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A class of generalized proportional-integral-derivative (PID) control with feedforward compensation (FFC) is obtained for a class of cascade integral systems by equivalence analysis of the cascade control and such the analysis is obtained by using the information of the model and outermost loop feedback. Firstly, a new type of error related to the traditional error such as proportional (P) or proportional integral (PI) is given. Secondly, by analyzing cascade control for a class of ideal cascade integral systems, the generalized PID control with FFC is presented based on the proposed new type of error. Then, the generalized PID control with FFC is extended to a class of non-ideal cascade integral systems to reduce the number of feedback loop and sensors. Finally, the simulation results of the speed/position servo system of direct current motor are given to verify the theoretical analysis results.