System Theory 2
System Theory 2 Teaching Team
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Based on the course System Theory 1, in which continuous-time control systems with continuous-time controllers were considered, the lecture System Theory 2 imparts extended mathematical methods to analyze and synthesize discrete-time systems in the time and frequency domain. Although many technical and non-technical systems can be steered by continuous-time controllers, the use of digital computers (e.g. in the form of microcontrollers) allows much better regulation procedures to be implemented. In addition, nowadays digital controls can be implemented at low cost, which is why their use is usually preferred.
The course System Theory 2 is intended to provide the students a deep understanding of discrete-time control systems. Besides the introduction of the z-transformation, the stability analysis of discrete-time systems and the design of control algorithms for sampling controls, the model of the state space representation is considered. On the basis of the state space representation, the so-called canonical forms are derived and system properties such as controllability and observability are discussed. In addition, different discrete-time control procedures in the state space are pointed out. In the end, solutions for control systems under uncertainty are presented, such as state estimations using the Kalman filter.
Online Lecture in Winter Semester 2021
In the winter semester 2021 the lecture System Theory 2 will be held online. Access to the live lectures held via zoom, and recordings of the lectures are provided to the students in the RWTHmoodle learning room of the course.
Detailed event overview
Linear discrete-time systems and sampling controls
Structure of sampling controls, sampling theory, quantization, D/A converters, discrete-time model of sampling control
Discrete-time systems in the time and frequency domain, analysis of sampling systems
System representation by differential equations, impulse response sequence, system representation by convolution sum, z-transformation, correspondence to Laplace-transformation, the transfer function of discrete-time systems, the stability of discrete-time systems, pole positions of continuous-time and discrete-time systems
Control algorithms for sampling control
Continuous-time and discrete-time PID controller, quasi-continuous sampling controls
State space representation, system description and analysis in the state space for linear continuous-time & discrete-time systems
Concept of the system states, state space model and solution of the state equations in the time domain, fundamental matrix, state-transition matrix, solution of the state equations in the frequency domain
Canonical forms for linear continuous-time & discrete-time systems
Controllable and observable canoncial forms, the duality between controllable and observable canoncial form, Jordan canonical form
Transformation of state equations to normal forms
Similarity transformation, transformation in diagonal form and Jordan canonical form, application of canonical transformations
Controllability & observability of linear continuous-time & discrete-time systems
Controllability and reachability, controllability matrix and controllability condition according to Kalman, observability, observability matrix and condition for observability, duality and dual systems
Synthesis of linear continuous-time & discrete-time control systems in the state space
Feedback of the state vector, feedback of the output vector, prefilter, controller synthesis by pole placement
State observer for linear continuous-time & discrete-time systems
State observer, gain matrix of the observer, observer synthesis by pole placement
State estimation using Kalman filter for linear systems
Probability calculations, Kalman filter, state estimation using the Kalman filter
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