I am looking for a technical term for the level of precision and clarity in the ability to control a system. For example, when configuring your smart phone, is it clear and intuitive how to configure it - does the control system closely parallel the actual system, or is it far more complicated? Can you access all parts of the underlying system or are certain parts blocked for no functional reason? The word I am looking for I think would have the flavor of the words bijective, orthogonal (those were my rejected attempts), or more simply clear and complete.
Usability is commonly used in software and web site design.
The word you are looking for is Intuitive.
As per google's definition-
(chiefly of computer software) easy to use and understand.
While designing a GUI or software it is important to make it intuitive so that the user needs minimum guidance in figuring out the usage flow.
When the inner workings of computer systems are not visible to the end user, the system as a whole is referred to as a black box.
You might also consider related terms, such as the degree of opacity of the system. An opaque system would have many fewer user-configurable controls than a transparent system.
It's worth noting that, with technical systems, "clear and complete" are often exact opposites. For example, the company Apple has been praised for increasing user accessibility to technology ("clear") but does not offer its typical end users as much configuration or control over the set up of its systems ("complete"). The more that the developer abstracts the inner workings of the system, the less "complete" or total the control over the inner workings has become. But since the inner workings of most technical systems is beyond the capability of the end user anyway, we gladly trade away that level of completeness for ease of use.
Take a simple calculator, as you might find on a desk in the 1980s. I have minimal control over this system. I can push buttons to display numbers, and I can perform only those calculations that the buttons allow. The processor inside that system might be more capable, but as the end user I don't have that degree of control. The "control system" (to user your term) is the grid of buttons. The "underlying system" would be the processor. In this case, the abstraction is done for good reason (arguably).
You could ask "How granular is control of the system via this interface?"
Although non-tecnical, a nuanced or responsive control system is desirable. Colloquial use of "tight" suggesting no tolerance of lack of response at any point.
The term affordance was popularized by Donald Norman in his book The Design of Everyday Things, and is well-understood among software usability professionals. This definition is from usabilityfirst.com:
A button, by being slightly raised above an otherwise flat surface, suggests the idea of pushing it. A lever, by being an appropriate size for grasping, suggests pulling it. A blinking red light and buzzer suggests a problem and demands attention. A chair, by its size, its curvature, its balance, and its position, suggests sitting on it.
An affordance is a desirable property of a user interface – software which naturally leads people to take the correct steps to accomplish their goals.
A technical term used to describe an accurate and precise control system is PID Control. PID refers to a type of feedback loop, which was originally based on analog electronic circuits, but has evolved to include digital computers and micro-controllers that use software algorithms. This type of feedback-based control system is called a PID controller, or a PID loop. The letters PID stand for proportional–integral–derivative. PID is a control-loop feedback technology that was originally used in industrial control systems and factory robots, but newer applications include automobile collision avoidance systems, aircraft fly-by-wire systems, and interactive home appliances, such as robot vacuum cleaners and lawn mowers. A PID controller continuously calculates an error value based on the difference between a desired setpoint and a measured real-world variable and then makes the necessary corrections for precise control of a process or mechanical action, based on human input. I'm not sure if this is what you had in mind, but without PID control, there would be no ability for people to precisely control any complex system in today's world.