Reconstructing a pitchfork bifurcation that is destroyed by an exogenous disturbance is important to control it. This paper extends the equivalent-input-disturbance (EID) approach to solve the problem of reconstructing a pitchfork bifurcation when there is an exogenous disturbance for the first time. A nonlinear term and a bifurcation parameter are designed in the system to reconstruct the pitchfork bifurcation. The bifurcation characteristics of the equilibriums of the system are analyzed by exploring the features of the EID-based system. This provides us analytic solutions for a system with a degree higher than four for the first time. Unlike other pitchfork-bifurcation control systems, the EID-based control system only rejects the disturbance and retains the nonlinearity. Numerical examples demonstrate the effectiveness of the presented method and show its superiority over others. The robustness of the reconstruction with respect to measurement noise and control of a pitchfork bifurcation are also shown by the examples.

重建受到外来干扰破坏的干草叉分叉对于控制它很重要。本文扩展了等效输入扰动（EID）方法，以解决首次出现外来干扰时重构音叉分叉的问题。在系统中设计了一个非线性项和一个分叉参数来重构干草叉分叉。通过探索基于EID的系统的特征来分析系统平衡的分叉特性。这首次为我们提供了度数高于4的系统的解析解决方案。与其他干草叉分叉控制系统不同，基于EID的控制系统仅抑制干扰并保留非线性。数值算例表明了该方法的有效性，并显示了其优越性。实施例还示出了相对于测量噪声的重建的鲁棒性和干草叉分叉的控制。