## Sunday, July 29, 2018

### Field Weakening, Part 2

Recall in a previous post we had found an analytic solution to the field weakening problem. Unfortunately, the model is useless in practice; high currents (which are needed to cancel large amounts of PM flux) result in much lower inductances (which serves to decrease the amount of flux being canceled), resulting in numbers which are implausible and wrong.

However, while back EMF depends on the inductances, flux linkage, currents, and speed, torque is independent of speed - the same $$(I_d, I_q)$$ will always produce the same torque, no matter what speed the motor is at. Furthermore, we already know the relationship between torque and the axis currents from stall testing, and we can used this data as a black box to look up torque outputs from $$I_d$$ and $$I_q$$ inputs.

We are going to make an additional huge assumption: at high speeds, the current is low. This is not necessarily true, but for motors designed to be aggressively field weakened, the achievable current is likely low due to the high inductances. This assumptions means we can use the voltage equations to compute the back EMF for most of the field weakened operating regime. Of course, there will be a transition around base speed where this assumption doesn't hold, but we can "fix that in post".

Armed with this, we can write a simple C++ program (source, executable, sample input) to search the entire space of $$I_d$$ and $$I_q$$ values. The program is not particularly good or fast, but the brute-force approach makes it very robust and trivially extensible to a saturated motor (just override the Vs2() function in the MotorModel class with a lookup table based one). In contrast, Newton's-method based approaches seem to fail if the voltage surface is too complex.

The program generates some very reasonable output; for example, the following plot of power and torque versus speed for the HSG at 160V:

The flat part of the torque-speed curve extends up to what would traditionally be called "base speed" [1]. A surface PM machine spends most of its time operating in this regime, as operating over base speed results in reduced power output and efficiency. In contrast, an IPM is a constant-power device past base speed; this has several implications for system design:

Hybrid vehicles: Field weakening is very important for hybrid vehicles.  Consumer hybrids have electric subsystems optimized for city driving. In order to optimize efficiency in this scenario, it is beneficial to have a high reduction between the motor and the wheels, to reduce the motor current required to accelerate the car. This typically means putting base speed somewhere around 40 mph, which means at highway speeds, the motor is operating well beyond base speed. Being able to produce power at these speeds is important for consistent performance.

There is also a class of emerging high-performance hybrids. Typically, these use a combination of one or two motors, a medium sized (around 5KWh) battery pack, and a very high power forced-induction internal combustion engine. The electric subsystem is used to compensate for the narrow power band of the ICE by adding additional low-speed torque. It also usually provides power to all four wheels, improving handling and launch performance. Finally, it improves the regulatory status of such cars by at least nominally increasing the fuel economy. Once again, we find it beneficial to place base speed at a relatively low speed in order to maximize the launch torque delivered to the wheels (and reduce the weight of motor required to deliver that torque to the wheels); consequently, field weakening is needed to prevent the top speed of the car from being voltage-limited.

Pure electric vehicles: It is widely known that most EV's have a single-speed gearbox. This is entirely due to the power-speed profile of an IPM [2]; as the motor can reach peak power at very low speeds, a variable-speed transmission is not necessary to maximize power output across the entire operating range of the vehicle.

In fact, we can simulate the broad power band of an IPM with a surface PM machine and a continuously-variable transmission. It is usually not desirable to do so [3]; multi-speed transmissions incur additional complexity, weight, cost, and losses, usually negating the improved torque density of the surface PM motor. The only cars that use surface PM motors (Honda, Hyundai) are hybrids which are strongly derived from existing gas-only cars and already have manual transmissions.

Combat robots [4]: Spinner weapons are very similar to cars - both are inertial loads that have highly variable speed profiles. Interior PM machines have obvious mechanical benefits, as the rotors are much more robust. In addition, having a virtually unlimited top speed makes match-ups more consistent. Having moderate weapon speeds is usually beneficial, as it improves energy transfer and tooth engagement. However, in the vertical-on-vertical matchup (which is becoming much more common), the robot with the higher blade speed hits first. In this case, being able achieve very high speeds can greatly improve chances of victory.

And of course, higher-speed weapons hit harder if they do engage, so having the option to spin up to very high energies can be beneficial in certain situations.

Notes

[1] Technically, base speed also depends on stator current, so the correct terminology would be 'the base speed of the motor is 2000 rpm at 180A'.

[2] Induction machines (Tesla) and synchronous reluctance motors (no one yet) have similar characteristics, and trade off torque density for reduced cost.

[3] There are some designs which use a 2-speed transmission to further improve efficiency below base speed.

[4] No one has done this yet, but someone should!

## Saturday, July 28, 2018

### IPM's: an overview

The brushless motors we typically see on the mass market are "surface PM" machines. In this configuration, the permanent magnets (PM's) are glued to the surface of a steel rotor. Torque is generated by rotating the magnetic field in the stator electronically, which in effect continuously "pulls" the PM's on the rotor towards the coils on the stator.

In contrast, all automotive PM motors are "interior PM" machines. This means the magnets are buried inside a steel rotor. While this seems counter-intuitive at first (doing this moves the magnets further from the stator and makes the rotor heavier), putting the magnets inside a chunk of steel gives the motor several features which are highly beneficial for traction applications.

Greatly increased inductance: The surface PM motor has low inductance. This is because the PM's have a much lower permeability than steel, effectively putting a huge air gap in the flux path. In contrast, the interior PM machine places the rotor steel very close to the stator teeth; the magnetic air gap is only the size of the physical air gap, and this greatly increases the inductance, often by a factor of 10 over a similarly-sized surface PM machine.

Having high inductance is important, because for traction applications, the switching frequency is primarily determined by the allowable current ripple (excessive current ripple increases the resistive losses in the copper and conduction and switching losses in the inverter). Being able to reduce the switching frequency can drastically reduce inverter losses. Conversely, for some types of very low inductance and resistance motors (Emrax, Yasa), system efficiency is much lower than what the motor specifications alone would indicate, as Si IGBT inverters have a hard time efficiently driving these types of motor.

Position varying inductance: Why does this matter? Recall that inductance stores energy, and torque is the angle derivative of the co-energy of a system (or, roughly speaking, the system will try to settle to its lowest energy state). This means that by properly manipulating the stator currents, we can use this varying inductance to generate torque: the so-called reluctance torque. Reluctance torque is beneficial because it behaves very differently from the torque generated by the attraction of the magnets to the stator (the PM torque); it grows with both d and q-axis current, and doesn't necessarily generate additional back EMF.

We typically assume that the inductances vary sinusoidally; the typical model therefore has two inductances, $$L_d < L_q$$, the "d-axis" and "q-axis" inductances.

Field weakening: Field weakening uses the stator inductance to generate a voltage that counters the back EMF produced by the permanent magnets. This is typically done by injecting current on the d-axis (on a surface PM motor, $$I_d$$ is normally close to zero). Field weakening is typically presented as an atypical operating regime, a way to get a little extra speed out of your motor after you've run out of volts. This is because surface PM motors have very low inductance and relatively high flux linkage, necessitating a large amount of d-axis current to cancel out the PM flux. Furthermore, $$I_d$$ only serves to generate heat on surface PM motors, and produces no additional torque.

In contrast, IPM's have a much higher ratio of inductance to flux linkage, which means the d-axis current needed to cancel the PM flux is much lower. Furthermore, because of reluctance torque, the d-axis current generates some torque, so it is not entirely wasted. In fact, well-designed IPM's have virtually no top speed; the top speed is not limited by available voltage, but rather by rotor mechanical integrity and hysteresis losses.

Higher speed operation: The rotor iron has an obvious benefit: it mechanically constrains the PM's and prevents them from flying off at high speeds. Running the motor faster makes the motor better. Being able to run a motor twice as fast means it can make twice the power, so despite their slightly lower torque density, IPM's can have higher power density than their surface PM counterparts.

### High Speed VCR 2018

I'm a huge enthusiast of thin desktops. I have no idea why - normally such systems are used for HTPC duties or in very space constrained labs and offices, but my desk is not particularly small and I don't even own a TV.  The low-profile cases are about as small as cases get (they have a smaller interior volume and footprint than the cubes), and fitting everything into <85mm z-height makes for an interesting challenge.

Core Component Thoughts

Most HTPC-type systems are built around the "small" platform - currently, Z370 on the Intel side, X470 on the AMD side. These platforms offer low latencies, high clock speeds, and tons of integrated connectivity, but don't offer many cores compared to the state of the art. In contrast, the "high-end" desktop platforms are derived from server hardware - the boards have loads of PCIe lanes but very little integrated functionality, and the CPU's have many cores lashed together in weird and wonderful ways (rings, grids, clusters, and in the AMD case, multiple dies).

There are currently two possible routes for a USFF high core count system - the current-generation X299e-ITX/ac, or the now-discontinued X99e-ITX/ac. The X299 offers access to the latest platform features and CPU architecture, but as LGA2066 is not shared with any Xeons, the CPU's are quite expensive - the 10c part costs $899 and prices only go up from there. X99, in comparison, is kind of long in the tooth by now, but the CPU's are more accessible; an 18c 2.3/3.6 part used to be about$500 on the used market, and will likely be again once major datacenter upgrades flood eBay with used CPU's. With current pricing, X299 is certainly the correct choice; the 2699 V3 will perform similarly to a 14-core i9, costs about the same right now, and the i9 offers a full generation of platform and core improvements.

There is also no reason to go with anything under 12 cores. Ryzen will get you to 8 cores on a very power efficient platform (trust me, you are not overclocking anything on a computer this dense), and the 10-core i9 costs much more than any of the 8-core processors since Intel charges a "PCIe tax".

Since I had a 2699 V3 available from the $500 days, I went with a X99 build (I had also hoarded an X99e-ITX from when they were$120 on eBay; prices have since jumped up to \$200-300). The final selection was:
• Motherboard/CPU: ASRock X99e-ITX + E5-2699 V3 - really no other choices here.
• RAM: Crucial Ballistix Sport LT DDR4-2400: I really like the Ballistix Sport LT series; the gray heatspreaders are inoffensive and functional, and the DIMMS are pretty low profile - there are no useless protrusions on the heatspreaders to run into the CPU cooler.
• Storage: Inland Professional 256GB NVMe - these are just reference Phison PS5008-E8 + Toshiba BiCS drives. They are incredibly cheap and offer better-than-SATA performance. Being M.2 also means one less cable to route in a case that is incredibly cramped with wires. My usual choice would be a Samsung 970 PRO, but at 3.6 GHz you can't really feel the difference between a fast drive and a slow one, especially when you take into account the Windows scheduler adding extra latency by moving threads between the many cores.
• Graphics: ...I should really get a real GPU for this thing, but based on previous experiences, anything but the really big cards (Asus STRIX line, I'm looking at you) will fit.

Everything Else

Building these things is really an arts-and-crafts project, especially when you have as many computers as I do.  As such, picking the not-computer parts of the computer is much harder than selecting the parts that do the computing.

Case

My usual case for this type of nonsense is the Silverstone ML08, which is nicely priced and is as thin as possible (the minimum allowable clearance for an ATX case is 58mm). Unfortunately, the extra tight cooler clearance makes fastening a cooler to the board nearly impossible, since 2011/2066 heatsink mounting screws have to go in from the top. I was also interesting in trying the latest crop of Silverstone cases, which add an extra inch or so of clearance in order to fit an ATX power supply. All the 83mm-clearance Silverstones are based on the same chassis, just with different trims. I went with the RAVEN RVZ03, since I am a fan of RGB lighting.

Power Supply

The RVZ03 somewhat misleadingly supports ATX power supplies. While it is true that the mounting holes are for an ATX supply, most supplies flat-out don't fit; the case really requires a 140mm or shallower power supply to leave cable clearance. Furthermore, like the ML08, the RVZ03 uses an internal right angle IEC extender to place the power jack on the case somewhere reasonable. This caused a ton of problems - the CX550M I bought had a power jack to close to the left side of the power supply, which cased the extender to collide with the side of the case, and Seasonic Focus+ 550W had a power switch which collided with the molding on the right-angle connector, cause the switch to get stuck in the "off" position.

I eventually gave up and bought Silverstone's own 500W SFX-L supply. The power supply fit great, but as the X99e-ITX has its power connectors rotated 90 degrees from most ITX boards (the 24-pin is in the upper left corner), the stock 24-pin cable wasn't long enough. Thankfully, Silverstone makes a long cable set for this exact purpose; the kit is amazing for small builds since the 24-pin cable is only 550mm long, which is ~100mm shorter than usual.

Cooler

This whole project was made possible by an obscure-and-discontinued Cooler Master GeminII S heatsink. Low-profile LGA20xx coolers are hard to find - the reference socket backplate uses studs that are tightened from the top, meaning the cooler has to leave sufficient clearance to allow the studs to be tightened. My original plan was to use a Hydro H55 with a slim fan; measurements showed that the clearance would be sufficient. Unfortunately, packing the tubing into the case was pretty much impossible - it could be made to fit, but there was no way to gauge if excessive force was being applied to vertical components on the motherboard. Silverstone claims that a silm fan + slim radiator AIO will fit in this case, but even that seems doubtful...

The stock GeminII S doesn't quite fit - the 25mm fan is about 3mm too tall. I started out by mounting a 15mm fan from a GeminII M4, but that wasn't quite enough, so some more work was required...

Stuffing It All In

This was definitely the hardest computer I've ever assembled. The 58mm Silverstone cases are pretty easy to work on - the top and the bottom both come out, the GPU mounts from the back, and there is an access hole behind the socket to install the CPU cooler. In contrast, the 83mm cases only have one removable side, and the GPU is mounted on a plastic subframe that installs from the top; this makes cable routing far less pleasant. Without the 550mm long 24-pin this would probably have been impossible - I don't think another 100mm of cable would have physically fit in the case.

Performance Tuning

The 2699 v3 has a 80C temperature limit - once it hits 80C, it slowly drops out of turbo to stabilize temperatures. It's a graceful falloff - rather than dithering between 800MHz and 2.8GHz like some processors would, it decreases the multiplier a bin at a time until it achieves thermal equilibrium.

Initial performance was poor; the processor would hit 80C and drop to about 2.2GHz, which is below even the base speed of the 2699 v3. More concerningly, Intel's throttling algorithm seems to favor the core over the uncore - uncore speeds were dropping by as much as 50%, which was sure to affect performance in some applications.

Fortunately, upon further investigation it appeared I had plugged the CPU fan in the 'SYS_FAN' header on the board, which caused the CPU fan to get stuck at its lowest speed (SYS_FAN tracks the chipset temperature, not the CPU temperature). Swapping headers greatly improved performance; the CPU now stabilized at 2.5GHz, and the uncore throttling was gone.

But we can do better! Most 25mm fans have a few mm of superfluous plastic on top - by milling that plastic off I was able to get a 25mm thick Corsair fan to barely ft the base. Installing the thicker fan bumped clock speeds up another 200 MHz, and and dropping Vcore by 50 mV in XTU allowed the processor to maintain 2.8GHz steady state under full load.

## Wednesday, July 18, 2018

### LinuxCNC on Laptops

Most people say LinuxCNC can't be run on laptops. This is false; for low-end applications like those Chinese '3020' routers, software stepping via the parallel port on an old laptop works fine.

Some tweaking is required on almost all laptops - specifically, the system management interrupt (SMI) needs to be disabled. Fortunately, from a fresh install of LinuxCNC this is quite easy.

First, connect to the internet. Then, install the prerequisite packages:

sudo apt-get install libpci-dev vim

Next, grab the smictrl sources from Github. smictrl is a user-space tool to read and write the SMI status register.

git clone https://github.com/zultron/smictrl.git

Build the tool:

cd smictrl
make

Copy it:

sudo cp smictrl /usr/local/bin

Make it start at startup

sudo vim /etc/rc.local