Introduction:
In control systems, negative feedback is used to stabilize the system and reduce errors. However, despite the presence of negative feedback, control systems can still have problems of instability. One of the reasons for this is the presence of non-linearities in the components used in the system.

Explanation:
- Non-linearities in components: Control systems are typically composed of various components such as amplifiers, sensors, and actuators. These components may exhibit non-linear behavior, which means that their output is not directly proportional to their input. Non-linearities can introduce instability in the control system because they can cause the system to respond in unpredictable ways. For example, if an amplifier exhibits non-linear distortion, it can introduce harmonics into the system, which can lead to instability.

- Dynamic equations of sub-systems: Control systems are often composed of multiple sub-systems that interact with each other. The behavior of these sub-systems is described by dynamic equations, which represent the relationship between the input and output of the sub-system. However, in practice, it is often difficult to know the exact dynamic equations of the sub-systems. This lack of precise knowledge can lead to instability in the control system because the controller may not be able to accurately predict and compensate for the behavior of the sub-systems.

- Mathematical approximations: Control systems are typically analyzed using mathematical models and techniques. However, these mathematical models often involve simplifications and approximations to make the analysis tractable. These approximations can introduce errors and inaccuracies in the analysis, which can lead to instability in the control system. For example, if a high-frequency component is approximated as a low-frequency component, it can lead to instability because the controller may not be able to respond quickly enough to changes in the system.

- Large negative phase angle at high frequencies: In control systems, the phase angle represents the time delay between the input and output signals. A large negative phase angle at high frequencies can indicate instability in the system. This can occur when the control system is not able to respond quickly enough to changes in the system, leading to oscillations and instability.

Conclusion:
In conclusion, control systems can still have problems of instability despite the presence of negative feedback. One of the reasons for this is the presence of non-linearities in the components used in the system. These non-linearities can introduce instability because they can cause the system to respond in unpredictable ways. It is important to carefully analyze and design control systems to mitigate the effects of non-linearities and ensure stability.