Control Systems Overview

Sources

1. RealPars, “PID Controller Explained” - 2021-12-20
2. MATLAB, “Everything You Need to Know About Control Theory” - 2022-10-27

Terminologies and Basic Concepts

• State observers or point estimators are systems that give an estimate of the internal state of a given real system. One use of it is in stabilizing a system through state feedback.
• Filters in control system can improve a system’s performance and stability by removing unwanted noise or disturbance from either input or output signals.
• Error is the difference between the setpoint and the process variable
• Degree of Freedom are the number of variables that can be controlled in the process

Controllers

• Controllers ensure that the process is as close as possible to the desired output regardless of disruptions. It does this by comparing the transmitter process variable (or PV signal) and the setpoint
• An on-off controller turns on when the measured is below the desired output and turns off when the measured is above the desired output.
• Proportional-integral-derivative (PID) controller determines the appropriate amount and speed for correction.
  • Proportional block creates an output signal proportional to the error signal’s magnitude
  • Integral block creates an output signal proportional to the error signal’s magnitude and duration
  • Derivative block creates an output signal proportional to the error signal’s rate of change
  • Controller tuning adjusts the P, I, and D depending on the specific process requirements

Control Theory

Goal: To control a system.

Parts:

1. Reference $r$
2. Feedback/Feedforward controller
3. Control inputs $u$ - intentional inputs to control the system.
4. Disturbances $d$ - unintentional inputs that affect the system despite being unwanted.
5. System
6. States - the system’s states change as the system dynamics interact with the external inputs
   • We can measure it with a sensor, though it will introduce noise; therefore, returning an inaccurate measurement of the state to the controller
   • Challenges:
     1. Reduce measurement noise
     2. Observe the state in a way that we estimate it by manipulating the measurements
7. State estimation
   • depends on the amount and type of noise, the type of state

Types of Controllers:

1. Feedforward or open loop: It takes in a reference $r$ and generates a control input/signal without needing to measure the system state
   • Can be very vulnerable to disturbances/uncertainty
   • Changes how we operate a system
2. Feedback or closed loop: Uses the reference and the current state of the system to determine the appropriate control inputs
   • In a situation where disturbances or errors affect the system, the controller can adjust the control inputs accordingly (self-correcting).
   • Changes the dynamics of a system; hence, it is more dangerous.
     • It makes it so that the future state of the system is determined by the current state of the system.
   • Types of feedback controllers.
     1. Linear, such as PID and full state feedback, that assume that the system has a linear nature.
     2. Non-linear, such as on-off, sliding mode, and gain scheduling.
     3. Robust, such as mu synthesis and rejection control, that focuses on satisfying requirements even when with uncertainties.
     4. Adaptive, such as extremum-seeking and model-reference adaptive, that adapt to the system over time
     5. Optimal, such as linear quadratic regulator, which focuses on minimizing the total cost and balances effort and performance
     6. Predictive, such as model predictive control, which stores a model in the controller that simulates the future state and determines the best control input to make the future state correspond to the simulated model.
     7. Intelligent, such as reinforcement learning and fuzzy control, that determines the best controller based on data

Two ways of modeling:

1. Using first principles
2. Using system identification to fit a model to a given data

Steps:

1. Planning the right reference for the feedback controller to produce the right controller input
2. Determine if feedback or feedforward
3. Produce a mathematical model of the system
4. Estimate the state if feedback
5. Simulation, analysis and test to evaluate the performance of the designed system