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 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.
 
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)
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--[[User:Soto|Luis 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]]

Latest 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. --Luis Soto 18:56, 1 October 2008 (PDT)