HL-2A plasmas heated by neutral beam injection (NBI) regularly exhibit n = 1 long-lived saturated magnetohydrodynamic instabilities. A reduction in the electron density and plasma stored energy and an increase in fast ion losses are usually observed in the presence of such perturbations. The observed long-lived saturated internal mode (LLM) occurs when the safety factor profile has a weak shear in a broad range of the plasma centre with qmin around unity. It is found that the ideal interchange mode can become marginally stable due to the weak magnetic shear reaching a critical value. The LLM, due to its pressure-driven feature, is destabilized by the strong interaction with fast ions in the low-shear region during the NBI. Furthermore, for the first time it is clearly observed that the LLMs can be suppressed by electron cyclotron resonant heating (ECRH), or by supersonic molecular beam injection in HL-2A plasmas. Low-n sidebands observed during the LLM are also suppressed by increasing the ECRH power. The control of LLMs is due to the change in the magnetic shear or in the pressure profile induced by the local heating or fuelling.