Parallel Distributed Compensation Framework Research Articles

Discrete Sliding-Mode Control for a Class of T-S Fuzzy Models with Modeling Error

This paper proposes a discrete sliding-mode controller for a class of nonlinear systems described by a T-S fuzzy model subject to modeling error, which may influence the system performance and the overall system stability. While most of existing literature treats the modeling error under the so-called parallel distributed compensation framework by using some norm-bounded matrices, the proposed control scheme in this paper integrates a feedback component, which mainly consists of fuzzy approximators to deal with the modeling error and an auxiliary component of the variable structure control with a sector to guarantee the global stability of the closed-loop system when the system state travels outside the sector. With the consideration of system stability, adaptive laws adjusting the parameters in the system are developed based on the Lyapunov synthesis approach. Finally, simulation results will confirm the effectiveness of the approach proposed in this paper.

Parallel Distributed Compensation Based Stabilization of A 3-DOF RC Helicopter: A Tensor Product Transformation Based Approach

This paper presents a control solution for the stabilization of the 3-DOF RC helicopter via the combination of the TP (Tensor Product) model transformation and the PDC (Parallel Distributed Compensation) control design framework. First we recall the nonlinear model of the RC helicopter and its simplified version, in order, to facilitate control design. Then we execute the TP model transformation on the simplified model to yield its TP model representation, that is a kind of polytopic model with specific characteristics, whereupon the PDC framework can immediately be applied. The control design considers practical control specifications such as: good speed of response and physical constrain on the control effort to avoid actuator saturations. We guarantee these specifications by LMI (Linear Matrix Inequality) conditions developed under the PDC frameworks. Further, we avoid the discrepancies, introduced via the simplification of the model, by applying LMI conditions specialized for robust control. By simultaneously solving these LMI conditions, we render a stabilizing nonlinear controller that achieves good speed of response with small control effort without actuator saturations. Simulation results are included to validate the control design. It will be pointed out that the resulting controller is equivalent with the controller successfully applied in the real control experiment of the helicopter presented in a recent paper.The main conclusion of this paper is, that the proposed design process is systematic, non-heuristic and straightforward, the stability proof of the resulting controller is tractable via the feasibility test of LMIs and, hence, exact. The whole design procedure is automatically computed via commercialized mathematical tools (MATLAB LMI Toolbox) without analytical interaction. The computational time is about minutes on a regular PC.

Trajectory Tracking by TP Model Transformation: Case Study of a Benchmark Problem

The main objective of this paper is to study the recently proposed tensor-product-distributed-compensation (TPDC)-based control design framework in the case of tracking control design of a benchmark problem. The TPDC is a combination of the tensor product model transformation and the parallel distributed compensation framework. In this paper, we investigate the effectiveness of the TPDC design. We study how it can be uniformly and readily executed without analytical derivations. We show that the TPDC is straightforward and numerically tractable, and is capable of guaranteeing various different control performances via linear matrix inequality (LMI) conditions. All these features are studied via the state feedback trajectory control design of the translational oscillations with an eccentric rotational proof mass actuator system. The trajectory tracking capability for various tracking commands is optimized here by decay rate LMI conditions. Constraints on the output and control of the closed-loop system are also considered by LMI conditions. We present numerical simulations of the resulting closed-loop system to validate the control design