Week 3

Question 1

What is a Signal?

Answer 1

A value that changes over time. There can be “input” and “output” signals

Question 2

What is a System?

Answer 2

A set of connected things which transforms a signal into another signal. Usually they take input signals and generate output signals.

Question 3

What is a State?

Answer 3

One or more variables (including output signals?)

x (t), xk

Question 4

What is a State Transition Law?

Answer 4

How state changes over time

Question 5

What is an Output?

Answer 5

The output of the system depends on the state

Question 6

What is Control Theory?

Answer 6

The branch of engineering which deals with the identification or modelling of systems and the design of methods to control their outputs.

Question 7

What is a Plant?

Answer 7

The given system we want to control

Question 8

What is a Setpoint?

Answer 8

The signal we want the systems output to be

Question 9

What is a Controller?

Answer 9

The system (sometimes just a function, i.e. no state) we design to control the plant

Question 10

What is an Error in relation to robotics?

Answer 10

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

Question 11

What is the Stability of a System?

Answer 11

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)

Question 12

What is Perturbation?

Answer 12

A signal, we cannot control, that affects the output of the plant

Question 13

Define Transient

Answer 13

The period of time from setting the setpoint until the system does what we actually requested (Nothing changes instantaniuosly)

Question 14

Define Steady State

Answer 14

Period of time we consider the system is behaving as we wanted (after settling time).

Question 15

Define Steady State

Answer 15

Period of time we consider the system is behaving as we wanted (after settling time).

Question 16

What are the characteristic of a Proportional Controller?

Answer 16

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)

Question 17

Summarise a Proportional Controller

Answer 17

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.

Question 18

What are the characteristics of a Proportional-Integral Controller?

Answer 18

Steady state reaches 100 (r = 100)

Slower than P controller

Perturbation disappears

Two numbers to find: 𝐾 and 𝑇_𝑖

Question 19

Summarise a Proportional-Integral Controller

Answer 19

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)

Question 20

What are the characteristics of a Proportional-Derivate Controller?

Answer 20

Speeds up the response (derivative predicts the future error)

Can stabilise unstable systems

Does not cancel perturbations

Phase lead controller used in reality

Question 21

Summarise a Proportional-Derivative Controller

Answer 21

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

Question 22

Summarise Microcontrollers

Answer 22

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

Question 23

What are the pros and cons of Sense-Plan-Act?

Answer 23

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.

Question 24

What are the pros and cons of Behavior-Based Control?

Answer 24

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).

Question 25

What are the pros and cons of Motor Schemas?

Answer 25

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.

Question 26

What are the pros and cons of Hybrid Architectures?

Answer 26

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.

Question 27

What are the characteristic of an Open Loop Controller?

Answer 27

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