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18 Nov 2020

# The Core Concepts of State-Space Control - Part 2

Skill-Lync

The first part of this blog introduced the concept of systems, types of systems, and what a state-space control system was. Now, let's learn about some of the current trends in this domain.

## Current Trends

### Self-Driving Cars

To make a driverless car travel from point A to point B, you would fix some points on the way that the system detects to guide the vehicle towards the destination. This scenario is called the problem of path tracking, and the method used to solve it is called model predictive tracking.

As mentioned in Part 1, a vehicular dynamics system takes in steering angle and vehicle velocity as inputs and generates the position of the vehicle as the output. The path-tracking system looks at the actual position of the car and the reference (ideal) position and modifies the next set of inputs accordingly.

### Powertrain Control

Powertrain control is a generic term to refer to any form of engine or transmission control. For example, imagine you are waiting at a traffic light with the engine on and the gear in neutral; the engine's RPM is called the idling RPM (it is not zero if the engine is on). Suppose you switch on the AC or the radio, how will the RPM change? That change can be modeled using state-space control systems.

Similarly, regulating the air-fuel ratio is another crucial application of state-space control. In recent times, you can also solve the problem of energy management in hybrid vehicles using this control system.

## Vehicle Control and Miscellaneous Applications

The overall stability of a car can be monitored using state-space techniques. You can notice some of these features on the car dashboard too.

Apart from the automotive sector, state-space systems find applications in the aerospace sector for motion and flight control, guided missiles in defense, and drone control.

### Solution Providers

#### Software

Engineers make use of sophisticated software packages to simulate system dynamics and handle matrix operations and differential equations. MATLAB/Simulink, dSPACE (hardware support too), and Arduino (primarily for academic or personal projects) are examples of such packages. At the same time, open-source programming languages like C++ are used to deploy control algorithms.

#### Hardware

Many automotive companies also provide control systems hardware, and some of the other leading players in this field are Bosch (mainly engine and fuel control systems), Delphi (propulsion control), and Continental.

## Technical Overview: The State-Space Approach

The "states" of a system refer to all the properties of the system, which can define it completely. In other words, the system, at any point in time, can be determined using these state variables (denoted by a vector X).

### An Example: Spring-Mass System

Consider the example of a spring-mass system: one end of a spring is attached to a surface, and the other end is attached to a mass. The state variables, in this case, are the position (x) and the velocity (v) of the mass. If you plot the position along one axis and velocity along the other axis, you can represent the system by a point on a two-dimensional coordinate plane.

The force equation - Newton's second law - is essentially a second-order differential equation. In the state-space model, you represent this equation using two first-order differential equations, which, in turn, can be written in a matrix form.

In the state-space control, you model the behavior of dynamic systems using differential equations in the state variables. This conversion from the dynamic form of an equation to a matrix form is the fundamental principle of the state-space approach.

## How to Design a Control System Using State-Space Approach?

The steps an engineer should take to implement a control system is given as follows:

1. Define the system and the control problem.
2. Identify the inputs and outputs.
3. Establish a state-space model.
4. Study the system characteristics (like stability).
5. Design a controller using an appropriate technique.
6. Analyze the closed-loop system.
7. Simulate the system behavior.
8. Test the system under the desired operating conditions.
9. Move on to the practical implementation.

### Educational Background

Students of the mechanical, electrical, or computer science engineering streams are most likely to come across state-space control systems in their line of study or work. Introductory courses cover topics like classical and modern control theory and system simulations.

After learning the basics, you can choose a specific sub-field within systems dynamics and specialize in that. To truly master the subject, you need to look for opportunities to get practical experience, like internships or projects.

Apart from this, you need to have some other skills when applying for jobs, like:

• Knowledge of automotive systems
• Strong mathematics fundamentals (probability, linear algebra)
• Core concepts of state-space control techniques
• Experience in using simulation software like MATLAB and programming languages

### Job Roles

Typical entry-level positions in this domain are systems engineer, powertrain control engineer, vehicle control engineer, etc. In these roles, you have to design a control architecture, model system dynamics, or apply control techniques to practical situations.

With some experience in the industry, you rise to a senior level to positions like Senior Control System Design Engineer or a Hardware-in-the-Loop (HIL) Simulation Engineer. These roles require you to develop your own methods and techniques for handling systems.

If you rise to the top management positions like Control Engineering Team Lead or Vehicle Control Technical Specialist, your job requirement would involve more of people management. You should train and drive other engineers to excel at their work and supervise the entire system rather than only one segment.

The domain of control systems is a high-demand one, especially with the advent of electric vehicles and autonomous driving technology. You have plenty of areas to specialize in, all of which will be relevant in the future.

#### Conclusion

Today, companies and recruiters consider the skillset and experience of a candidate more than just their educational background. If you are a student of mechanical, electrical, or computer science, learning about state-space systems opens up several job positions for your career ahead.

Even if you belong to another discipline, you can undergo a rigorous course on an introduction to state-space control systems to become a suitable candidate for such jobs.

Check out the master's engineering courses offered by Skill-Lync and start learning today!

Author

Author

Skill-Lync

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