A new design of linear quadratic control (LQ) is proposed for batch processes with partial actuator faults and unknown disturbance. The autoregressive model built through input-output process data is transformed into a new non-minimal state space (NMSS) model in which the process state variables and tracking error are combined, then a new LQ control scheme is derived based on minimax optimization. Unlike LQ based on traditional NMSS model (TNMSSLQ), the process state variables and tracking error can both be regulated in the proposed method. Monotonic situations of optimal performance cost are further derived to yield sufficient conditions for both nominal and robust system stability. Finally, an injection velocity control example is illustrated to show the effectiveness.