ME 357 09 A Introduction to State Space Modeling

Описание: State Space Modeling for Mechanical Systems (Time Domain) - A, B, C, D Matrices and MATLAB Simulation

In this ME 357 System Dynamics I lesson, we build intuition for state-space modeling and compare it to transfer function modeling. You will see why state-space is often the cleanest option for multi-input and multi-output systems, non-zero initial conditions, and more realistic input signals.

What you will learn
When to use state-space vs transfer functions (and the tradeoffs)
How to define the state vector x, input vector u, and output vector y
How to construct the A (state), B (input), C (output), and D (feed-through) matrices
How to check matrix sizing for n states, m inputs, and p outputs
How to numerically simulate state equations in MATLAB using ode45

State-space basics (time-domain form)
State-space representation overview:
https://en.wikipedia.org/wiki/State-s...

Key model form:
x_dot = A x + B u
y = C x + D u

Matrix dimensions (sanity check)
A is n x n
B is n x m
C is p x n
D is p x m

MATLAB tools mentioned
ode45 (numerical ODE solver):
https://www.mathworks.com/help/matlab...

ss (state-space models in Control System Toolbox):
https://www.mathworks.com/help/contro...

tf (transfer function models in Control System Toolbox):
https://www.mathworks.com/help/contro...

Concepts to keep on your radar for controls
Observability:
https://en.wikipedia.org/wiki/Observa...

Controllability:
https://en.wikipedia.org/wiki/Control...

More lessons in this series
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Timestamps
0:03 Goals and learning outcomes
1:12 What a state-space model is (time-domain viewpoint)
2:05 When state-space is the better choice (MIMO, non-zero ICs, complex inputs)
4:16 Stability preview: eigenvalues and eigenvectors idea
5:22 Converting higher-order ODEs into first-order form
6:41 Defining x, u, y and the A, B, C, D matrices
10:48 Step-by-step workflow for mechanical systems
12:49 Identifying inputs vs states
16:03 Isolating x_dot and building A and B (mapping equations)
17:39 Building C and D, and checking matrix sizes