This paper focuses on establishing the closed-form formulas to design a proportional-integral-derivative-acceleration-jerk (PIDAJ) controller for fourth-order pla- nts. After plant modeling, the analog PIDAJ controller in continuous-time domain can be designed by utilizing the proposed formulas in a vector-matrix form. Based on bilinear transform, the digital PIDAJ controller in discrete-time domain can then be achieved. The use of the proposed formulas to determine the PIDAJ controller's parameters for controlling the air-fuel ratio of an engine is described as an application example to con- _rm their feasibility. MATLAB simulation results con_rm the consistency between step responses of the example system controlled by the designed controllers in continuous-time domain and discrete-time domain.
