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State-Space Representation of Control Systems
Published in Anatasia Veloni, Alex Palamides, Control System Problems, 2012
Anatasia Veloni, Alex Palamides
A state observer estimates (or observes) the state variables by comparing the difference between the measured and the estimated states, and by using feedback, the error converges asymptotically to zero. A state observer (depending on the type) can estimate all system states or only a minimum required number of state variables.
Fluid temperature predictions of geothermal borefields using load estimations via state observers
Published in Journal of Building Performance Simulation, 2021
Iago Cupeiro Figueroa, Massimo Cimmino, Ján Drgoňa, Lieve Helsen
Extending the methodology developed by Cupeiro Figueroa, Drgoňa, and Helsen (2019b); Cupeiro Figueroa et al. (2018), this paper proposes a method to estimate the load history of non-monitored operational borefield installations using state observers to obtain accurate borefield fluid predictions. State observers are feedback systems that provide an estimate of the internal states of a given model from measurements of the inputs and outputs of the real system to minimize the next-step output error. They are widely used in model-based optimal control applications to minimize the error on the current state of the system model and improve the accuracy of the predictions. The performance of these state observers to estimate the borefield load history and predicting the fluid temperature is assessed in both the short and long terms. Section 2 elaborates on the methodology used. Section 3 describes the case study building from which the data are extracted and further details on the experiment set-up, such as the initialization of the states . The resulting vectors of aggregated loads and the fluid temperature predictions from the simulations are discussed in Section 4. Finally, conclusions are drawn in Section 5.
Analytical solutions to the matrix inequalities in the ILF control-observer scheme for non-cooperative rendezvous with unknown inertia parameters
Published in International Journal of Control, 2020
For the cases that not all system states are available, the state observer becomes an efficient tool to design the control law using the measurements of partial states. Using ILF method, Polyakov, Efimov, and Perruquetti (2014) introduced a finite-time differentiator, and Lopez-Ramirez, Polyakov, Efimov, and Perruquetti (2016) designed the finite-time and fixed-time observer. Constructive schemes are built for the observer parameter tunings, but a parameterised system of nonlinear matrix inequalities (NLMIs) needs to be solved. The mentioned NLMIs depend on a scalar parameter λ and have to be satisfied for any λ in a closed interval, which costs much computation to obtain the feasible solution to these NLMIs by numerical methods. We constructed an analytical solution to the LMIs for tuning the controller gains in Tian et al. (2016), which motivates us to extend the previous work by finding an analytical solution to the NLMIs for the selection of observer gains.
Visual detection and tracking with UAVs, following a mobile object
Published in Advanced Robotics, 2019
Diego A. Mercado-Ravell, Pedro Castillo, Rogelio Lozano
The second explored method consists of a Luenberger state observer [29]. A state observer provides estimates of the internal states of the system from the input and output measurements. Let us consider the discrete-time kinematic model of the altitude at instant k where γ is the output and the input is . Then, a Luenberger observer is proposed, according to the following equations: Note the use of a hat on the variables to indicate that they are state estimates rather than the real ones. In order to guarantee that the estimated states converge asymptotically to the real ones, the observer gains are chosen such that the matrix has all its eigenvalues inside the unit circle.