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In control theory , a state observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications. Knowing the system state is necessary to solve many control theory problems; for example, stabilizing a system using state feedback.

In most practical cases, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs.

## State feedback observer simulink tutorial pdf

A simple example is that of vehicles in a tunnel: the rates and velocities at which vehicles enter and leave the tunnel can be observed directly, but the exact state inside the tunnel can only be estimated. If a system is observable , it is possible to fully reconstruct the system state from its output measurements using the state observer.

These equations simply say that the plant's current outputs and its future state are both determined solely by its current states and the current inputs. Although these equations are expressed in terms of discrete time steps, very similar equations hold for continuous systems.

The observer model of the physical system is then typically derived from the above equations. Additional terms may be included in order to ensure that, on receiving successive measured values of the plant's inputs and outputs, the model's state converges to that of the plant. The previous example was for an observer implemented in a discrete-time LTI system.

However, high observer gain leads to a peaking phenomenon in which initial estimator error can be prohibitively large i.

For example, sliding mode control can be used to design an observer that brings one estimated state's error to zero in finite time even in the presence of measurement error; the other states have error that behaves similarly to the error in a Luenberger observer after peaking has subsided. Sliding mode observers also have attractive noise resilience properties that are similar to a Kalman filter.

Multi observer can be adapted to every system where High Gain Observer is applicable. These observers contain a cubic term in their estimation error dynamics.

A cubic observer may be used to reduce the peaking phenomenon and increase observer performance. The cubic observer is described by the following equations:. This choice guarantees stability and uniqueness of the origin as the equilibrium point of the estimation error dynamics. Sliding mode observers can be designed for the non-linear systems as well.

For simplicity, first consider the no-input non-linear system:. There are several non-approximate approaches for designing an observer.

## Control Design via State-space: MatLab/Simulink Example

The two observers given below also apply to the case when the system has an input. That is,. One suggestion by Krener and Isidori [6] and Krener and Respondek [7] can be applied in a situation when there exists a linearizing transformation i. Ciccarella, Dalla Mora, and Germani [10] obtained more advanced and general results, removing the need for a nonlinear transform and proving global asymptotic convergence of the estimated state to the true state using only simple assumptions on regularity.

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As discussed for the linear case above, the peaking phenomenon present in Luenberger observers justifies the use of a sliding mode observer. The sliding mode observer uses non-linear high-gain feedback to drive estimated states to a hypersurface where there is no difference between the estimated output and the measured output.

The non-linear gain used in the observer is typically implemented with a scaled switching function, like the signum i. Hence, due to this high-gain feedback, the vector field of the observer has a crease in it so that observer trajectories slide along a curve where the estimated output matches the measured output exactly.

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So, if the system is observable from its output, the observer states will all be driven to the actual system states. Additionally, by using the sign of the error to drive the sliding mode observer, the observer trajectories become insensitive to many forms of noise. Hence, some sliding mode observers have attractive properties similar to the Kalman filter but with simpler implementation.

As suggested by Drakunov, [11] a sliding mode observer can also be designed for a class of non-linear systems.

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The idea can be briefly explained as follows. In practice, it switches chatters with high frequency with slow component being equal to the equivalent value. Applying appropriate lowpass filter to get rid of the high frequency component on can obtain the value of the equivalent control, which contains more information about the state of the estimated system.

The observer described above uses this method several times to obtain the state of the nonlinear system ideally in finite time. In particular,.

## State observer

That is, the requirement is an observability condition. In the case of the sliding mode observer for the system with the input, additional conditions are needed for the observation error to be independent of the input.

For example, that. Multi observer extends High Gain Observer structure from single to multi observer, with many models working simultaneously. This has two layers: the first consists of multiple High Gain Observers with different estimation states, and the second determines the importance weights of the first layer observers. The algorithm is simple to implement and does not contain any risky operations like differentiation.

These factors are changed to provide the estimation in the second layer and to improve the observation process. The mapping error is specified as.

The created mapping gives a lot of flexibility in the estimation process. The Bounding [13] or Interval observers [14] constitute a class of observers that provide two estimations of the state simultaneously: one of the estimations provides an upper bound on the real value of the state, whereas the second one provides a lower bound.

The real value of the state is then known to be always within these two estimations.

## Description

These bounds are very important in practical applications, [15] [16] as they make possible to know at each time the precision of the estimation. From Wikipedia, the free encyclopedia. August Journal of Process Control. Categories : Classical control theory Time series.

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