Accurate tracking control of nonminimum phase systems relies on the calculation of the ideal internal dynamics (IID). Traditional IID calculation methods fail when applied to nonminimum phase nonhyperbolic systems (systems with nonhyperbolic zero dynamics). Recently, we propose the optimal bounded inversion method for IID calculation, which obtains IID by solving a trajectory optimization problem. In this paper, we extend our previous result and show that optimal bounded inversion can also deal with nonminimum phase nonhyperbolic systems. More than that, it is also possible to achieve different control goals by setting different cost functions. Particularly, three cases are investigated in this paper. The first uses minimal initial value deviation as the cost function, resulting in "T-IID" which can achieve accurate output tracking. The second applies minimal terminal value as the cost function, resulting in "S-IID" which leads to a final rest for the system. The last combines "T-IID" and "S-IID" to achieve a compound goal. The effectiveness is verified through Matlab simulations of a two-cart inverted-pendulum system.