Proportional-Integral-Derivative controller is remained as the most widely used controller for many industrial applications even though it was developed decades ago. This is because of its simplicity, satisfactory control performance and robustness. The classical and empirical PID tuning rules are applicable only to the FOPDT and cannot guarantee its optimality. The Ziegler-Nichols frequency response method is regarded as a basis of relay feedback auto-tuning because it uses the only information at the phase crossover frequency. The Ziegler-Nichols tunings are quite aggressive for lag- dominant processes but sluggish for delay-dominant processes. The IMC-PID settings yield good servo performance and robustness, they result in poor LD (load disturbance) rejection for lag-dominant plants. We have proposed a new method of determining LQ index in consideration of dominant pole placement for desired performance and derive a simple LQR-PID tuning formula via IMC-like H∞ approach for first order plus dead-time systems. We have determined the weight for sensitivity function so that LQ optimization is equivalent to the H∞ optimization of the weighted sensitivity function. The proposed PID controller has the same performance as LQR controller and the tuning method is simple, since it does not need to solve the Riccati algebraic equation. We also present other two tuning methods for PID controller: LQR-like and pole-placement-like ones. The new contributions in this paper are: determination of LQ index for dominant poles placement and optimal weight for sensitivity, and derivation of LQR-PID tuning methods via IMC-like approach, LQR and pole-placement approaches. The effectiveness of the proposed methodology and the identity of the PID parameters tuned by those three methods have been demonstrated via simulation.