This can be converted to state-space form by For example, for a plant transfer function P(s) = 1/(s^2 + s) To convert between state space and transfer function in Scilab, use commands ss2tf and tf2ss. Moreover, though in our robot joint example the states are conveniently joint position and velocity, for the general case the states might not have any physical meaning, and hence could not be measured.įor a system represented by (6) and (7), it is easy to show that the corresponding transfer function equals Note that this representation is not unique, but depends on how the states are defined. (6) is called a state equation, and (7) an output equation. Where x,u,y represent the state, input, and output vectors, respectively. In general, a linear time-invariant (LTI) system can be described as Define the system states as the joint position and velocityīy using these state variables, (1) can be rewritten as a system of first order differential equations To simplify the notation, the time dependent is omitted. A dynamic equation that governs the motion can be written as Let us take our simple DC motor joint model as an example. Indeed, the modern control approach is so eternal that later developments have to be called post-modern.įirst, we give some review on state-space representation, which is essential for the state feedback design discussed later on. * This terminology is commonly used in the control literature, regardless of calling a 50-year-old approach modern could sometimes create confusion to a beginner. In contrast to the frequency domain analysis of the classical control theory, modern control theory formulates the time-domain data as a system of first-order differential equations in matrix form called state-space representation, which is a mathematical model of the given system as a set of input, output, and state variable. State feedback control, the topic of this study module, can be thought of as a foundation for the so-called “modern control *” originated since ’60. Append an integrator to state feedback to eliminate steady-state error.Design state feedback using simple pole-placement procedure.How to convert data between state-space and transfer function form.Understand state-space representation of a system.This article is contained in Scilab Control Engineering Basics study module, which is used as course material for International Undergraduate Program in Electrical-Mechanical Manufacturing Engineering, Department of Mechanical Engineering, Kasetsart University.
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