Vehicle suspension control 1: Linearize nonlinear systems

Name: Vehicle suspension control 1: Linearize nonlinear systems
Rating: 5.0 (24 reviews)

Master Linearizing Nonlinear Systems for Vehicle Suspension Control: Stability, State-Space, Laplace and Poles Explained

Highest Rated

Created byMark Misin Engineering

Last updated 11/2025

English

What you'll learn

Linearize a nonlinear system using Taylor series
Learn the concepts of poles and stability in control systems
Learn the concepts of Laplace and Transfer functions in the context of control systems
Differentiate between Linear and Nonlinear, and also Time Variant and Time Invariant systems

Course content

5 sections • 77 lectures • 7h 5m total length

Introduction to the course structure4:22
Modeling the vehicle - springs & dampers5:37
Modeling the vehicle - Newton's 2nd law 13:31
Modeling the vehicle - Newton's 2nd law 211:11
Static equilibrium - intro2:44
Static equilibrium - obtaining it from the differential equations8:00
Static equilibrium - verifying the calculations using Statics8:19
Compute ECS and theta equilibrium from derived formulas with precise values and verify via statics using the sum of forces and moments from the free-body diagram, noting theta in degrees.
Linear vs Nonlinear systems9:13
Linear vs Nonlinear systems: example 12:06
Explore how to test linearity in an ode by applying the superposition principle to two cases, identifying linear versus nonlinear behavior and guiding future checks.
Linear vs Nonlinear systems: example 25:15
Checking the linearity of the truck system6:00
Motivation for Linearization and Modal Analysis 15:20
Motivation for Linearization and Modal Analysis 25:12
Follow up0:31

Modeling a mass-spring system8:24
Solving a homogeneous mass-spring system6:36
Solving a non-homogeneous mass-spring system 15:55
Solve a non-homogeneous mass-spring system with external force by linear superposition of homogeneous and particular solutions, then determine constants k1 and k2 from initial conditions.
Solving a non-homogeneous mass-spring system 23:10
Solve a non-homogeneous mass-spring system by obtaining the homogeneous and particular solutions. Verify correctness by substituting derivatives into the differential equation and use initial conditions to form the general solution.
Taking differential equations to the state space form9:14
Transform second-order differential equations into a state-space form by defining states x1 as position and x2 as velocity, yielding A and B matrices and revealing poles as eigenvalues of A.
Introducing Laplace6:20
Taking Laplace and its inverse manually8:35
Taking the Laplace of the 1st derivative3:16
Taking the Laplace of the 2nd derivative1:58
Taking the Laplace of the integral4:38
Using Laplace to solve the mass-spring system4:49
Introduction to transfer functions (SISO)3:28
Introduction to transfer functions (MIMO)4:38
Introduction to Dirac Delta 16:32
Introduction to Dirac Delta 27:08
Introduction to Dirac Delta 36:48
Taking Dirac Delta to Laplace8:26
Overdamped systems6:05
Critically damped systems5:09
Underdamped systems11:19
Stability and the poles6:28
Introducing the unit step (Heaviside) function7:36
The solution of the mass-spring-damper system1:44
Checking the equivalence of two systems with Laplace2:12
Transfer function and the impulse response7:31
Introduction to Time-Variant systems6:27
Time-Variant vs Time-Invariant systems 16:48
Time-Variant vs Time-Invariant systems 25:29
Time-Variant vs Time-Invariant systems 33:49
Demonstrate time-variant versus time-invariant systems and why Laplace fails for nonlinear and ltv cases, then highlight numerical ode solutions and Euler's method for validation.
Introduction to Euler's numerical method 1 (linear systems)8:57
Introduction to Euler's numerical method 1 (nonlinear systems)3:19
Introduction to Euler's numerical method 1 (Dirac Delta)4:03
Double impulse example3:00
General inputs applied to linear ODE-s 13:17
General inputs applied to linear ODE-s 24:43
General inputs applied to linear ODE-s 35:37
Introduction to convolution integral 17:35
Introduction to convolution integral 28:56
Laplace and the nonlinear systems5:16

Introduction to 1 dimensional Taylor series 16:27
Introduction to 1 dimensional Taylor series 26:28
Introduction to 1 dimensional Taylor series 3 (example)8:24
Introduction to Taylor series for multiple dimensions and equations5:40
Linearizing the truck (no control inputs) 18:24
Linearizing the truck (no control inputs) 27:13
Linearizing the truck (no control inputs) 35:09
Derive the linearized truck model by organizing dynamics into M, C, and K matrices, applying a small-angle approximation so C and K become symmetric for modal analysis.
Linearizing the truck (with control inputs) 19:16
Linearizing the truck (with control inputs) 23:35
Linearizing the truck (with control inputs) 33:19
Linearizing the truck (with control inputs) 45:58
Linearizing the truck (with control inputs) 55:42
Linearization - the big picture 16:50
Linearization - the big picture 24:57
Linearizing time-variant systems3:38

Requirements

It's important to know Calculus

Description

Unlock the power of control systems with the course, "Vehicle Suspension Control 1: Linearize Nonlinear Systems." This comprehensive program is designed for engineers and enthusiasts eager to master the art of linearizing nonlinear systems, enabling the application of effective linear control techniques.

In this course, you will delve into essential concepts such as Laplace transforms, poles, and system stability. Gain a solid understanding of impulse response and state-space equations, which are crucial for analyzing dynamic systems. We will also explore the differences between time-variant and time-invariant systems, as well as linear and nonlinear systems.

By the end of this course, you will be equipped with the skills to linearize complex systems around equilibrium points, making it easier to design controllers that ensure system stability and performance. Whether you are a beginner or looking to enhance your existing knowledge, this course is structured to guide you step-by-step through practical applications and theoretical foundations.

Join me to transform your understanding of vehicle suspension systems and control theory. Enroll today to elevate your engineering skills and apply what you've learned in real-world scenarios. Don't miss this opportunity to deepen your expertise in nonlinear system control—your journey towards becoming a proficient control engineer starts here!

Who this course is for:

Engineering students
Engineering professionals

Vehicle suspension control 1: Linearize nonlinear systems

What you'll learn

Explore related topics

Course content

Modeling the suspension system14 lectures • 1hr 17min

Essential Background - Differential equations for Control Systems39 lectures • 3hr 45min

Linearization of nonlinear systems (Result: Linear 2nd order system)15 lectures • 1hr 31min

Linearization of nonlinear systems (Result: Linear state-space system)5 lectures • 25min

Last Words4 lectures • 8min

Requirements

Description

Who this course is for: