This chapter is devoted to the mathematical description of the basic elements and processes pertaining to the embedded control systems. The models obtained as a result of this description are important for the design of controllers which have to ensure the necessary performance and robustness of the closed-loop system. The main point of the chapter is the derivation of adequate continuous-time and discrete-time models of the plant, sensors, and actuators. For this aim, we implement various analytic and numeric tools available in control theory and control engineering practice. These tools include modeling, linearization, and discretization of dynamic plants, system identification, modeling of uncertain systems, and stochastic modeling. We demonstrate the usage of different MATLAB® functions and Simulink® blocks intended to build accurate and reliable models of embedded system components.

Chapter Contents:

• 2.1 Plant modeling
• 2.2 Linearization
• 2.2.1 Analytic linearization
• 2.2.2 Symbolic linearization
• 2.2.3 Numeric linearization
• 2.3 Discretization
• 2.3.1 Discrete-time models
• 2.3.2 Discrete-time frequency responses
• 2.3.3 Discretization of continuous-time models
• 2.3.4 Discretization of time delay systems
• 2.3.5 Choice of the sampling period
• 2.3.6 Discretization of nonlinear models
• 2.4 Stochastic modeling
• 2.4.1 Stochastic linear systems
• 2.4.2 Discretization of stochastic models
• 2.4.3 Optimal estimation
• 2.5 Plant identification
• 2.5.1 Identification of black box model
• 2.5.2 Identification of gray-box model
• 2.6 Uncertainty modeling
• 2.6.1 Structured uncertainty models
• 2.6.2 Representing uncertain models by LFT
• 2.6.3 Deriving uncertain state-space models from Simulink® models
• 2.6.4 Unstructured uncertainty models
• 2.6.5 Mixed uncertainty models
• 2.6.6 Discretization of uncertain models
• 2.6.7 Deriving uncertainty models by identification
• 2.7 Sensor modeling
• 2.7.1 Allan variance
• 2.7.2 Stochastic gyro model
• 2.7.3 Stochastic accelerometer model
• 2.7.4 Sensor data filtering
• 2.8 Notes and references

Inspec keywords: embedded systems; uncertain systems; closed loop systems; stochastic systems; control system synthesis; discrete time systems; numerical analysis; continuous time systems

Other keywords: continuous-time models; controller design; stochastic modeling; dynamic plant linearization; Simulink; uncertain system modelling; discrete-time models; system modeling; Matlab function; actuators; control engineering practice; sensors; embedded control systems; dynamic plant discretization; closed-loop system; embedded system components; system identification; mathematical description; control theory

Subjects: Other numerical methods; Discrete control systems; Time-varying control systems; Control system analysis and synthesis methods