Difference between revisions of "In lecture 1.2, y(x) was used as a function of the state variables. Is y a generic function of vector x?"

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In control theory, we usually use y to represent the output of a system. This output can be a subset of the state variables x1, x2, x3, etc. depending on the # of states and the states that are accessible for measurement by the sensors. For example, if we have sensor matrix C = [1 0], this could mean that only the first state is accessible by the sensors (or that we don't care about the dynamics of the second state in a 2-D system) and the output will be y = Cx = [1 0]*[x1 x2]' = x1. Thus, in this example the output y is a function of only state x1. You will learn later in the course that an "observer" can be used to estimate states that are not accessible for measurement by the sensors.
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In control theory, we usually use y to represent the output of a system. This output can be a subset of the state variables x1, x2, x3, etc. depending on the # of states and the states that are accessible for measurement by the sensors. For example, if we have sensor matrix C = [1 0], this could mean that only the first state is accessible by the sensors (or that we don't care about the dynamics of the second state in a 2-D system) and the output will be y = Cx = [1 0]*[x1 x2]' = x1. Thus, in this case the output y is a function of only state x1. You will learn later in the course that an "observer" can be used to estimate states that are not accessible for measurement by the sensors.
 
--[[User:Soto|Soto]] 18:56, 1 October 2008 (PDT)
 
--[[User:Soto|Soto]] 18:56, 1 October 2008 (PDT)
 
[[Category: CDS 101/110 FAQ - Lecture 1-2]]
 
[[Category: CDS 101/110 FAQ - Lecture 1-2]]
 
[[Category: CDS 101/110 FAQ - Lecture 1-2, Fall 2008]]
 
[[Category: CDS 101/110 FAQ - Lecture 1-2, Fall 2008]]

Revision as of 01:58, 2 October 2008

In control theory, we usually use y to represent the output of a system. This output can be a subset of the state variables x1, x2, x3, etc. depending on the # of states and the states that are accessible for measurement by the sensors. For example, if we have sensor matrix C = [1 0], this could mean that only the first state is accessible by the sensors (or that we don't care about the dynamics of the second state in a 2-D system) and the output will be y = Cx = [1 0]*[x1 x2]' = x1. Thus, in this case the output y is a function of only state x1. You will learn later in the course that an "observer" can be used to estimate states that are not accessible for measurement by the sensors. --Soto 18:56, 1 October 2008 (PDT)