Important PID Concepts | Understanding PID Control, Part 7

Summary

This video delves into key concepts in PID control, focusing on cascaded loops and discrete systems. Cascaded loops, involving interconnected inner and outer PID controllers, help isolate system issues and handle disturbances at different speeds. The video explains the benefits of this approach, such as faster motor response and more stable altitude control. It also introduces discrete PID controllers, emphasizing the differences between continuous and discrete systems. Finally, the video highlights why continuous control is often preferred for designing and tuning controllers before transitioning to discrete systems for digital implementation.

Takeaways

• 😀 Cascaded loops are essential in complex systems like drones, where multiple feedback loops work together to achieve precise control.
• 😀 Cascade control allows isolating problems in a system, as you can test individual loops (e.g., motor control) separately from others (e.g., altitude control).
• 😀 Teams can work on different parts of a system, with one focusing on the motor control loop and another on the altitude loop, especially if the motor comes with an integrated controller.
• 😀 Cascaded loops allow the inner loop to respond quickly to local disturbances (like motor issues), while the outer loop can focus on slower disturbances (like wind gusts), improving overall system stability.
• 😀 A single-loop controller would struggle to handle quick disturbances, as it would need to be tuned aggressively, leading to issues like reacting to sensor noise.
• 😀 Tuning cascaded loops can be done separately if the inner loop is much faster than the outer loop, but if they operate at similar speeds, tuning requires more consideration of both loops together.
• 😀 There are several methods for tuning cascaded loops, including iterative approaches, state-space methods, and auto-tuning tools like those available in MATLAB and Simulink.
• 😀 Discrete PID controllers are different from continuous ones because digital computers process data at sample times, meaning adjustments occur at intervals rather than continuously.
• 😀 The key difference in discrete control is that the sample time (rate of updates) affects system behavior, with slower sample times potentially leading to less accurate control.
• 😀 Tuning a discrete PID controller typically starts in the continuous domain (S domain) before converting to the discrete domain (Z domain), ensuring that sample time doesn't impair system performance.

Q & A

What is cascade control and how does it work in PID systems?

Cascade control involves using two or more nested PID control loops. In the example of a quadcopter drone, one loop controls the motor speed (inner loop) and the other controls the altitude (outer loop). The outer loop adjusts the setpoint for the inner loop, allowing the system to handle disturbances at different speeds and ensuring more effective performance.

Why is cascade control preferred over a single PID loop for systems like a drone?

Cascade control allows easier isolation of problems in the system, as each loop can be tested independently. It also enables teams to work on different parts of the system (e.g., one team works on the motor controller and another on the altitude controller). Moreover, it allows each loop to operate at different speeds to address specific disturbances and errors effectively.

How do cascaded loops help with disturbance rejection in systems like a quadcopter?

In cascade control, the inner loop (motor control) reacts quickly to local disturbances, such as changes in motor speed or battery voltage, preventing noticeable effects on the outer loop, which controls altitude. This allows the outer loop to be tuned more conservatively, focusing on slower disturbances like wind gusts, which enhances overall system stability.

What are the challenges in tuning cascaded PID loops?

Tuning cascaded PID loops becomes more difficult when both loops have similar bandwidths. In such cases, the inner loop's performance directly affects the outer loop's response. Methods like iterative tuning, multi-input multi-output system tuning, or auto-tuning using software tools like MATLAB can be used to address these challenges.

What are the benefits of separating tuning for inner and outer loops in cascaded systems?

When the inner loop operates much faster than the outer loop, it can be tuned separately, assuming the inner loop’s response is instantaneous. This simplifies tuning the outer loop as it can be treated like a single loop. This separation helps in achieving optimal performance for each loop without interference from the other.

How does sample time impact the behavior of discrete PID controllers?

Sample time plays a crucial role in discrete PID controllers. If the sample time is short relative to the system dynamics, the behavior will resemble a continuous system. However, as the sample time increases, the system’s response becomes less accurate, which is akin to viewing a strobe light with slower flashing – the controller's ability to react is compromised.

Why is it easier to solve PID control problems in the continuous domain (S domain) rather than in the discrete domain (Z domain)?

The continuous domain offers more tools and methods for solving PID control problems. Additionally, many systems being controlled are inherently continuous. Therefore, modeling both the plant and controller in the continuous domain simplifies the problem. Discrete control becomes useful when dealing with digital computers that update at fixed sample times.

What is the difference between continuous and discrete PID controllers?

A continuous PID controller operates smoothly with time, while a discrete PID controller updates at fixed sample times, based on a digital computer's clock. This difference impacts the performance, especially when the sample time is not fast enough to capture rapid changes, which can lead to less accurate control compared to a continuous system.

How do quantization and transport delay affect digital PID controllers?

Quantization refers to the rounding off of values when converting analog signals to digital, leading to a loss of precision. Transport delay is the time it takes for a signal to travel through the system. Both of these factors can degrade the performance of a digital PID controller, especially when the sample time is too long or the system requires high precision.

What is the primary reason for learning continuous control before discrete control in PID systems?

The primary reason is that continuous control is easier to model and solve, with more available tools. Since many plants are continuous in nature, modeling both the plant and the controller in the continuous domain simplifies the problem. Discrete control is used when implementing on digital computers, but this is done after understanding the continuous domain behavior.