The pointing performance of a truss structure on orbit that is used for a large space telescope is discussed. To achieve advanced science missions, large and precise support structures such as truss structures are needed. However, the preciseness of the structure might be lost due to various disturbances on orbit. Therefore, to realize ultra-large and precise support structures, active shape control of the structures is needed. To control the shape, we use artificial thermal expansion caused by heaters instead of mechanical actuators. Control systems without mechanical mechanisms have high reliability, which is very attractive for use on orbit. However, there are some constraints regarding the usage of heaters. The control input is restricted to positive inputs because heaters can give off heat but cannot dissipate heat actively, and there will be upper limits on the heat input. To improve the control performance under such constraints, we apply "Model Predictive Control (MPC)" as a feedforward control method with preview information. In this paper, we mainly show the effectiveness of MPC compared with PI control, which is one of the typical feedback control methods. We developed a structural mathematical model and a thermal mathematical model in order to evaluate the performance of the control system. It is confirmed through numerical simulations that the total error is reduced by MPC compared with PI control.