AME Unit 11 Q3

Proportional band (PB) is a term used in control systems to define the range of process variable error over which the controller output changes from minimum to maximum. It’s essentially the range of error within which the controller takes action.

Key Points:

• Expressed as a percentage: Proportional band is typically expressed as a percentage of the input span.
• Inversely related to gain: A wider proportional band corresponds to a lower gain, while a narrower proportional band corresponds to a higher gain.
• Impact on control: A wider PB means the controller is less sensitive to changes in the process variable, while a narrower PB means it’s more sensitive.

Example:

If a controller has a proportional band of 20%, it means that the controller output will change from minimum to maximum as the process variable error varies by 20% of the input span.

In essence, the proportional band determines how aggressively the controller responds to changes in the process variable.

Integral action is a control mode that accumulates the error between the desired setpoint and the measured process variable over time. This accumulated error is then used to adjust the control output.  

1. Integral (Reset) Control | Closed-loop Control Systems | Textbook

2. Empirical Process Control: Part 2 | AIChE

How it works:

• The controller continuously calculates the error between the setpoint and the process variable.   1. Proportional–integral–derivative controller – Wikipedia en.wikipedia.org
• This error is integrated over time, meaning it’s added up continuously.   1. Integral Action and PI Control – Control Guru controlguru.com
• The result of this integration is used to adjust the control output.   1. Integral (Reset) Control | Closed-loop Control Systems | Textbook control.com

Purpose:

• Eliminate steady-state error: The primary purpose of integral action is to eliminate the steady-state error, which is the difference between the desired setpoint and the actual process variable when the system has settled.
• Improve system performance: By reducing or eliminating steady-state error, integral action can improve the overall performance of a control system.

Important Considerations:

• Overshoot: Excessive integral action can lead to overshoot, where the process variable exceeds the setpoint before settling.
• Oscillations: Improper tuning of the integral term can cause the system to oscillate around the setpoint.
• Integral windup: If the control output saturates (reaches its maximum or minimum value), the integral term can continue to accumulate error, leading to a large overshoot when the output becomes unsaturated.

In summary, integral action is a valuable tool for improving control system performance, but it must be tuned carefully to avoid negative effects.

Derivative action is a control mode that responds to the rate of change of the error between the setpoint and the process variable. In simpler terms, it anticipates future errors based on the current rate of change.  

1. Derivative (Rate) Control | Closed-loop Control Systems | Textbook

2. What is PID control algorithm? | 5 Answers from Research papers – Typeset.io

How it works:

• The controller calculates the rate of change of the error.   1. Proportional–integral–derivative controller – Wikipedia en.wikipedia.org
• This rate of change is multiplied by a derivative gain to produce a derivative output.   1. Proportional–integral–derivative controller – Wikipedia en.wikipedia.org
• The derivative output is added to the control signal.   1. Proportional–integral–derivative controller – Wikipedia en.wikipedia.org

Purpose:

• Improve system stability: Derivative action helps to dampen oscillations and improve system stability by anticipating changes in the process variable.   1. Understanding Derivative in PID Control www.controleng.com
• Reduce overshoot: By predicting the future behavior of the system, derivative action can help to reduce overshoot.   1. Understanding Derivative in PID Control www.controleng.com

Important Considerations:

• Sensitivity to noise: Derivative action can be sensitive to noise in the process variable, as it amplifies rapid changes.   1. The PID Controller & Theory Explained – NI – National Instruments www.ni.com
• Tuning: Proper tuning of the derivative gain is crucial to avoid instability and performance degradation.

In summary, derivative action is a valuable tool for improving control system performance, but it must be used carefully to avoid negative effects.

PID tuning can be a complex process, but there are some simplified methods that can provide a good starting point. One common approach is the Ziegler-Nichols method. However, it’s important to note that this method often provides a starting point, and further adjustments might be necessary to achieve optimal performance.

Ziegler-Nichols Method

This method involves two steps:

Step 1: Determine Ultimate Gain (Ku) and Ultimate Period (Pu)

• Set the integral and derivative terms to zero (P-only control).
• Gradually increase the proportional gain until the system starts to oscillate continuously. This gain is called the ultimate gain (Ku).
• The time for one complete oscillation is the ultimate period (Pu).

Step 2: Calculate Initial PID Gains

• Using the following formulas, calculate the initial values for the PID controller:
  • Proportional gain (Kp) = 0.6 * Ku
  • Integral gain (Ki) = 1.2 * Ku / Pu
  • Derivative gain (Kd) = 0.075 * Ku * Pu

Step 3: Fine Tuning

• The initial PID values obtained from the Ziegler-Nichols method often provide a good starting point, but they might not be optimal for your specific system.
• Gradually adjust the PID gains based on the system’s response.
• Consider using advanced tuning methods or software tools for more precise tuning.

Important Considerations:

• Safety: Always prioritize safety when tuning a PID controller. Start with conservative values and gradually increase them.
• System Dynamics: The Ziegler-Nichols method assumes a first-order system with a time delay. It might not be suitable for all systems.
• Iterative Process: Tuning a PID controller is often an iterative process. Be prepared to make adjustments based on the system’s behavior.

Remember: This is a simplified approach. For complex systems, more advanced tuning methods or software tools might be necessary.

there are other methods for tuning PID controllers beyond the Ziegler-Nichols method. Here are a few:  

1. Comparison Between Three Tuning Methods of PID Control for High Precision Positioning Stage – ResearchGate

Classical Methods:

• Cohen-Coon Method: Similar to Ziegler-Nichols but uses a different set of tuning equations, often providing more conservative results.
• Process Reaction Curve Method: Based on the process response to a step change in the input. It involves analyzing the resulting curve to determine controller parameters.   1. 9.3: PID Tuning via Classical Methods – Engineering LibreTexts eng.libretexts.org

Advanced Methods:

• Relay Feedback Method: An automated method that involves introducing a relay element into the control loop to induce oscillations. The frequency and amplitude of these oscillations can be used to calculate PID parameters.   1. A Review of Relay Auto-tuning Methods for the Tuning of PID-type Controllers warwick.ac.uk
• Optimal Tuning: Involves using mathematical optimization techniques to find the best PID parameters based on a specific performance index (e.g., minimizing overshoot, settling time).
• Model-Based Tuning: Requires a mathematical model of the process. The PID parameters are calculated based on the model’s characteristics.   1. 3 Ways to Build a Model | Understanding PID Control, Part 5 – MathWorks www.mathworks.com
• Auto-Tuning: Some controllers have built-in auto-tuning features that automatically determine PID parameters based on process behavior.   1. PID Control tuning – Novus Blog – blog.novus.com.br

Iterative Tuning:

• Manual Tuning: This involves adjusting the PID parameters based on trial and error, observing the system’s response, and making adjustments accordingly. While time-consuming, it can provide valuable insights into the system’s behavior.   1. Mastering PID Tuning: The Comprehensive Guide – Wevolver www.wevolver.com

It’s important to note that the best tuning method depends on the specific application, process characteristics, and desired performance objectives. Often, a combination of methods or iterative adjustments is required to achieve optimal results.

The Cohen-Coon method is a classical tuning method for PID controllers that provides an alternative to the Ziegler-Nichols method. It offers improved performance, especially when dealing with systems with a significant dead time.  

1. Cohen-Coon Autotuning Method – NI – National Instruments

2. PID tuning methods – INCATools

Key Differences from Ziegler-Nichols:

• Requires more information: While Ziegler-Nichols uses only the ultimate gain and period, Cohen-Coon requires additional process parameters: process gain, time constant, and dead time.   1. Cohen-Coon Tuning Rules – Control Notes – OptiControls blog.opticontrols.com
• Better performance: Cohen-Coon often provides better control performance, especially for systems with larger dead times.   1. Cohen-Coon Autotuning Method – NI – National Instruments www.ni.com

Steps Involved:

1. Determine process parameters:
   • Process gain (K): The ratio of the change in output to the change in input.
   • Time constant (T): A measure of how quickly the process responds to a change in input.   1. Time constant – Wikipedia en.wikipedia.org
   • Dead time (Td): The time delay between a change in input and the start of the output response.
2. Calculate PID parameters:
   • Using the following formulas, calculate the initial values for the PID controller:
     • Proportional gain (Kp) = K * (1.2 * T + 0.6 * Td) / T
     • Integral gain (Ki) = K * 0.6 / T
     • Derivative gain (Kd) = K * Td / 8

Advantages:

• Often provides better performance than Ziegler-Nichols for systems with significant dead time.   1. 9.3: PID Tuning via Classical Methods – Engineering LibreTexts eng.libretexts.org
• Relatively simple to implement.

Limitations:

• Requires more process information than Ziegler-Nichols.   1. PID tuning methods – INCATools www.incatools.com
• May not be as accurate as advanced tuning methods for complex systems.

Like the Ziegler-Nichols method, Cohen-Coon provides a starting point for tuning. Further adjustments may be necessary based on the specific system and desired performance.

The Process Reaction Curve (PRC) method is a practical approach for tuning PID controllers. It involves subjecting a process to a step change in input and analyzing the resulting output response.  

1. 9.3: PID Tuning via Classical Methods – Engineering LibreTexts

Steps Involved:

1. Introduce a Step Change: Apply a step change to the process input (e.g., setpoint or manipulated variable).   1. 9.3: PID Tuning via Classical Methods – Engineering LibreTexts eng.libretexts.org
2. Record the Response: Record the process output as it responds to the step change.   1. Typical process reaction curve | Download Scientific Diagram – ResearchGate www.researchgate.net
3. Identify Process Parameters: From the recorded data, determine the following parameters:
   • Dead time (Td): The time delay between the input change and the start of the output response.   1. 9.3: PID Tuning via Classical Methods – Engineering LibreTexts eng.libretexts.org
   • Time constant (T): A measure of how quickly the process responds to a change in input.   1. Time constant – Wikipedia en.wikipedia.org
   • Process gain (K): The ratio of the change in output to the change in input.
4. Calculate PID Parameters: Using various tuning correlations (like those proposed by Ziegler-Nichols or Cohen-Coon), calculate the PID controller parameters based on the determined process parameters.

Advantages:

• Relatively simple to implement.
• Provides insights into process dynamics.
• Can be used for a variety of processes.

Limitations:

• Requires careful data collection and analysis.
• Accuracy depends on the quality of the process model.
• May not be suitable for highly nonlinear or complex processes.

Essentially, the PRC method provides a systematic way to extract information about a process from its response to a step change and use that information to tune a PID controller.

While there isn’t a definitive “most common” PID controller tuning method specifically for superyachts, the Ziegler-Nichols method is often a starting point.

This is due to its simplicity and the fact that it doesn’t require a detailed process model. However, given the complexity and importance of systems on superyachts (e.g., stabilization, propulsion, climate control), more advanced methods are increasingly being adopted.

Factors influencing the choice of tuning method:

• System complexity: For simpler systems, Ziegler-Nichols might suffice. For complex systems with multiple interacting variables, advanced methods like model-based tuning or optimization techniques are preferred.
• Safety criticality: In safety-critical systems (e.g., propulsion, stabilization), robust tuning methods and extensive testing are essential.
• Performance requirements: The desired level of performance (e.g., overshoot, settling time) will influence the choice of tuning method.
• Available resources: Some methods require specialized equipment or software, which might not be available or cost-effective.

Trend towards advanced methods:

Given the increasing complexity of superyachts and the demand for higher performance and safety, there’s a growing trend towards using more advanced PID tuning methods. These include:

• Model-based tuning: This method leverages detailed models of the system to optimize PID parameters.
• Auto-tuning: Some controllers have built-in auto-tuning features that can automatically adjust PID parameters based on system behavior.
• Optimization techniques: Advanced algorithms can be used to find optimal PID parameters based on specific performance criteria.

Ultimately, the best tuning method for a superyacht system depends on a variety of factors and often involves a combination of different approaches.

Model-based tuning is a PID controller tuning method that leverages a mathematical model of the process to determine optimal controller parameters. This approach offers a more systematic and potentially more accurate method compared to empirical tuning methods like Ziegler-Nichols or Cohen-Coon.  

1. PID tuning methods – INCATools

Key Steps:

1. Process Modeling: Develop a mathematical model that accurately represents the dynamic behavior of the process. Common models include first-order plus dead time (FOPDT) models, transfer functions, or state-space representations.
2. Model Validation: Verify the accuracy of the developed model through experimental data or simulation.
3. Controller Design: Use the process model to design the PID controller. This often involves solving optimization problems to find the optimal PID parameters based on desired performance criteria (e.g., minimizing overshoot, settling time, or steady-state error).   1. PID Controller Design and model-based control tuning article – BIN95.com bin95.com
4. Simulation and Refinement: Simulate the closed-loop system with the designed PID controller to evaluate performance. Iterate on the model and controller parameters as needed.
5. Implementation and Testing: Implement the tuned PID controller on the real system and fine-tune parameters based on actual performance.

Advantages of Model-Based Tuning:

• Improved performance: Often leads to better control performance compared to empirical methods.
• Predictability: Allows for predicting system behavior before implementation.
• Handles complex systems: Can be applied to more complex processes with multiple inputs and outputs.

Challenges:

• Model accuracy: The accuracy of the model is crucial for successful tuning.
• Computational complexity: Developing and analyzing complex models can be computationally intensive.
• Model uncertainty: Real-world processes often exhibit uncertainties, which can affect the accuracy of the model-based tuning.

Common Techniques:

• Internal Model Control (IMC): Based on the concept of inverting the process model to design the controller.   1. Full article: Design of internal model control-proportional integral derivative controller with improved filter for disturbance rejection – Taylor & Francis Online www.tandfonline.com
• Optimal Control: Formulates the tuning problem as an optimization problem and uses techniques like linear quadratic regulator (LQR) or model predictive control (MPC) to find optimal parameters.   1. What Is Optimal Control? – MATLAB & Simulink – MathWorks nl.mathworks.com

By leveraging the power of mathematical modeling, model-based tuning offers a systematic and potentially more effective approach to PID controller design.

The relay feedback method is an automated tuning technique that involves replacing the PID controller with a relay in a closed-loop system. This creates stable oscillations, from which information about the process can be extracted to determine PID parameters.

1. Relay Feedback Autotuning Technique – NI – National Instruments

2. Full Closed-Loop Tests for the Relay Feedback Autotuning of Stable, Integrating, and Unstable Processes | ACS Omega

How it works:

1. Replace PID with Relay: The PID controller is temporarily replaced with a relay, which has two output states (on and off).
2. Induce Oscillations: The relay’s output switches between its two states, causing the process to oscillate.
3. Measure Oscillation Parameters: The amplitude and period of the oscillations are measured.
4. Calculate PID Parameters: Using the measured oscillation parameters and tuning rules (often based on Ziegler-Nichols), the PID controller parameters are calculated.   1. A Review of Relay Auto-tuning Methods for the Tuning of PID-type Controllers warwick.ac.uk
5. Implement PID Controller: The calculated PID parameters are applied to the system.

Advantages:

• Simplicity: The method is relatively easy to implement.
• Automation: The tuning process can be automated.   1. 12: Relay Feedback Methods – Process Identification and PID Control [Book] – O’Reilly www.oreilly.com
• Robustness: It can be applied to a wide range of processes.   1. Full Closed-Loop Tests for the Relay Feedback Autotuning of Stable, Integrating, and Unstable Processes | ACS Omega pubs.acs.org

Disadvantages:

• Can be time-consuming: Inducing oscillations can take time.
• Potential for process disturbance: Creating oscillations can disrupt normal operation.
• Accuracy: The accuracy of the resulting tuning depends on the process and the chosen tuning rules.

Common Applications:

• Industrial processes where automatic tuning is desired.
• Systems with frequent changes in operating conditions.

The relay feedback method is a valuable tool for tuning PID controllers, especially when manual tuning is impractical or time-consuming.