Beyond normal means ...
There are many reasons for getting dizzy, some of them are related to vestibular damage, or damage to your hearing nerves or ear canals.
I can't tell you how many different types of bodily ailments can affect your balance, as I have been researching everything and anything that affect some restoration of my balance while I continue to practice Aikido.
That is not to say that drills, vestibular practice methods to retrain your brain, or correction of diet and exercise won't increase your rolling time or decrease your dizzy spells, but if all else fails, sitting out rolls, or modification will have to suffice.
Ninety percent of learning what works for Aikido is not necessary to include rolls, or pins / manipulations at full speed.
You can find a number of things to research in Vestibular links, or look up Meniere's disease which includes a number of separate causes for uncontrolled dizzyness. If you cannot locate the exact problem, then modification of practice should be considered. It may as humbling as anything you will do in your life to excuse yourself from practice as you regain your balance as you tell the room to stop spinning, but then I have found it more irritating to either be too dizzy not to drive at all, or be forced to watch practice rather than participate at any level.
There are too many factors ranging from diet to physical damage to the body that can cause this uncontrolled dizzyness ... check out some links, find information, and try to locate your particular restrictions.
If I had started Aikido in my early twenties instead of my mid forties, I would have said that you could overcome that dizzyness with just minor training or will power, but deterioration has taught me differently.
There are many drills to help you get balance, but there are also many other factors that will need to be addressed. Take some time to research, it will give you some things to look for, and maybe increase the quality of your life ... like doing Aikido.