Week 3 Flashcards
What is a Signal?
A value that changes over time. There can be “input” and “output” signals
What is a System?
A set of connected things which transforms a signal into another signal. Usually they take input signals and generate output signals.
What is a State?
One or more variables (including output signals?)
x (t), xk
What is a State Transition Law?
How state changes over time
What is an Output?
The output of the system depends on the state
What is Control Theory?
The branch of engineering which deals with the identification or modelling of systems and the design of methods to control their outputs.
What is a Plant?
The given system we want to control
What is a Setpoint?
The signal we want the systems output to be
What is a Controller?
The system (sometimes just a function, i.e. no state) we design to control the plant
What is an Error in relation to robotics?
The difference between the setpoint and the output of the plant i.e. what we want the plant to do vs. what it is really doing
What is the Stability of a System?
Has many different definitions. BIBO stability (Bounded Input Bounded Output) is widely used: If the input of the system stays within some bounds the output will also be bounded (i.e. nothing blows up)
What is Perturbation?
A signal, we cannot control, that affects the output of the plant
Define Transient
The period of time from setting the setpoint until the system does what we actually requested (Nothing changes instantaniuosly)
Define Steady State
Period of time we consider the system is behaving as we wanted (after settling time).
Define Steady State
Period of time we consider the system is behaving as we wanted (after settling time).
What are the characteristic of a Proportional Controller?
Steady state: doesn’t reach 100 (r = 100)
Much faster than Open Loop
Better behaviour if perturbed (5×)
Negative K will blow up the system (positive feedback)
Summarise a Proportional Controller
It is simple and works most of the times.
One parameter to select (good techniques for linear systems)
The plant makes a big difference on the result (integrator?, unstable?, response time?).
The plant makes a big difference on the result (oscillations?, overshooting?, steady state error?, perturbations?).
Rules of thumb (true for “simple” systems):
Bigger Ks increase overshooting and oscillations, reduce steady state error and response time.
Warning! Account for physical limits.
What are the characteristics of a Proportional-Integral Controller?
Steady state reaches 100 (r = 100)
Slower than P controller
Perturbation disappears
Two numbers to find: 𝐾 and 𝑇_𝑖
Summarise a Proportional-Integral Controller
Corrects small errors in the steady state
Two parameters to tune, 𝐾 and 𝑇_𝑖 (good techniques for linear systems)
Can turn stable plants to unstable in closed-loop
Can slow down or speed up (for the right plant and 𝑇_𝑖) the response time
Can overshoot (worse transient)
Rules of Thumb:
𝑇_𝑖≈ “characteristic time” of the plant, good and easy choice
Dangerous with saturation (physical limits of the plant)
What are the characteristics of a Proportional-Derivate Controller?
Speeds up the response (derivative predicts the future error)
Can stabilise unstable systems
Does not cancel perturbations
Phase lead controller used in reality
Summarise a Proportional-Derivative Controller
It does not exist but it can be approximated.
Speeds up the response (better transient)
Can turn unstable systems into closed-loop stable
Sensitive to sensor noise (worse steady state)
Rules of Thumb:
𝑇_𝑑 ≈ “characteristic time” of the plant, good and easy choice
Physical limits, when changing setpoint 𝑢 spikes
Summarise Microcontrollers
Include RAM and ROM memory
Interrupt controller for external events
Timer/Counter to measure time
Pulse Width Modulation (PWM) outputs to control motors
Analog and digital I/O ports to connect sensors
Serial interface to communicate with PC
Used for embedded systems and real-time systems
What are the pros and cons of Sense-Plan-Act?
Pros:
Easy to design, understand and analyse from a human viewpoint.
Formalisable through logic.
New AI results can be incorporated.
Cons:
Slow reaction time. No real time.
Monolitic, difficult to include new sensors, actuators. . .
Hard to debug.
Problems to solve: Sensor fusion, frame problem.
What are the pros and cons of Behavior-Based Control?
Pros:
Fast reaction time, works in real world/real time.
Don’t need to plan the whole system beforehand (incremental).
Easy to debug. Add new layer once the lower one works.
Distributed control, no central decission maker.
Cons:
Limited habilities without explicit representations.
Need to plan the system beforehand (wiring).
What are the pros and cons of Motor Schemas?
Pros:
It works in biology.
Fast reaction time, works in real world.
Exploits parallelism.
Modular, each schema can be added independently.
Simplicity of central decission maker.
Cons:
Centralised behaviour/schema sequencing.
Motor fusion problem.
What are the pros and cons of Hybrid Architectures?
Pros:
Fast reaction time at the lowest level.
Easy to design (incremental) and understand.
Simple user interface.
Cons:
Centralised planner.
Sensor fusion design and motor fusion sequencing.
Conditions to switch modules.
What are the characteristic of an Open Loop Controller?
Controller is the inverse of the plant
Many times is just impossible
Sensitive to changes in the environment
Simple, but bad strategy
Still, sometimes is used
