41 research outputs found
Robust Control of the Knee Joint Angle of Paraplegic Patients considering Norm-Bounded Uncertainties
A proposal for the knee position control design of paraplegic patients with functional electrical stimulation (FES) using control systems and considering norm-bounded uncertainties is presented. A state-space representation of the knee joint model of the paraplegic patient with its nonlinearity is also demonstrated. The use of linear matrix inequalities (LMIs) in control systems with norm-bounded uncertainties for asymptotic stability is analyzed. The model was simulated in the Matlab environment. The matrix K of state space feedback was obtained through LMIs
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Identification of fractional-order transfer functions using exponentially modulated signals with arbitrary excitation waveforms
This paper proposes a new identification method based on an exponential modulation scheme for the determination
of the coefficients and exponents of a fractional-order transfer function. The proposed approach has a broader
scope of application compared to a previous method based on step response data, in that it allows for the use of
arbitrary input signals. Moreover, it dispenses with the need for repeated simulations during the search for the
best fractional exponents, which significantly reduces the computational workload involved in the identification
process. Two examples involving measurement noise at the observed system output are presented to illustrate the
effectiveness of the proposed method when compared to a conventional output-error optimization approach based
on the polytope algorithm. In both examples, the proposed method is found to provide a better trade-off between
computational workload and accuracy of the parameter estimates for different realizations of the noise.
Keywords: Fractional order systems, system identification, transfer function
On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties
This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure
Stabilizability and Disturbance Rejection with State-Derivative Feedback
In some practical problems, for instance in the control of mechanical systems using
accelerometers as sensors, it is easier to obtain the state-derivative signals than the state
signals. This paper shows that (i) linear time-invariant plants given by the state-space
model matrices {A,B,C,D} with output equal to the state-derivative vector are not observable
and can not be stabilizable by using an output feedback if det(A)=0 and (ii) the
rejection of a constant disturbance added to the input of the aforementioned plants, considering
det(A)≠0, and a static output feedback controller is not possible. The proposed
results can be useful in the analysis and design of control systems with state-derivative
feedback
Metodologia para rastreamento com modificação dos zeros e rejeição de distúrbio aplicada a sistemas incertos
Redução 'H IND.2 e 'H INFINITO' de modelos atraves de desigualdades matriciais lineares : otimização local e global
Orientador: Pedro Luis Dias PeresTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho aborda o problema de redução de modelos para sistemas dinâmicos lineares, contínuos e discretos no tempo, tendo como critérios as normas 1i2 e 1ioo da matriz de transferência associada ao erro de redução. Primeiramente, são apresentados e discutidos os principais métodos de redução de modelos existentes na literatura. A seguir, o problema de redução 1i2 e 1ioo de modelos é formulado em termos de desigualdades matriciais bilineares, assim como o problema de redução 1i2 de ordem de controlador (neste caso, a formulação apresentada difere das demais existentes na literatura). São propostos algoritmos de otimização local para a redução 1i2 e 1ioo de modelos contínuos e discretos no tempo, com ou sem incertezas, baseados na iteração entre dois subproblemas formulados em termos de desigualdades matriciais lineares. Esses algoritmos não possuem convergência garantida e, como mostrado, são dependentes da inicialização. Finalmente, são propostos algoritmos de otimização global para a redução 1i2 e 1ioo de modelos e para a redução 1i2 da ordem de controladores para sistemas contínuos no tempo. Estes algoritmos têm convergência para o ótimo global garantida em tempo finito e são baseados na técnica de otimização branch-and-bound, com subproblemas convexos na forma de desigualdades matriciais linearesAbstract: This work addresses the problem of mo deI reduction for continuous and discrete-time linear dynamic systems, using as criteria the 1-l2 and the 1-loo norms of the transfer matrix associated to the reduction error. First, some important mo deI reduction methods in the literature are presented and discussed. Then, the problem of1-l2 and 1-loo model reduction is formulated in terms of bilinear matrix inequalities, as well as the problem of controller order reduction with criterion 1-l2 (in this case, the formulation presented differs from the existing ones in the literature). Local optimization algo rithms are proposed to solve the problem of 1-l2 and 1-loo model reduction for continuous and discrete-time systems, with or without uncertainties, based on the iteration between two subproblems formulated in terms of linear matrix inequalities. These algorithms do not have convergence assured and, as shown, depend on the initialization. Finally, global optimization algorithms are proposed to solve the problem of 1-l2 and 1-loo model reduction and the 1-l2 controller order reduction for continuous-time systems. These algorithms have convergence assured to the global optimum in finite time, being based on branch-and-bound optimization techniques, with convex subproblems in terms of linear matrix inequalitiesDoutoradoTelecomunicações e TelemáticaMestre em Engenharia Elétric
Otimização global para os problemas de redução H2 de modelos e redução H2 da ordem do controlador
A branch and bound algorithm is proposed to solve the H2-norm model reduction problem and the H2-norm controller reduction problem, with conditions assuring convergence to the global optimum in finite time. The lower and upper bounds used in the optimization procedure are obtained through linear matrix inequalities formulations. Examples illustrate the results