Matlab中feedback函数负反馈场景参数用法的疑问

Let's break down your two key questions about MATLAB's feedback function step by step—this is a common point of confusion, so you're not alone!

First Confusion: feedback(G*C, -1) vs feedback(G*C, 1, -1) #

First, let's recap the core syntax and behavior of feedback:

• The standard call is sys = feedback(sys1, sys2, sign)
  • sys1: Forward path transfer function
  • sys2: Feedback path transfer function
  • sign: Optional, defaults to -1 (negative feedback). Use +1 for positive feedback.

The closed-loop transfer function formula is:

• For negative feedback (sign=-1): sys = sys1 / (1 + sys1*sys2)
• For positive feedback (sign=+1): sys = sys1 / (1 - sys1*sys2)

Now let's analyze your two cases:

1. feedback(G*C, -1):

   • Here, sys1 = G*C (forward path), sys2 = -1 (feedback path), and sign uses the default -1.
   • Plugging into the formula: (G*C) / (1 + (G*C)*(-1)) = (G*C)/(1 - G*C) — this is actually a positive feedback loop, not negative.
   • If your documentation claims this creates a negative feedback loop for G and C, there's likely a misinterpretation of the context. Maybe the documentation was referring to a rearranged loop structure where the feedback path's sign is folded into sys2?

2. feedback(G*C, 1, -1):

   • Here, sys1 = G*C, sys2 = 1, sign=-1.
   • Formula result: (G*C)/(1 + (G*C)*1) = (G*C)/(1 + G*C) — this is a negative feedback loop with a unit feedback path around the combined G*C forward path.

If you're trying to create the classic negative feedback loop where the forward path is G and feedback path is C, the correct call is actually feedback(G, C) (defaults to negative feedback), which gives G/(1 + G*C)—that's the standard form.

Second Confusion: Why feedback(G, 1) is Negative Feedback #

Let's clarify why feedback(G, 1) gives a negative feedback loop:

• sys1 = G (forward path), sys2 = 1 (unit feedback path), sign defaults to -1 (negative feedback).
• Applying the formula: G / (1 + G*1) = G/(1 + G) — this is the standard unit negative feedback closed-loop transfer function, which matches what the documentation is doing.

If you used feedback(G, -1), you'd get G/(1 + G*(-1)) = G/(1 - G), which is a positive feedback loop—not what you want for unit negative feedback.

The key takeaway is:

• The sign parameter controls whether you subtract (-1) or add (+1) the feedback signal to the input.
• The sys2 parameter is the transfer function of the feedback path itself. For unit feedback, that's 1, and the default sign=-1 handles the negative feedback subtraction.

内容的提问来源于stack exchange，提问作者rrz0