Nameplate current refers to continuous load at rated RPM.
Maximum current, aka. stall current, is when the RPM is zero, due to no back-EMF voltage, which is generated by the rotating magnetic field.
You can think this as a power source you are going to design (ideally, should really be a current source, but due to lack of competence in PWM controller design, voltage sources are often created instead), which drives a voltage source (the motor!) through a series resistor (wires, motor windings, brushes). The motor "voltage source" voltage depends on its RPM only. The DC current is then limited by the series resistance only!
Big and efficient motors try to optimize the series resistance to zero. Hence, they can take almost unlimited current; similar to LEDs, you drive them with current source.
In some cases, where you can guarantee that the motor will spin up just fine and then provide power for a controlled mechanical load, and you have a strong power source (such as a huge battery), you do connect the motor "directly". It jerks, takes an enormous current spike, and runs. Fuse can be used to protect it. But this use case is not very useful if you want to control pretty much anything.
So, we want a speed and/or torque controller. And for that, we need a current mode controller.
Since we don't have all the information, we need to assume, but this is going to be an illustrative example:
Let's assume that 125V, 27A, and 2980W (4HP) ratings all apply at the same time, and the 4HP is mechanical power output. This means the motor is 2980W/(27A*125V) = 88% efficient - which sounds about right for a big motor with continuous duty. If we further assume that 60% of these losses are resistive (rest being magnetization hysteresis aka iron losses and friction losses), this means I^2*R losses of 237W. From this, we'll calculate the resistance of R = P/I^2 = 0.33 ohms. Sounds about right magnitude.
From this, let's apply the 125V voltage to the motor which is not running, the rpm is at 0. The current will be:
I = U/R = 125V/0.33 ohms = 379A (!)
This is the stalled rotor current: if you force the rotor to stall, you get this until the motor windings burn out (a few seconds, maybe tens of seconds). Of course, only portion of this current is generating actual torque: the torque capability is maxed out (with iron completely saturated) way earlier, typically at around 2-4 times the nominal current rating. Which is why you need active current control as well.
Now, luckily, there is some inductance in the motor. Quite a lot of it. It takes milliseconds to reach this current. So, doing PWM on the "block diagram level" is fairly easy. With a big motor, the PWM could run at 2-3 kHz, and even an Arduino analog input could be used to produce the current measurement feedback!
Power stage PCB design and layout is the most difficult part.
But, you definitely need a current feedback. High bandwidth, isolated hall effect module from LEM or similar is often easiest. Or go with ground referenced shunt and an amplifier. But without current limit, you can never know what you are doing. Of course, you could write some code that gradually ramps up the PWM duty to smoothly rise the motor RPM and experiment so that you never exceed sensible currents. But any mechanical issue or any corner case would throw it of and require extra logic. So that's why you simply use current mode control. As an additional bonus, you can use the current setpoint as fairly good torque control directly. In a treadmill, you would most likely want to limit both torque and speed. The former limits sudden jerks very well. Usually, a torque control with maximum speed limit is very useful - similarly to LED power supplies that provide adjustable constant current with an open circuit voltage safety limit.
Re IGBT: for lowest losses, consider MOSFETs. IGBTs are great at supplies well over the 200-300V range, but they have a diode-like "constant" (actually logarithmic) voltage drop, so you are always losing around 2-3V on the IGBT. At 350-400V DC bus and 600V rated IGBTs, this is not a big percentage, but for much lower, you'd benefit from the MOSFETs resistive Rds(on) behavior.