More degrees of freedom not only enable multiphase drives to be fault-tolerant but also allow non-sinusoidal electromotive forces (NS-EMFs) in high-quality vector control. NS-EMFs lead to lower costs of design and manufacturing of electrical machines. However, the presence of multi-harmonics in NS-EMFs possibly generates pulsating torque in both healthy and faulty conditions of multiphase drives. To facilitate the use of NS-EMFs, this two-part study proposes control schemes to adaptively improve torque quality of multiphase drives in dealing with multi-harmonics of NS-EMFs. The proposed schemes are based on a simple but effective type of artificial intelligence, Adaptive Linear Neuron (Adaline). The knowledge of multiphase drives including the harmonic ranks of NS-EMFs and the rotor position is exploited to design the online-trained optimal Adalines. The first part of this study is to propose a control scheme using an Adaline for healthy mode with high-quality torque regardless of numerous harmonics in NS-EMFs. The second part of this study introduces a control scheme using another Adaline for open-circuit faults. The proposed schemes are numerically and experimentally validated on a seven-phase permanent magnet synchronous machine (PMSM) possessing a high total harmonic distortion (THD=38%) of NS-EMFs. A demonstration video is provided with this paper.