Model predictive control (MPC) is an advanced method to deal with optimization control of multivariable, large inertia and constrained systems [18]. In order to solve the control problem of MGT-CCHP system, an observer-based model predictive control algorithm is used [19]. The simulation results show that the control performance of the MPC is obviously improved compared with the PID controller for MGT-CCHP system. A self-tuning MPC control method is proposed to improve the performance of the MPC for MGT-CCHP system [20]. In [21; 22], a data-driven MPC controller is proposed to improve the operation quality of the MGT-CCHP system. In [23], a supervisory MPC controller is proposed to improve the economic efficiency. However, these MPC controllers designed for the MGT-CCHP system do not consider the nonlinearity of the system. When the MGT-CCHP system runs on a wide range of load changes, the nonlinearity of the MGT-CCHP system will lead to the performance degradation of the controller, even if the controller parameters are well tuned. Therefore, it is necessary to design a nonlinear MPC controller to improve control performance. In general, MGT-CCHP system is divided into two sets of systems in actual operation, MGT-based combined cooling and power system (MGT-CCP) and MGT-based combined heating and power system (MGT-CHP); consequently, it is more practical to study control methods for these two kinds of combined systems individually. This paper proposes a coordinated predictive control by using a generalized predictive control (GPC) for MGT system and a Hammerstein generalized predictive control (HGPC) for the CCP system. First, the dynamic characteristics and nonlinearity distribution of the MGT and CCP processes are analyzed by step response and Vinnicombe gap (V-gap) metric, which provides a basis for the selection of advanced control strategies. Secondly, the Hammerstein identification method of the single-input and single-output (SISO) system proposed in [24] is extended to the multi-input single-output (MISO) system, which is used to model the nonlinear CCP system. Third, the HGPC method was proposed to improve the performance of the predictive control for the nonlinear CCP system. Finally, the coordinated predictive control strategy is designed with the hybrid of GPC and HGPC for the MGT-CCP system to meet the simultaneous cooling and power load-tracking requirements. The major contribution of this study is that a coordinated predictive control strategy with GPC and HGPC is designed to overcome the nonlinear and multiple-variable control problems in the MGT-CCP system. The minor contributions of this study are summarized below:  
1. The nonlinearity distribution of the MGT-CCP system is first analyzed using V-gap;
2. The MISO Hammerstein model of the CCP system is first established to capture its nonlinearity, which is beneficial to the design of the controller;
3. The proposed GPC-HGPC coordinated control strategy has been validated to effectively improve the simultaneous cooling and power load tracking capability of the MGT-CCP system when accessing with renewable energy. The proposed coordinated predictive controller is implemented on a 80 kW MGT-CCP simulator. The rest of the article is organized as follows: Section 2 analyzes the dynamics and nonlinearity of MGT-CCP system; Section 3 introduces the identification of multivariate Hammerstein ARMAX models; The Hammerstein-GPC controller and the coordinated control strategy for the MGT-CCP are proposed in Section 4. The simulation results and conclusions are given in the Sections 5 and 6, respectively.