Electronics Guide

Block Diagram Representation

Control systems are typically represented using block diagrams that show signal flow through the system. The essential elements include:

• Reference input (setpoint): The desired value of the controlled variable
• Summing junction: Compares reference to feedback, producing the error signal
• Controller: Processes the error and generates control output
• Plant (process): The system being controlled
• Sensor: Measures actual output and provides feedback signal
• Feedback path: Returns measured output to the summing junction

The error signal equals the difference between reference and feedback: Error = Reference - Feedback. In negative feedback systems, this error drives the controller to reduce the difference, forcing actual output toward the desired value.

Transfer Functions and Loop Gain

The behavior of a control system is characterized by transfer functions that relate output to input in the frequency domain. For a system with forward path gain G and feedback path gain H, the closed-loop transfer function is:

Closed-loop gain = G / (1 + GH)

The product GH is called the loop gain and determines many system characteristics. When loop gain is large (GH >> 1), the closed-loop gain approaches 1/H, becoming nearly independent of the forward path gain G. This explains why feedback systems are less sensitive to component variations than open-loop systems.

The loop gain also determines stability. If the loop gain reaches -1 at any frequency (magnitude of 1 with 180 degrees phase shift), the system becomes unstable and oscillates. Stability analysis examines how closely the loop gain approaches this critical value.

Stability Margins

Stability margins quantify how far a system is from instability:

• Gain margin: The additional gain that would cause instability at the frequency where phase shift is 180 degrees. Typical designs target 6 dB or more.
• Phase margin: The additional phase shift that would cause instability at the frequency where gain is unity. Typical designs target 45 degrees or more.

Systems with adequate stability margins respond smoothly to disturbances without excessive ringing or oscillation. Marginal stability causes prolonged ringing, while inadequate margins lead to outright oscillation.

Transient Response Characteristics

The transient response describes how a system responds to changes in setpoint or disturbances:

• Rise time: Time for output to rise from 10% to 90% of final value
• Settling time: Time for output to remain within a specified band (typically 2% or 5%) of final value
• Overshoot: Maximum excursion beyond the final value, expressed as percentage
• Steady-state error: Remaining error after transients have settled

These parameters involve tradeoffs. Faster response generally increases overshoot, while reducing overshoot typically slows response. Controller tuning balances these competing requirements based on application needs.

Proportional Control

Proportional control produces an output directly proportional to the error signal:

Output = Kp x Error

where Kp is the proportional gain. Higher proportional gain produces faster response but can cause instability if set too high. Proportional-only control always results in steady-state error because some error must exist to produce the control output needed to counteract disturbances.

An op-amp proportional controller uses a simple inverting or non-inverting amplifier configuration. The gain is set by the feedback resistor ratio:

• Inverting: Kp = -Rf / Rin
• Non-inverting: Kp = 1 + Rf / Rin

Integral Control

Integral control produces output proportional to the accumulated error over time:

Output = Ki x integral of Error dt

The integrator continues to increase its output as long as any error exists, eventually driving steady-state error to zero. This is the primary advantage of integral action: it eliminates offset errors that proportional control cannot remove.

An op-amp integrator uses a capacitor in the feedback path:

Ki = 1 / (R x C)

The time constant RC determines the integration rate. Faster integration (smaller RC) provides quicker correction of steady-state error but can destabilize the system by adding phase lag.

Integral windup is a practical concern: if the error persists while the actuator is saturated, the integrator continues accumulating, causing delayed response when conditions change. Anti-windup techniques limit the integrator output or freeze integration when saturation is detected.

Derivative Control

Derivative control produces output proportional to the rate of change of error:

Output = Kd x d(Error)/dt

Derivative action anticipates future error by responding to how fast the error is changing. When error is increasing rapidly, derivative action provides early corrective action, reducing overshoot and improving stability.

An ideal op-amp differentiator uses a capacitor at the input:

Kd = R x C

However, ideal differentiators amplify high-frequency noise. Practical implementations limit the derivative bandwidth by adding a resistor in series with the input capacitor, creating a filtered derivative:

Derivative with filter: Kd x s / (1 + s x Tf)

where Tf is the filter time constant, typically set to Kd/10 for reasonable noise rejection while maintaining derivative effectiveness.

Combined PID Implementation

A complete PID controller combines all three terms:

Output = Kp x Error + Ki x integral(Error) + Kd x d(Error)/dt

Analog PID controllers can use separate op-amp stages for each term, summed at the output, or integrated designs that combine functions. The parallel form uses three distinct circuits whose outputs are summed. The series form cascades proportional-integral and proportional-derivative stages.

A practical analog PID circuit using parallel architecture includes:

• Input buffer to prevent loading the error signal source
• Proportional stage with adjustable gain
• Integrator with adjustable time constant and anti-windup limiting
• Filtered differentiator with adjustable gain and bandwidth
• Summing amplifier to combine the three outputs
• Output buffer or driver stage as needed for the actuator

PID Tuning Methods

Proper tuning of PID parameters is essential for good performance. Several methods exist:

• Ziegler-Nichols method: Increase proportional gain until continuous oscillation, then calculate PID parameters from the critical gain and oscillation period
• Cohen-Coon method: Based on process reaction curve parameters
• Trial and error: Start with proportional-only, add integral to eliminate offset, add derivative to reduce overshoot
• Software tools: Modern control systems often include auto-tuning features

General tuning guidelines:

• Start with low gains and increase gradually
• Tune proportional gain first for acceptable response speed
• Add integral action slowly to eliminate steady-state error
• Add derivative action conservatively if overshoot is excessive
• Iterate to optimize the balance between speed, accuracy, and stability

DC Motor Speed Control

DC motors offer straightforward speed control because speed is approximately proportional to applied voltage. A basic speed control system includes:

• Speed sensor: Tachometer generator or encoder providing voltage or pulses proportional to speed
• Reference input: Potentiometer or voltage source setting desired speed
• Error amplifier: Compares reference to feedback
• Driver stage: Provides power to drive the motor, often using PWM

A simple proportional controller works well for many applications but exhibits speed droop under load. Adding integral action eliminates this error, maintaining constant speed despite load variations.

For bidirectional control, an H-bridge driver allows the motor to run in either direction. The control signal determines both speed (via PWM duty cycle) and direction (via bridge switching pattern).

Speed Sensing Methods

Accurate speed measurement is essential for precision control:

• DC tachometer: Generates voltage proportional to speed; simple but requires brush maintenance
• Optical encoder: Produces digital pulses; count frequency for speed or count pulses for position
• Hall effect sensors: Detect magnetic field variations; commonly integrated into brushless motors
• Back-EMF sensing: Measures motor voltage during off-time to estimate speed without additional sensors

Encoder-based speed measurement uses frequency-to-voltage conversion or period measurement. High resolution encoders (thousands of pulses per revolution) provide accurate speed measurement even at low speeds.

PWM Motor Drive

Pulse-width modulation (PWM) provides efficient motor drive by switching the motor supply rapidly on and off. The motor's inductance smooths the current, so the motor responds to the average voltage determined by the duty cycle:

Average voltage = Supply voltage x Duty cycle

PWM frequencies typically range from 1 kHz to 20 kHz. Lower frequencies may cause audible noise; higher frequencies increase switching losses. The PWM frequency should be high enough that current ripple is acceptably small but low enough for efficient switching.

Key PWM controller features include:

• Voltage-controlled oscillator or fixed frequency with variable duty cycle
• Dead-time insertion to prevent H-bridge shoot-through
• Current limiting to protect motor and driver
• Soft-start to limit inrush current

Current Loop Control

High-performance motor control often uses a cascaded control structure with an inner current loop and outer speed loop. The current loop provides several advantages:

• Faster response because current can change more quickly than speed
• Built-in current limiting for protection
• Improved linearity by controlling torque (proportional to current) rather than voltage
• Better disturbance rejection

The inner current loop uses a current sensor (shunt resistor or Hall effect sensor) and typically proportional-integral control. The outer speed loop commands the current loop setpoint based on speed error.

Temperature Sensing

Various sensors measure temperature for control systems:

• Thermocouples: Wide range, rugged, self-powered but require cold junction compensation and have low output
• RTDs: Excellent accuracy and stability, linear response, require excitation current
• Thermistors: High sensitivity, fast response, nonlinear but can be linearized
• Semiconductor sensors: Linear, easy interface, limited temperature range
• Infrared sensors: Non-contact measurement, good for moving or inaccessible objects

Sensor placement significantly affects control performance. The sensor should measure the temperature of interest, not be influenced by heating element radiation, and respond quickly enough for effective control.

Heating Element Drive

Heating elements are typically controlled by varying applied power:

• Proportional time base: Heater cycles on and off with variable duty cycle over a fixed period (typically seconds to minutes)
• Phase-angle control: SCR or triac controls the portion of each AC cycle delivered to the heater
• Zero-crossing control: SCR or triac switches at zero crossings, varying the number of complete cycles delivered
• PWM for DC heaters: Direct duty cycle control of DC heating elements

Zero-crossing control generates less electrical noise than phase-angle control but provides coarser resolution. Time-proportioning control works well for processes with large thermal mass where cycling temperature variations are smoothed.

PID Temperature Control

Temperature systems typically have large time constants and significant dead time, making them challenging to control. PID tuning for temperature control often emphasizes:

• Moderate proportional gain to avoid overshoot during heating
• Significant integral action to eliminate offset
• Careful derivative action to anticipate temperature changes without amplifying noise

Many temperature controllers include auto-tuning features that automatically determine PID parameters by applying test perturbations and analyzing the response.

For systems requiring both heating and cooling, the controller must manage two actuators. Approaches include split-range control (one output for heating, another for cooling) or a single bipolar output driving both systems.

On-Off Temperature Control

Simple on-off (bang-bang) control remains common for applications where precision is not critical. The heater turns fully on when temperature falls below setpoint and fully off when temperature exceeds setpoint. Hysteresis (dead band) prevents rapid cycling:

Turn on when: Temperature < Setpoint - Hysteresis/2

Turn off when: Temperature > Setpoint + Hysteresis/2

On-off control is simple and reliable but produces temperature oscillation around the setpoint. The oscillation amplitude depends on system thermal mass, heater power, and hysteresis setting.

Light Sensing

Various sensors measure light intensity:

• Photodiodes: Fast response, linear over wide range, require amplification
• Phototransistors: Built-in gain simplifies circuits but slower response and less linear
• Photoresistors (LDRs): Simple interface, slow response, spectral response differs from human eye
• Photomultipliers: Extreme sensitivity for low-light applications
• Light-to-frequency converters: Digital output proportional to light intensity

Sensor spectral response should match the application. Photopic response filters match human eye sensitivity, while specific wavelength filters may be needed for scientific or industrial applications.

Lamp Dimming Control

Different lamp types require different control approaches:

• Incandescent lamps: Phase-angle control or PWM; respond slowly due to thermal mass
• LED arrays: PWM control; fast response enables high-frequency dimming
• Fluorescent lamps: Electronic ballast with dimming control; complex interface requirements
• HID lamps: Generally not suitable for continuous dimming control

LED dimming offers the fastest response and widest dimming range. PWM frequencies above 200 Hz eliminate visible flicker, while frequencies above 1 kHz eliminate issues with video recording.

Constant Light Output Systems

Maintaining constant light output compensates for lamp aging and supply variations:

• Light sensor measures actual illumination
• Controller compares to setpoint
• Drive circuit adjusts lamp power to maintain constant output
• As lamp ages and output decreases, drive power automatically increases

This approach extends useful lamp life by compensating for gradual degradation and ensures consistent performance over time.

Automatic Exposure Control

Camera exposure control represents a specialized light regulation application. The system measures scene brightness and adjusts aperture, shutter speed, or sensor sensitivity to achieve proper exposure.

Key considerations include:

• Scene brightness measurement (center-weighted, matrix, or spot metering)
• Target exposure level based on scene analysis
• Dynamic range limitations of the imaging sensor
• Response speed requirements for moving subjects

Basic ALC Architecture

A typical ALC system includes:

• Variable gain amplifier (VGA): Amplifier whose gain responds to a control voltage
• Level detector: Measures output signal amplitude
• Error amplifier: Compares detected level to reference
• Control voltage generator: Processes error to drive the VGA

The feedback loop adjusts VGA gain to maintain constant output level: when output rises above the setpoint, the control voltage reduces gain; when output falls below setpoint, gain increases.

Variable Gain Amplifier Techniques

Several approaches implement voltage-controlled gain:

• FET-based VGAs: Use JFET or MOSFET as voltage-controlled resistor in amplifier feedback
• Multiplier-based VGAs: Analog multiplier with signal and control inputs
• Current-controlled amplifiers: OTAs or transimpedance amplifiers with variable bias
• PIN diode attenuators: For RF applications, PIN diode resistance varies with DC bias
• Digital potentiometers: Stepped gain adjustment with digital control

The VGA should maintain good linearity across its gain range and have gain that is predictable function of control voltage, typically logarithmic (dB per volt).

Attack and Release Time Constants

ALC dynamics are characterized by attack and release times:

• Attack time: How quickly the system responds to increasing signal level
• Release time: How quickly the system responds to decreasing signal level

Fast attack prevents output overload when signal suddenly increases. Slower release prevents gain pumping on transient signals. The optimal balance depends on the application and signal characteristics.

Asymmetric time constants use separate attack and release paths, often with a diode steering arrangement. The detector may use peak detection for fast attack or RMS detection for average level control.

Audio Compressor and Limiter Circuits

Audio dynamics processors are specialized ALC circuits:

• Compressor: Reduces dynamic range by attenuating signals above a threshold; ratio determines how much gain reduction occurs
• Limiter: Extreme compression (high ratio) that prevents output from exceeding a set level
• Expander: Opposite of compressor; reduces gain for signals below threshold
• Noise gate: Extreme expansion that mutes signals below threshold

Key parameters include threshold, ratio, attack time, release time, and makeup gain. These circuits use various detection methods (peak, RMS, or program-dependent) and control characteristics (hard knee or soft knee) to achieve desired audio effects.

Servo System Components

A typical servo system includes:

• Command input: Desired position, often from potentiometer, encoder, or digital interface
• Position feedback: Sensor measuring actual position (potentiometer, encoder, resolver)
• Error amplifier: Compares command to feedback
• Servo amplifier: Provides power to drive the motor
• Motor: Converts electrical power to mechanical motion
• Mechanical load: The object being positioned

The system operates to minimize position error: any difference between commanded and actual position produces a motor drive signal that moves the load toward the commanded position.

Position Feedback Devices

Accurate position feedback is essential for servo performance:

• Potentiometer: Simple, absolute position, limited resolution and life
• Optical encoder: High resolution, incremental or absolute types, requires index for absolute position
• Resolver: Robust, absolute position, analog output requires conversion
• LVDT: Linear position sensing, very rugged and accurate
• Hall effect sensors: Used with magnetic scales for linear or rotary position

Incremental encoders count pulses to track position changes; a home or index position establishes the absolute reference. Absolute encoders provide unique codes for each position, maintaining knowledge of position even after power loss.

Analog Servo Circuits

A basic analog position servo uses potentiometers for both command and feedback. The circuit compares the two potentiometer voltages, amplifies the difference, and drives the motor:

• When command exceeds feedback, motor drives in one direction
• When feedback exceeds command, motor drives in opposite direction
• When command equals feedback, motor stops

Adding derivative feedback improves stability by providing damping. Tachometer feedback adds velocity information, helping to prevent overshoot and oscillation.

RC Hobby Servos

RC servos are self-contained position servos widely used in robotics and hobby applications. They include motor, gearbox, position potentiometer, and control electronics in a compact package.

Standard RC servo control uses pulse-width encoding:

• Pulse width varies from 1 ms (full left) to 2 ms (full right)
• 1.5 ms pulse commands center position
• Pulses repeat at approximately 50 Hz (20 ms period)

The servo's internal circuit converts pulse width to voltage, compares to the position potentiometer, and drives the motor accordingly. No external feedback processing is required.

Cascaded Control Architecture

High-performance position control typically uses cascaded loops:

• Position loop (outer): Compares commanded to actual position, outputs velocity command
• Velocity loop (middle): Compares commanded to actual velocity, outputs torque/current command
• Current loop (inner): Controls motor current for desired torque

Each inner loop is faster than the outer loop it serves. The current loop responds in microseconds, velocity loop in milliseconds, and position loop in tens of milliseconds. This hierarchy enables each loop to be tuned independently and provides natural limiting at each level.

Motion Profiling

Rather than commanding step changes in position, motion profiles generate smooth trajectories:

• Trapezoidal profile: Constant acceleration, constant velocity, constant deceleration phases
• S-curve profile: Limits jerk (rate of change of acceleration) for smoother motion
• Polynomial profiles: Customized profiles matching specific requirements

Motion profiling reduces mechanical stress, improves tracking accuracy, and enables coordinated multi-axis motion where multiple axes must arrive at their destinations simultaneously.

Following Error and Tracking

During motion, the actual position typically lags behind the commanded position. This following error depends on:

• Velocity: higher speed produces larger following error
• Acceleration: changing velocity adds to following error
• Controller gains: higher gains reduce following error but may compromise stability
• System friction and loading: disturbances that the controller must overcome

Feedforward control can dramatically reduce following error by commanding the expected control signal needed for the planned motion, supplementing feedback correction. Velocity feedforward compensates for motion-induced following error; acceleration feedforward compensates for inertial loads.

Position Control Tuning

Position loop tuning follows the general principle of tuning inner loops before outer loops:

1. Tune current loop for fast, stable response (typically done by drive manufacturer)
2. Tune velocity loop for desired bandwidth and damping
3. Tune position loop for acceptable following error and settling
4. Add feedforward if following error during motion is excessive
5. Verify stability with expected disturbances and load variations

Why Adaptive Control

Fixed-gain controllers are designed for specific operating conditions. When conditions change, performance may degrade:

• Load variations: Motor controllers may need different tuning for light and heavy loads
• Operating point changes: Nonlinear systems behave differently at different operating points
• Component aging: System dynamics change as components wear or drift
• Environmental changes: Temperature, humidity, or other factors affect system behavior

Adaptive control addresses these challenges by continuously or periodically adjusting controller parameters to maintain desired performance.

Gain Scheduling

Gain scheduling is the simplest form of adaptation, using pre-programmed parameter sets for different operating conditions:

• Identify key operating variables that affect optimal tuning
• Tune controller for multiple operating conditions
• Store parameter sets and select based on measured conditions
• Smoothly interpolate between parameter sets if needed

Gain scheduling requires prior knowledge of how parameters should vary but is simple to implement and predictable in behavior. It works well when operating conditions can be measured and their effects on optimal tuning are understood.

Model Reference Adaptive Control

Model Reference Adaptive Control (MRAC) adjusts controller parameters to make the actual system response match that of a reference model that represents desired behavior:

• Reference model defines ideal response to commands
• Comparison of actual and model response reveals performance error
• Adaptation algorithm adjusts controller parameters to reduce error
• Over time, actual response converges to match model response

MRAC systems automatically compensate for plant variations without requiring explicit knowledge of how the plant has changed.

Self-Tuning Regulators

Self-tuning regulators combine system identification with controller design:

• System identification algorithms continuously estimate plant parameters from input-output data
• Controller design algorithms calculate optimal parameters for the estimated plant
• The process repeats, tracking plant changes over time

This approach separates identification from control, allowing independent selection of identification and control algorithms. Care must be taken to ensure identifiability (excitation sufficient to estimate parameters) and stability during adaptation.

Practical Adaptation Considerations

Implementing adaptive control requires attention to several practical issues:

• Excitation requirements: Adaptation requires input variations to identify system behavior; some systems need explicit test signals
• Adaptation rate: Must be slow enough to filter noise but fast enough to track actual changes
• Parameter constraints: Limit adapted parameters to prevent instability from identification errors
• Switching and initialization: Handle transitions between operating modes carefully
• Verification: Adaptive systems are harder to verify than fixed controllers; extensive testing is essential

Circuit Construction

Reliable control circuit construction requires attention to:

• Power supply decoupling: Place bypass capacitors near each IC; use bulk capacitance at power entry points
• Ground routing: Separate analog signal grounds from power grounds; use star topology or ground planes
• Signal integrity: Shield sensitive signals, use twisted pairs for long runs, avoid routing signals near switching circuits
• Thermal management: Consider heat from power stages; keep precision circuits away from heat sources

Stability Verification

Before deployment, verify control system stability:

• Check stability across the full operating range
• Test with expected disturbances and load variations
• Verify stability margins with measurement or simulation
• Test behavior with sensor failures or disconnection
• Verify safe behavior during power-up and power-down

Safety Considerations

Control systems must be designed with safety in mind:

• Fail-safe design: System should enter safe state if control fails
• Current and voltage limiting: Protect against runaway conditions
• Watchdog supervision: Independent monitoring for processor-based controllers
• Emergency stops: Hardware-level shutdown that cannot be defeated by software
• Isolation: Proper isolation between control circuits and hazardous voltages

Testing and Commissioning

Systematic testing ensures reliable operation:

• Test individual components before assembling complete system
• Verify sensor calibration and feedback polarity
• Start with low gains and verify stability before increasing
• Test transient response with step inputs
• Verify disturbance rejection under realistic conditions
• Document controller parameters and test results