Can you provide an example from the scriptures of Sai Baba's Udi being used to cure a psychological or sleep-related problem?

Yes, Chapter 35 recounts a specific incident where Udi provided a remedy for a sleep-related affliction. A gentleman from Bandra was unable to sleep peacefully because he was tormented nightly by dreams of his deceased father. After all other efforts failed, a Sai devotee advised him to use Baba's sacred ash. The instructions were to apply a little Udi to his head before sleeping, tie a packet of it under his pillow, and keep Sai in his thoughts. As Chapter 35 states, the man followed this advice and immediately fell into a deep, peaceful sleep, and the troubling dreams never returned, demonstrating the Udi's power to remove such distress.