Feedback Control Fundamentals

Feedback control represents the foundation of automatic control systems in HVAC applications. By continuously measuring the controlled variable and comparing it to the desired setpoint, feedback controllers automatically compensate for disturbances, component variations, and changing operating conditions. This self-correcting mechanism enables precise environmental control without constant manual adjustment.

Closed-Loop Control Architecture

The closed-loop feedback control system consists of five essential components working in coordination. The reference input establishes the desired setpoint for the controlled variable. The controller compares the measured value to the setpoint and generates a control signal based on the error. The actuator converts this control signal into physical action, manipulating the process. The sensor measures the controlled variable and feeds this information back to the controller, completing the loop.

The fundamental distinction between open-loop and closed-loop control lies in the presence of measurement feedback. Open-loop control applies predetermined actions without measuring results, making it vulnerable to disturbances and parameter variations. A manual damper represents open-loop control, remaining at a fixed position regardless of actual temperature. Closed-loop feedback control continuously monitors outcomes and adjusts actions accordingly, automatically compensating for unmeasured disturbances.

Error Signal Generation

The control error forms the driving force for all feedback control action:

$$e(t) = r(t) - y(t)$$

Where $e(t)$ represents the instantaneous error, $r(t)$ is the setpoint reference, and $y(t)$ is the measured controlled variable. This error signal quantifies how far the system deviates from desired operation at each instant.

For a VAV box controlling zone temperature, if the setpoint is 72°F and the measured temperature is 75°F, the error equals -3°F. The negative error indicates the space is too warm, requiring cooling action. The controller processes this error according to its control algorithm to determine the appropriate damper position.

The sign convention for error affects controller action direction. Direct-acting controllers increase output as error increases, appropriate for heating applications where higher valve opening produces higher temperatures. Reverse-acting controllers decrease output as error increases, suitable for cooling applications where closing a valve increases temperature.

Disturbance Rejection

Feedback control’s primary advantage lies in automatic disturbance rejection. Disturbances represent unmeasured influences that affect the controlled variable. In HVAC systems, disturbances include solar heat gain, occupancy loads, infiltration, equipment heat generation, and outdoor temperature variations.

When a disturbance affects the controlled variable, it creates an error signal. The feedback controller responds to this error by adjusting the manipulated variable to counteract the disturbance’s effect. The controller does not need to know the disturbance source or magnitude; it simply responds to the resulting error.

Consider a conference room with a temperature control system. When occupants enter, their body heat represents a disturbance that increases room temperature. The feedback controller detects this temperature rise, recognizes the positive error, and opens the cooling valve to remove the additional heat load. The control system automatically compensates without requiring occupancy sensors or load calculations.

The speed and completeness of disturbance rejection depend on controller tuning and system dynamics. Aggressive controller gains provide rapid rejection but risk instability. Conservative gains ensure stability but allow larger temporary deviations. System time constants determine how quickly the controlled variable can physically respond to control actions.

Load Changes and Transient Response

Load changes represent step disturbances that test control system performance. When building loads shift due to weather changes, occupancy variations, or equipment cycling, the control system must maintain setpoint despite these variations.

The transient response following a load change reveals control quality. A well-tuned system quickly returns to setpoint with minimal overshoot. An under-damped system exhibits oscillations before settling. An over-damped system approaches setpoint slowly without oscillations. An unstable system shows growing oscillations.

Response characteristics depend on the interaction between controller parameters and process dynamics. Fast processes allow aggressive tuning, while slow processes with significant dead time require conservative approaches. The ratio of dead time to time constant determines the fundamental difficulty of controlling a process.

Measurement Feedback and Sensor Dynamics

Accurate measurement forms an essential requirement for effective feedback control. The sensor must detect changes in the controlled variable with sufficient accuracy, speed, and resolution. Sensor errors directly translate to control errors since the controller responds to measured values rather than true values.

Sensor dynamics introduce lag between actual process changes and measured values. A temperature sensor with a large thermal mass responds slowly to temperature changes, creating a delay in the feedback loop. This delay degrades control performance and can destabilize aggressive control tuning.

Sensor location critically affects control quality. Placing a temperature sensor in a location with poor air mixing produces measurements that do not represent average space conditions. The control system maintains the sensor’s local environment at setpoint while other areas deviate. Proper sensor placement ensures measured values accurately reflect the variable requiring control.

Measurement noise represents rapid random fluctuations superimposed on the true signal. Electrical interference, air turbulence, and sensor limitations contribute noise. While averaging can reduce noise impact, excessive averaging slows measurement response and degrades control performance.

Steady-State Error and Offset

Steady-state error quantifies the permanent deviation between setpoint and actual value after transients decay. Proportional-only control systems exhibit inherent steady-state error called offset. The controller requires a persistent error to maintain a non-zero output, preventing exact setpoint tracking.

The magnitude of steady-state error depends on controller gain and load magnitude. Higher gains reduce offset but increase oscillation tendency. The fundamental limitation arises because proportional action alone cannot distinguish between different steady-state operating points at the same error.

For a proportional-only heating system with gain $K_p$ controlling a room, if the load changes require an additional 20% valve opening to maintain setpoint, the controller must operate with a permanent error of $20% / K_p$. If $K_p = 2$ (%/°F), the offset equals 10°F, clearly unacceptable for comfort control.

Integral action eliminates steady-state error by accumulating error over time. The integral term continues increasing or decreasing until error reaches zero, enabling exact setpoint tracking. This explains why PI or PID control predominates in HVAC applications despite added complexity.

Reference Setpoint Changes

Setpoint changes represent commanded step inputs that test control system tracking capability. When an occupant adjusts a thermostat, the control system must drive the controlled variable to the new setpoint efficiently. The desired response minimizes rise time while avoiding excessive overshoot and settling time.

The optimal response to setpoint changes differs from optimal disturbance rejection. Disturbance rejection benefits from aggressive control action to minimize deviations. Setpoint tracking may prefer gradual ramps to avoid abrupt actuator movements and occupant discomfort from rapid environmental changes.

Some advanced controllers employ setpoint weighting or filtering to shape setpoint response independently from disturbance rejection. This allows optimization of both response types rather than accepting a compromise. In HVAC applications, gradual setpoint transitions improve comfort and reduce mechanical stress.

Control System Performance Metrics

Quantitative metrics evaluate feedback control performance objectively. Integral of absolute error (IAE) accumulates total deviation magnitude over time, providing a single number characterizing control quality. Integral of squared error (ISE) penalizes large deviations more heavily. Integral of time-weighted absolute error (ITAE) emphasizes eliminating persistent errors.

Rise time measures how quickly the controlled variable reaches a specified percentage of the final value, typically 90% or 95%. Settling time indicates when the response enters and remains within a tolerance band around the final value, often ±2% or ±5%. Peak overshoot quantifies maximum excursion beyond the final value as a percentage.

These metrics enable objective comparison of different controller tunings or control strategies. However, metrics optimized for one aspect may degrade others. Minimizing rise time typically increases overshoot. Eliminating overshoot increases settling time. Practical control design balances competing objectives based on application priorities.

Feedback Loop Limitations

Feedback control cannot compensate instantaneously for disturbances due to fundamental physical limitations. Dead time delays the observable effect of control actions, preventing the controller from knowing whether recent actions are appropriate until the dead time expires. During this period, the controller continues responding to outdated information.

Actuator rate limits restrict how quickly control actions can change. Slow valve actuators cannot instantly modify flow even if the controller commands rapid changes. The controlled variable continues deviating while the actuator moves toward the commanded position.

Sensor bandwidth limits the frequency of disturbances that feedback control can reject. Rapid fluctuations average out within the sensor’s response time, making them invisible to the controller. Only disturbances slower than the sensor’s bandwidth can be effectively rejected.

These limitations explain why feedback control alone cannot achieve perfect control. Advanced strategies like feedforward control and cascade control address specific limitations by adding measurement points or anticipatory actions. Understanding these fundamental constraints guides realistic expectations and appropriate control strategy selection for demanding applications.