This paper focuses on the operation improvement of garbage power plants, which are a key disposal technology for household waste, construction waste, etc. However, the low of the furnace temperature can cause a sharp increase in dioxins and result in consequences of severe environmental pollution. To enhance the control performance of the combustion system for garbage power plants, proportional-integral-derivative based on predictive (PID-predictive) and proportional-integral based on predictive (PI-predictive) controllers are designed for the combustion system, which is dominated by time delay. By equaling the desired dynamic characteristics and the closed-loop system combined with the combustion system and controller, the PID-predictive and PI-predictive can be designed. The comprehensive comparison of the tracking performance, disturbance rejection ability, measurement noise rejection performance and ability to handle system uncertainties is carried out with PI, active disturbance rejection control, delay active disturbance rejection control and Smith predictor active disturbance rejection control. Simulation results show that PID-predictive and PI-predictive obtain similar control performance, and have a faster tracking speed than other comparative controllers. The disturbance rejection ability of PID-predictive and PI-predictive is weaker than delay active disturbance rejection control and Smith predictor active disturbance rejection control, and is stronger than PI and active disturbance rejection control. When the controlled process has system uncertainties, PID-predictive and PI-predictive still obtain satisfactory control performance.