The main purpose of this paper is to predict the phenomenon of pilot-induced oscillations (PIOs) by the use of parameter plane approach. The position-limited and rate-limited are always existed in the practical pilot-vehicle systems. Based on the approximation of classical describing functions, the stability of linearized pilot-vehicle systems can be easily analyzed. In addition, the impacts on the stability under the parameter variations of controller or plant have to be considered for the robust design by utilizing parameter plane approach. In our work, a PID pilot-vehicle system with rate-limited is given for analyzing PIOs first. Although this control structure is simple, some complex situations are happened. Furthermore, the effect of phase delay is also addressed. Finally, we also extend the stability analysis to a pilot-vehicle system with multiple nonlinearities. Computer simulations demonstrate the prediction of PIOs by this approach.