Prescribed performance control with a standard second-order transient response for strict feedback affine nonlinear systems

In this paper, a novel prescribed performance control method is proposed. The proposed controller features with standard second-order transient performance. By using a standard second-order response performance function and a new error transformation method, the prescribed performance of the system is achieved in a preset range of the performance function. The error transformation method is universal, therefore, it can also be applied to other performance functions. The proposed controller is designed by the backstepping technique based on Lyapunov stability. By using the proposed controller, the asymptotic stability can be achieved. The proposed controller is firstly tested on a simple second-order system, which can be directly controlled by the proposed control method. Then, the proposed controller is tested on a complex quaternion based aircraft attitude stabilisation system. The proposed method cannot be directly applied to the attitude control system, so some advanced derivations are conducted. The simulation results are given for each of the closed-loop systems and some analysis is conducted. Expected results with prescribed performance are illustrated and some comparisons are made.