To overcome the complex features of boiler combustion system

such as multivariable inputs and outputs

strong coupling

strong interference and long hysteresis

a new multivariate PID-MAC algorithm combing the state-space equation based model algorithm control(MAC)with the PID control was proposed.Moreover

the Lyapunov's second stability theorem was employed to prove this algorithm renders the system closed-loop stabilization.Simulation experiments with gas boiler show this control strategy has advantages like small steady-state error and short rise time during PID control

and small overshoot of MAC.Furthermore

to some extent

it gets rid of long regulation time of PID control and large steady-state error of MAC.