where \(L=0.25a_{eff}B_{T}/B_{\perp}\) is the effective connection length. This equation shows that obtaining a field-null configuration, i.e., minimizing the poloidal magnetic field \(B_{\perp}\), can significantly reduce the required toroidal electric field for a successful plasma breakdown, which is essential as the available toroidal electric field is quite limited on large superconducting machines, such as ITER [9]. Optimizing the field-null configuration is delicate work, as \(B_{\perp}\) is determined not only by currents in the active controlled magnetic coils but also by the eddy currents in various passive conductive structures. Special attention should be paid to the treatment of passive eddy currents, which could be as large as tens to hundreds of kilo-amperes and can significantly influence \(B_{\perp}\) during the breakdown stage due to the high inductive voltage, as has been demonstrated in the WEST tokamak [10]. To address this problem, various methods have been proposed. In the early 1990 s, a model-based approach was developed to optimize the coil voltage waveforms for tokamak startup [11; 12]. It utilizes the eigenvalue transformation [13] to express the field values like \(B_{\perp}\) linearly in terms of coil voltages, with the effect of eddy currents implicitly included. This transfers the optimization problem of \(B_{\perp}\) to minimizing a quadratic cost function, which is much easier to solve. This approach has been widely used for designing field-null configurations on several devices, like ITER [12], EAST, KSTAR [14] and HT-6M [15]. Based on similar principles, more integrated approaches have also been proposed to optimize the whole startup scenario including breakdown and the following processes, like plasma current ramp-up and equilibrium formation [7; 9; 16; 17]. Yet, these approaches rely on the assumption of piecewise linear coil voltage waveforms, which could pose a limit for both the tuning flexibility and the consistence with arbitrary waveforms when applying feedback-control algorithms. Other approaches include the one based on flux expansion in DIII-D [5] and adjusting the currents of a specific set of coils empirically to compensate for the influence of eddy currents, such as on HL-3 (previously named HL-2M) [18; 19]. Neither of these approaches has an explicit, self-consistent treatment of eddy currents, which limits the accuracy of \(B_{\perp}\) compensation and the quality of designed field-null configurations. On the other hand, issues related to feedback control often lack mentioning in the literature, which requires attention as it is fundamental in filling the gap between modeling and experiments, and the deviation from feedforward trajectories could significantly impact the field-null configuration. In this paper, a model-based scheme for optimizing the field-null configuration is proposed and applied on HL-3, which is a medium-sized copper tokamak aimed at exploring the route to high-performance plasma operation [20; 21]. The scheme is based on an integrated forward simulation model of the tokamak circuit system, including both the active coils and passive conductors, which is developed within the MATLAB(r) Simulink(tm) framework. The scheme does not require additional assumptions of coil voltage waveforms, such as being piecewise linear, which could make it more straightforward and flexible when designing the coil current and voltage waveforms. Similar to other model-based schemes, this one has the advantage of being self-consistent as well, and the passive eddy currents are precisely treated by applying an iterative optimization approach. A large field-null area with \(|B_{\perp}|\leq 1\)\(G\) is obtained when applying this scheme for a breakdown scenario design on HL-3, which can be steadily sustained for over 15 milliseconds to guarantee the robustness of breakdown. The corresponding coil current waveforms are also provided as the control targets to be used in experiments.