I have one question about loop control as I attach two pictures.

There are two types of control; the single loop control and the multi loop control.

In the single-loop control there are two valves which should be controlled; the one is the heating valve, the other is humid valve.
In the multi-loop control there are three valves which should be controlled; the one is the heating valve, the other is the humid valve and the third is the cooling valve.

how can I control the valve in these each cases and what is the exact different between single loop control and multi loop control?

Thanks.

That all depends on your objective.

Single loop control usually means that you pair up inputs and outputs. Each output is controlled by exactly one input, usually using a feedback loop.

Multi-loop control means just that...you can have multiple inputs or multiple outputs controlled by some combination of loop controllers, or cascade the output of one loop to the input of another.

For instance it is very common with a 3-position control (heat, off, cool) to control both heating and cooling output valves (which are on-off valves, not analog controls) with a single temperature control loop. It is also not uncommon to cascade the output of the temperature control loop output into a relative humidity controller by utilizing knowledge of relative vs. absolute humidity to automatically bias the humidity controller and control humidity more tightly by removing the disturbances caused by the temperature control loop when the temperature control loop is affected by say a change in setpoints.

Another common cascaded arrangement is in many AC or DC drives where the speed, acceleration, and current may be 3 seperate cascaded loops. This allows each loop to be tuned to for instance restrict acceleration or current to prevent overshoot, wind-up, or jerk problems.