogously controlled time-delay system and the digitally controlled sampled-data time-delay system is significantly reduced. The proposed method gives very good performance in dealing with systems with delays in excess of several integer sampling periods and shows good robustness to sampling period selection.