Example of polynomial controller synthesis for a non-square object with one input and two outputs

Polynomial methods for synthesizing controllers for automatic control systems with linear objects are becoming increasingly common. The synthesis of multichannel controllers is particularly difficult, which is caused by the need to use matrix polynomial calculus. However, this approach mainly considers objects with the number of inputs equal to the number of outputs. This is due to the convenience of solving a system of linear algebraic equations in matrix polynomial calculus. In this paper, we consider a polynomial method for synthesizing regulators for a non-square object, that is, one whose number of inputs is not equal to the number of outputs. The selected system contains not only a non-square object, but also a non-square controller.

On the synthesis of a polynomial controller for enlarging the stability domain for nonlinear discrete system

This paper aims to propose an algebraic method for estimating the stability region for nonlinear discrete systems. The main contribution is the improvement of an existing technique to enlarge the initial stability region in which the asymptotic stability is guaranteed. To deal with the maximization issue, a state feedback controller is proposed to extend the largest estimation of attraction domain of nonlinear polynomial discrete systems. The proposed approach is illustrated and validated on an isothermal stirred tank reactor.

Polynomial Controller Design Using Disturbance Observer

Disturbance observer-based control provides a promising approach to handle system disturbance and improve robustness. In this paper, a new fuzzy disturbance observer (FDO) is proposed into the SOS-based approach, where the polynomial fuzzy model is used to develop the system controller. Compared with other works published so far, the FDO mainly features two things: 1) the estimation error between the FDO and disturbance shrinks asymptotically to zero if the disturbance has a constant steady-state value; 2) parameters involved in the FDO is adjusted on the basis of the polynomial fuzzy model which is basically nonlinear. Finally, computer simulations are provided to illustrate the effectiveness of the proposed approach.

Synchronization of Chaotic Systems Using Sampled-Data Polynomial Controller

This paper presents the synchronization of two chaotic systems, namely the drive and response chaotic systems, using sampled-data polynomial controllers. The sampled-data polynomial controller is employed to drive the system states of the response chaotic system to follow those of the drive chaotic system. Because of the zero-order-hold unit complicating the system dynamics by introducing discontinuity to the system, it makes the stability analysis difficult. However, the sampled-data polynomial controller can be readily implemented by a digital computer or microcontroller to lower the implementation cost and time. With the sum-of-squares (SOS) approach, the system to be handled can be in the form of nonlinear state-space equations with the system matrix depending on system states. Based on the Lyapunov stability theory, SOS-based stability conditions are obtained to guarantee the system stability and realize the chaotic synchronization subject to an H∞ performance function. The solution to the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. Simulation examples are given to illustrate the merits of the proposed sampled-data polynomial control approach for chaotic synchronization problems.