Control and Robotics

Modern Control, Speech Processing & Robotics Notes

Beginner-Friendly Notes on Modern Control Topics

1. Control of Robots Through Speech Signals

1.1 Introduction

Speech-controlled robots combine speech processing, artificial intelligence, and control systems to allow robots to respond to human voice commands.

1.2 Key Components

• Speech Signal Processing: Noise reduction and feature extraction.
• Automatic Speech Recognition (ASR): Converts speech to text.
• Language Understanding: Interprets text into commands.
• Robot Control System: Executes motion using PID, LQR, MPC, etc.

1.3 Challenges

• Noise and variability in speech
• Real-time processing
• Safety during robot-human interaction

1.4 Applications

• Assistive robots
• Industrial automation
• Service robots

2. Autonomous Vehicles (AVs)

2.1 Introduction

Autonomous vehicles use sensors, perception algorithms, trajectory planning, and control systems to operate without human input.

2.2 Architecture

1. Perception: Cameras, LiDAR, RADAR.
2. Localization: GPS and SLAM.
3. Decision & Planning: Behavior and path planning.
4. Control: Steering, throttle, braking using PID, MPC, etc.

2.3 Challenges

• Uncertain environments
• Weather effects
• Human driver interaction
• Safety and regulations

2.4 Applications

• Self-driving cars
• Delivery robots
• Autonomous public transport

3. Control for Differential Games

3.1 Introduction

Differential games study control problems involving two or more players with conflicting objectives, influencing the same dynamic system.

3.2 Basic Form

dot{x} = f(x, u, v)

3.3 Value Function

V(x,t) = inf_u sup_v J(u, v)

3.4 Hamilton–Jacobi–Isaacs (HJI) Equation

∂V/∂t + H(x, ∇V) = 0

The HJI equation describes optimal behavior in adversarial dynamic systems.

3.5 Applications

• Pursuit–evasion games
• Collision avoidance
• Multi-agent autonomous driving
• Security and defense

4. Control of Structures

4.1 Introduction

Structural control aims to reduce vibrations and improve stability in buildings, bridges, towers, and aerospace structures.

4.2 Types of Control

• Passive Control: TMDs, base isolators.
• Active Control: Uses actuators and sensors.
• Semi-active Control: MR dampers and variable devices.

4.3 Control Methods

• PID
• LQR
• H-infinity control
• MPC

4.4 Applications

• Earthquake-resistant buildings
• Wind-resistant tall structures
• Aerospace vibration control

5. Summary Table

Topic	What It Studies	Key Tools	Applications
Speech-Controlled Robots	Robots responding to voice commands	ASR, NLP, PID, MPC	Service robots, healthcare
Autonomous Vehicles	Self-driving navigation & safety	Perception, MPC, Trajectory Planning	Cars, drones, delivery systems
Differential Games	Control with competing players	HJI equations, value functions	Defense, multi-agent control
Structural Control	Vibration suppression	LQR, H∞, dampers	Buildings, bridges, aircraft

Formant Control Coding (FCC) in Speech Synthesis

Formant Control Coding (FCC) is a method used in speech synthesis and speech signal processing to manipulate and control the formants of human speech. Formants are the resonant frequencies of the vocal tract that are responsible for the distinct sound quality of vowels and other speech sounds. In a speech synthesis system, controlling these formants is crucial for producing more natural-sounding synthetic speech.

What are Formants?

Formants are the key frequency bands in the vocal spectrum that shape the sound of speech. These are created by the resonance of the vocal tract when sound is produced by the vocal cords. The first two or three formants (F1, F2, and sometimes F3) are particularly important for vowel identification:

• F1 (First Formant): Corresponds to openness of the vocal tract.
• F2 (Second Formant): Front-back spectrum dimension.
• F3 (Third Formant): Helps distinguish specific consonants and vowels.

In synthetic speech, formants are often modeled and synthesized artificially in order to replicate the speech characteristics of a human voice.

What is Formant Control?

In speech synthesis systems, formant control involves manipulating these formants (primarily F1, F2, and F3) to change the quality, tone, and intelligibility of synthetic speech.

Formant Control Coding (FCC) is a specialized technique for encoding, controlling, and modifying these formants for different purposes, such as improving speech quality, mimicking certain voices, or adjusting speech to different acoustic environments.

How Formant Control Coding Works

1. Formant Analysis

LPC and other spectral tools estimate human formants.

2. Formant Encoding

Formants are encoded efficiently for synthesis.

3. Formant Synthesis

Formants are used with a vocal tract model to generate speech.

4. Control Mechanism

• Pitch control via formant shifts.
• Voice quality changes via spectral transformation.

5. Naturalness Adjustment

FCC allows fine tuning of voice timbre, identity, emotion, etc.

Applications of Formant Control Coding

• TTS Systems
• Speech Synthesis in Robotics
• Voice Transformation & Mimicry
• Assistive Technology

Advantages of FCC

• Improved naturalness
• Flexibility in voice shaping
• Better voice quality
• Efficient encoding

Example

• Text input: “Hello, how are you?”
• Formants extracted then encoded.
• Formants adjusted to produce gender/age changes.

Key Technologies Related to FCC

• LPC
• Harmonic Models
• Articulatory Synthesis

Conclusion

FCC improves naturalness, flexibility, and intelligibility of synthetic speech using resonant frequency manipulation.

PID, LQR, and MPC in Robotic Control

Robotic systems use controllers to track trajectories and ensure stable behavior. Here we compare PID, LQR, and MPC.

1. PID Control

PID uses Proportional, Integral and Derivative actions:

• P reacts to current error
• I corrects accumulated error
• D predicts future error

PID Equation

u(t) = Kp * e(t) + Ki * ∫ e(t') dt' + Kd * de(t)/dt

Advantages

• Simple
• Effective in many cases

Disadvantages

• Tuning required
• Poor for nonlinear systems

2. LQR Control

dot{x}(t) = A * x(t) + B * u(t)

Cost function:

J = ∫ (xᵀQx + uᵀRu) dt

Pros

• Optimal
• Works well with noise

Cons

• Requires linear model
• Needs accurate parameters

3. MPC Control

min Σ (x - x_desired)ᵀQ(x - x_desired) + uᵀRu

Subject to:

x(k+1) = A x(k) + B u(k)

Advantages

• Handles constraints
• Works with nonlinear systems

Disadvantages

• High computation
• Requires accurate model

Comparison Table

Feature	PID	LQR	MPC
Control Type	Feedback	Optimal	Predictive
Constraints	No	No	Yes
Nonlinearity	Poor	Poor	Good

Conclusion

PID is simple but limited; LQR is optimal for linear systems; MPC is the most advanced but computationally heavy.

Further Reading

1.