Mathematics · Differential Equations
Control-System Phase Margin instability phase boundary in degrees Solver
Rearrange the control-system phase margin relationship and solve for instability phase boundary in degrees.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use a=c+b with phase margin=-45 and open-loop phase at gain crossover in degrees=-135.
- instability phase boundary in degrees=-180.
- Substitution into c=a−b reconstructs -45.
Understand Control-System Phase Margin: solve instability phase boundary in degrees
One idea, three depths
Choose how deeply to explain Control-System Phase Margin: solve instability phase boundary in degrees
Control-System Phase Margin: solve instability phase boundary in degrees: Rearrange the control-system phase margin relationship and solve for instability phase boundary in degrees.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Control-System Phase Margin: solve instability phase boundary in degrees to answer this question: rearrange the control-system phase margin relationship and solve for instability phase boundary in degrees? Enter phase margin and open-loop phase at gain crossover in degrees; the calculator shows instability phase boundary in degrees. For example: instability phase boundary in degrees=-180 and open-loop phase at gain crossover in degrees=-135 produce phase margin=-45. The answer tells you instability phase boundary in degrees.
Age 15Explain it to a 15-year-oldConnect it to the formula
Under the standard negative-feedback convention, phase margin is the instability boundary minus the open-loop phase at gain crossover. This page isolates instability phase boundary in degrees and verifies it in the original relationship. The rule is a=c+b. Its input values are phase margin, open-loop phase at gain crossover in degrees, and the main result is instability phase boundary in degrees. For example: instability phase boundary in degrees=-180 and open-loop phase at gain crossover in degrees=-135 produce phase margin=-45.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated control-system phase margin: solve instability phase boundary in degrees relation over the valid real-number domain stated below. The implemented relation is a=c+b, evaluated from phase margin, open-loop phase at gain crossover in degrees to produce instability phase boundary in degrees. Under the standard negative-feedback convention, phase margin is the instability boundary minus the open-loop phase at gain crossover. This page isolates instability phase boundary in degrees and verifies it in the original relationship. Sign and wrapping conventions can reverse the displayed subtraction; report the convention explicitly.
Inputs and valid domain
- phase margin must be a finite real number.
- open-loop phase at gain crossover in degrees must be a finite real number.
Important boundary: Sign and wrapping conventions can reverse the displayed subtraction; report the convention explicitly.
The formula
a=c+b
How the calculator works through it
It substitutes phase margin, open-loop phase at gain crossover in degrees into the formula and exposes every numerical step above. The main output is instability phase boundary in degrees, accompanied by Reconstructed phase margin.
Read the result correctly
The instability phase boundary in degrees is the direct answer to “rearrange the control-system phase margin relationship and solve for instability phase boundary in degrees.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
instability phase boundary in degrees=-180 and open-loop phase at gain crossover in degrees=-135 produce phase margin=-45.
Where this model stops being reliable
Sign and wrapping conventions can reverse the displayed subtraction; report the convention explicitly.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Control-System Phase Margin: solve instability phase boundary in degrees works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Control-System Phase Margin: solve instability phase boundary in degrees uses a=c+b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Derivatives and changing systems
A derivative describes the changing quantity that Control-System Phase Margin: solve instability phase boundary in degrees models or approximates.
Review this foundation about 7 min
Optional enrichment
- Exponential solution behaviour
Exponential behaviour helps you recognise common growth, decay and response patterns related to Control-System Phase Margin: solve instability phase boundary in degrees.
Review this foundation about 7 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read phase margin, open-loop phase at gain crossover in degrees.
- Evaluate the principal relationship: a=c+b.
- Return instability phase boundary in degrees and check the domain conditions described above.
Python
from math import *
def control_phase_margin_solve_a(c, b) -> float:
return (c + b)
assert abs(control_phase_margin_solve_a(-45, -135) - -180) < 1e-6 * max(1.0, abs(-180))
C
#include <assert.h>
#include <math.h>
double control_phase_margin_solve_a(double c, double b) {
return (c + b);
}
int main(void) {
const double expected = -180;
const double actual = control_phase_margin_solve_a(-45, -135);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double control_phase_margin_solve_a(double c, double b) {
return (c + b);
}
int main() {
constexpr double expected = -180;
const double actual = control_phase_margin_solve_a(-45, -135);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double control_phase_margin_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global control_phase_margin_solve_a
section .text
control_phase_margin_solve_a:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
addsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = control_phase_margin_solve_a(c, b)
result = (c + b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, b_] := (c + b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Calculus Volume 1
Read OpenStax Calculus: Derivatives and integrationCite this book
- APA 7
- Strang, G., & Herman, E. (2016). Calculus volume 1. OpenStax. https://openstax.org/books/calculus-volume-1/pages/1-introduction
- MLA 9
- Strang, Gilbert, and Edwin Herman. Calculus Volume 1. OpenStax, 2016, https://openstax.org/books/calculus-volume-1/pages/1-introduction.
- Chicago author-date
- Strang, Gilbert, and Edwin Herman. 2016. Calculus Volume 1. Houston, TX: OpenStax. https://openstax.org/books/calculus-volume-1/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Control-System Phase Margin instability phase boundary in degrees Solver. MW SysArc Tools. https://math.mwsysarc.com/differential-equations/control-phase-margin-instability-phase-boundary-in-degrees-solver
MLA 9
MW SysArc. “Control-System Phase Margin instability phase boundary in degrees Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/differential-equations/control-phase-margin-instability-phase-boundary-in-degrees-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Control-System Phase Margin instability phase boundary in degrees Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/differential-equations/control-phase-margin-instability-phase-boundary-in-degrees-solver.
Harvard
MW SysArc (2026) ‘Control-System Phase Margin instability phase boundary in degrees Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/differential-equations/control-phase-margin-instability-phase-boundary-in-degrees-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_control_phase_margin_solve_a_2026,
author = {{MW SysArc}},
title = {Control-System Phase Margin instability phase boundary in degrees Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/differential-equations/control-phase-margin-instability-phase-boundary-in-degrees-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Control-System Phase Margin instability phase boundary in degrees Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/differential-equations/control-phase-margin-instability-phase-boundary-in-degrees-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Control-System Phase Margin: solve instability phase boundary in degrees do?
Rearrange the control-system phase margin relationship and solve for instability phase boundary in degrees.
How does the Control-System Phase Margin: solve instability phase boundary in degrees work?
The calculator applies a=c+b. Under the standard negative-feedback convention, phase margin is the instability boundary minus the open-loop phase at gain crossover. This page isolates instability phase boundary in degrees and verifies it in the original relationship.
What can I learn from the Control-System Phase Margin: solve instability phase boundary in degrees?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .