Arduino PID Controller for BAR30 Pressure Sensor Guide

This section establishes the theoretical foundation of control systems and introduces proportional control. A PID controller, developed by Nicholas Minorsky in 1922, is a control structure used in closed-loop systems that compares input and output to generate control signals. Control theory deals with dynamic systems, and the 'plant' refers to the system being controlled (originating from Industrial Revolution terminology). Open-loop systems lack feedback and cannot compensate for disturbances, while closed-loop systems measure output and provide feedback. The proportional controller multiplies error by a constant (KP) to produce output, but this creates steady-state error where the system never exactly reaches the set point because zero error produces zero output. The integral controller addresses this by accumulating total error over time, mathematically corresponding to finding the area under the error curve.

The PID controller is the most widely used closed-loop control system, combining Proportional (P), Integral (I), and Derivative (D) components. P generates output proportional to current error, I sums error over time to eliminate steady-state error, and D predicts future error based on rate of change. These three components work together to provide stable control with zero steady-state error, fast response, and no oscillations. The mathematical expression includes gains Kp, Ki, and Kd for each component respectively.

This section covers the foundational concepts of closed-loop control systems and PID (Proportional-Integral-Derivative) regulation. A closed-loop system consists of four key components: setpoint (desired value), comparator (error calculation), regulator (control logic), and actuator (executive element). The PID controller combines three distinct actions: proportional action provides immediate correction proportional to current error, integral action eliminates steady-state error through time accumulation, and derivative action anticipates future errors by responding to rate-of-change, thereby improving system stability. These principles form the theoretical basis for industrial automation and process control applications.

The closed loop transfer function is T(s) = G(s) / (1 + G(s)H(s)), where the denominator is the characteristic equation. Poles determine stability: left half-plane poles indicate stable systems. PID controllers (Proportional, Integral, Derivative) are widely used because they are simple, robust, and effective. The proportional term responds to error magnitude, the integral term eliminates steady state error, and the derivative term anticipates future errors. Proportional controllers decrease rise time but cause steady state error and amplify noise. Integral controllers eliminate steady state error but can cause actuator windup. Derivative controllers reduce overshoot but amplify high frequency noise. Root locus plots show how poles move as gain varies.

A PID controller is a closed-loop feedback system consisting of three components: Proportional (P) responds immediately to current error, Integral (I) accumulates past errors to ensure complete correction, and Derivative (D) predicts future errors based on current rate of change. Using cruise control as an example: P applies immediate gas adjustment when speed drops, I remembers any remaining deficit to apply gradual correction, and D anticipates hills or declines to prevent overshooting. The combination creates stable, responsive control without excessive oscillation.

Connect I²C pressure sensor to Arduino: SCL to pin A5, SDA to pin A4, VDD to 5V, GND to ground. Two pins are NC (not connected). The sensor measures pressure from -100 to +300 kPa (approximately -1 to +3 bar). Use Wire library for I²C communication instead of bit-banging.

I²C (Inter-Integrated Circuit) is a serial communication protocol using two lines: SDA (Serial Data) and SCL (Serial Clock). Multiple devices can share the same bus by using unique addresses. The processor communicates with sensors like the IMU and barometer over this bus, allowing multiple sensors to be connected with minimal wiring.

The I2C (Inter-Integrated Circuit) protocol, developed by Philips in the 1980s, is a synchronous two-wire communication interface (SCL for clock, SDA for data) that enables a single master device to communicate with multiple slave devices within an electronic system. The protocol operates at frequencies typically between 100 kHz and 400 kHz, with some devices supporting up to 5 MHz. Communication begins with a Start condition (SCL high, SDA falling edge) and ends with a Stop condition (SCL high, SDA rising edge). Data transfer involves sending a 7-bit slave address followed by a read/write bit, with slaves responding via acknowledgment (ACK) or non-acknowledgment (NACK) signals. For writing, the master sends 8-bit data to a specific register; for reading, the master initiates a Restart condition, sends the same address with a read bit, and the slave transmits 8-bit data back. External pull-up resistors are required due to the open-drain configuration of the bus lines.

I2C (Inter-Integrated Circuit) is a widely-used synchronous serial communication protocol developed by Philips in 1982 that enables short-distance data transfer between devices using only two wires: Serial Data (SDA) and Serial Clock (SCL). The protocol operates in a master-slave architecture where the master initiates communication by sending a start condition, followed by the 7-bit slave address and a read/write bit, then exchanging data bytes with individual acknowledgments from the receiver, and terminating with a stop condition. Key technical aspects include the open-drain configuration with pull-up resistors (typically 1-10kΩ) that determine bus speed, and support for multiple operating modes ranging from Standard Mode (100 kbps) to Ultra-Fast Mode (5 Mbps).

This comprehensive section covers I²C communication principles and device interaction. Topics include: (1) the two-wire I²C protocol using clock (SCL) and data (SDA) lines; (2) device addressing with the MS5611 found at address 0xEE; (3) understanding the five basic commands: reset, program memory read, D1 conversion (temperature), D2 conversion (pressure), and ADC read; (4) scanning I²C buses to identify connected devices; (5) configuring the Bus Pirate for I²C mode at appropriate speeds; (6) enabling power and pull-up resistors for reliable communication; and (7) establishing a foundation for manual sensor interrogation.

Hydrostatic pressure increases linearly with depth according to the formula P = ρgh, where ρ is fluid density, g is gravitational acceleration, and h is depth; by analyzing pressure-time graphs and knowing the sensor's velocity, one can determine the depth profile and calculate fluid density from pressure readings at specific depths.

There is a direct relationship between water column height and pressure: every 10 meters of water column produces approximately 1 bar of pressure. This relationship allows conversion between pressure measurements and liquid level. The bar is a common unit for measuring pressure, though other units like PSI or kg/cm² are also used. Understanding this relationship is fundamental for interpreting hydrostatic sensor readings.

This segment covers pressure-depth relationships (P = P₀ + ρgh), barometer readings and atmospheric pressure, and hydraulic press force calculations. The instructor demonstrates how to calculate pressure at different depths in fluids, how to interpret barometer readings to determine atmospheric pressure, and how to calculate forces in hydraulic systems using the area ratio principle (F₁/A₁ = F₂/A₂).

Pressure in a fluid increases with depth according to P = P₀ + ρgh, where P₀ is surface pressure, ρ is fluid density, g is gravitational acceleration, and h is depth. The slope of a pressure-depth graph equals ρg. To convert between units, divide Pascals by 10⁵ to get bars. The intercept on the pressure axis represents the surface pressure.

The hydrostatic pressure formula P = ρgh calculates the pressure exerted by a fluid at a given depth, where ρ is fluid density, g is gravitational acceleration, and h is depth; this explains why pressure increases with depth and is independent of container shape or volume, allowing calculation of maximum depth for waterproof devices like watches rated at 10 BAR (1000 kPa) which can withstand approximately 102 meters of water depth.