Quantitative feedback theory technique and applications. Quantitative feedback theory QFT technique has emerged as a powerful multivariable control system design method. This design method addresses real-world problems with structured plant parameter … Expand.
View 1 excerpt, cites background. A hybrid state-space approach to sampled-data feedback control. This paper develops a state-space theory for the study of linear shift-invariant finite-dimensional hybrid dynamical systems. By hybrid system, we mean an inputoutput operator relating hybrid … Expand. View 1 excerpt, cites methods. Strategies for non-uniform rate sampling in digital control theory.
Multi-axis numerical control. The use of short sampling period in adaptive control has not been described properly when controlling the real process by adaptive controller. On one hand faster disturbance rejection due to short … Expand. Enter your name or username to comment. Enter your email address to comment.
Enter your website URL optional. Search this website Type then hit enter to search. Share via. Copy Link. Powered by Social Snap. Copy link. Copy Copied. It should come as no surprise that a discrete system and a continuous system will have different characteristics and different coefficient matrices.
If we consider that a discrete system is the same as a continuous system, except that it is sampled with a sampling time T, then the relationships below will hold. The process of converting an analog system for use with digital hardware is called discretization. We've given a basic introduction to discretization already, but we will discuss it in more detail here. Of primary importance in discretization is the computation of the associated coefficient matrices from the continuous-time counterparts.
Comparing this equation to our regular solution gives us a set of relationships for converting the continuous-time system into a discrete-time system.
Here, we will use 'd' subscripts to denote the system matrices of a discrete system, and we will use a 'c' subscript to denote the system matrices of a continuous system. If the A c matrix is nonsingular, and we can find it's inverse, we can instead define B d as:.
The differences in the discrete and continuous matrices are due to the fact that the underlying equations that describe our systems are different. Continuous-time systems are represented by linear differential equations, while the digital systems are described by difference equations. High order terms in a difference equation are delayed copies of the signals, while high order terms in the differential equations are derivatives of the analog signal.
If we have a complicated analog system, and we would like to implement that system in a digital computer, we can use the above transformations to make our matrices conform to the new paradigm. Because the coefficent matrices for the discrete systems are computed differently from the continuous-time coefficient matrices, and because the matrices technically represent different things, it is not uncommon in the literature to denote these matrices with different variables.
For instance, the following variables are used in place of A and B frequently:. As a matter of notational convenience, we will use the letters A and B to represent these matrices throughout the rest of this book. Now, let's say that we have a 3rd order difference equation, that describes a discrete-time system:. Again, we say that matrix x is a vertical vector of the 3 state variables we have defined, and we can write our state equation in the same form as if it were a continuous-time system:.
We can find a general time-invariant solution for the discrete time difference equations. Let us start working up a pattern. We know the discrete state equation:. If the system is time-variant, we have a general solution that is similar to the continuous-time case:.
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