Apologies for my less-than-cordial response earlier.
I believe what you have said is the common opinion of non controls engineer of controls engineering. In fact, this is so common that I have a slides specifically for this that (nonexhaustively) lists the challenges in control design:
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So regardless of my feelings, your comment needs to be responded to technically for the benefit of the wider audience. So why is control design very involved? First of all, Laplace and Fourier transforms are tools for linear, continuous-time, and classical control. This is introductory control theory taught to undergrads. If undergrad control theory is all that you know you will make very very bad design choices - I know this because I thought I knew controls then I learned a lot more. I will try to give examples of how Laplace fails for the issues that I list.
- Model uncertainty
All or most control design depends on models. Famous saying, "all models are wrong, some are useful". So the controller that you design on your software is not guaranteed to work in real-world. Uncertainty quantification is a field in itself and NOT a trivial task.
- Stabilization
This is the stabilization of unstable systems. Unstable systems impose fundamental limitations on the performance that can be achieved by a control system. Stabilization is related to uncertainty since if you knew the system perfectly, you would not need feedback control. However, since there is always uncertainty, you require feedback stabilization. A simple example that makes this point:
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- Noise
Noise affects all kinds of control systems and is unavoidable. There can be white noise, biases, sinusoids, each having a different effect on a control system. The control system must be designed and tested to be resilient to these effects.
- Accessibility
Before you embark on control design, you need to analyze whether or not it is even possible to achieve your control goals. You need to think about accessibility, which is can you make your system do something that you want. It may not always be possible, for which you will need to change your sensors and actuators.
- Nonlinearity
Linear systems are a fiction taught in undergrad. All real systems are nonlinear to varying degrees. If Laplace is all that you know, you are oblivious to the reality of nonlinearities. The most common nonlinearity present in all control systems is actuator saturation. Laplace won't help you with this. An undergrad will design a control system totally oblivious to this.
- Time dependence
Real systems often vary with time - wear and tear, changes in mass/configuration. Your control system needs to account for these things.
- NMP zeros
This is a linear effect but a very bad one at that. Some systems have "initial wrong-way behaviour". This can be attributed to nonminimum-phase (NMP) zeros. If a system has NMP zeros there are fundamental limitations on your control performance. Physical example is trying to balance a pole on your finger. Imagine that you are balancing a pole and I ask you to move left. Record yourself while doing this and you'll see that you actually move slightly right first, which causes a tilt in the pole to the left and then you move left. This is in effect a NMP zero in the dynamics of the pole. As you can imagine all rockets have NMP zeros like this. How do you deal with NMP zeros? What limitations do they impose? A control designer needs to understand this.
A very dangerous idea that my undergrad professor taught us was simply cancel system dynamics with controller dynamics. Well if you attempt to cancel a NMP zero with a controller pole you get a hidden instability where your simulation looks stable for a while but your actuator demand is going to infinity, which is obviously never going to be achievable.
- Delays
All control systems have delays. Some are large, some small, most unavoidable. Unmodeled delays can very easily cause destabilization. Linear analysis (Laplace) leads you to irrational transfer functions for delays. Good luck analyzing that with Laplace.
- Sensors
Sensors have bandwidth (the frequencies that they can sense), static and dynamic response (how the sensor converts measured quantity to voltage and in what time/with what dynamics), sensitivity, quantization effects, tonnes more. Almost all sensors are nonlinear - so again good luck using Laplace to model your sensors. Most undergrads will simply ignore the presence of a sensor and assume things like speed are measured perfectly. Here's a good article on the complexities of sensors alone:
The author explains sensor specifications which quantify the ability of sensor to provide measurements of physical variables. Sensor manufacturer typically provide information about sensor specifications in the form of a specification sheet. The concepts described will help one interpret the...
ieeexplore.ieee.org
The placement of sensors is also very important and dictates what the system dynamics look like. The placement of a sensor can lead to NMP zeros.
- Actuators
Actuators have many of the same issues as sensors but are even harder to design and manufacture. These are again almost always nonlinear and lead to all kinds of static and dynamic effects. Maybe Laplace will help you with very crude approximations but that's it. Actuator saturation is the biggest thing to worry about - an aileron can't move further than maybe 30 degrees, what if your controller asks for 50????
The placement of actuators is also very important and dictates what the system dynamics look like. Sensor and actuator placement is a science on its own.
- Loop coupling
Systems have many control systems that are often interacting. These interactions are almost always nonlinear and cannot be analyzed with Laplace. There are adhoc techniques that people use like the one below to be able to use linear techniques but these are after all just approximations that can break down pretty badly in some cases.
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- Computing limitations
What good is your controller if the computer on your aircraft cannot implement it in real time? A control designer strives to find the simplest controller that will meet the specifications. This is more of an art than a science.
- Diagnosability
When your control system does something unexpected, how do you troubleshoot it? The more complex it is, the more difficult it is to debug. Roughly speaking the following picture shows what is true:
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Do you design a simple controller that you can diagnose but give poor performance or do you design a complex controller that you cannot troubleshoot if it fails?
- Digital effects
Almost all controllers are digital these days. Laplace gets thrown out of the window if all you want to do is digital design. All Laplace will let you do is continuous-time design with discretization APPROXIMATIONS. What you need are z-transforms so you can actually do digital design. There are aliasing effects, sampling effects, quantization effects, sampling zeros (which can be NMP). Your typical undergrad is oblivious of the existence of these effects and will kill you if you let him or her design your control system.
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- Constraints
Almost always there are physical constraints like how much you can move your actuator or how many g's you can pull. Your controller needs to respect these constraints while achieving its design goals. Laplace tells you nothing about constraints or what to do about them. For example, a missile autopilot has very strict constraints on fin deflection and maximum lateral g's. With Laplace, you're maybe going to do trial and error and hope for the best. Your controller asks for 50 g when your missile can only do 40g, the controller fails because what it thinks should happen, didn't happen and your missile is an expensive shurlee.
So in conclusion, control systems design is a very involved process that requires the designer to keep in mind a plethora of real-world effects/issues. I have barely scratched the surface in this post. There are many many more effects that Laplace won't help you with.
Thinking that you know control design because you learned linear, continuous-time, classical theory is extremely dangerous and I suggest that you use this post to learn about each aspect of "problems". Control systems are a matter of life and death and cannot be trivialized.
My undergraduate controls professor was someone who thought he knew controls design because he knew linear, continuous-time, classical theory, and therefore he inculcated this dangerous belief into us. That's how common this belief is. I was quite horrified how dangerous this was when I actually learned controls. This guy is a very senior person in SUPARCO these days. He would say stupid stupid and dangerous things like just cancel system dynamics with controller dynamics.
EDIT: An absolutely amazing and famous lecture that is must watch on this topic:
