PLC-Driven 3-Speed Motor Circuit

I need a compact motion circuit that slides a carriage from right to left at three distinct speeds, all triggered in sequence from a single push button. The mechanical side is fixed: a DC motor matched with an inline gear set will provide the drive... (Budget: ₹600 - ₹1500 INR, Jobs: Arduino, Circuit Design, Control Engineering, Electrical Engineering, Electronics, Motor Control, PCB Layout, PLC)