Fractional order proportional integral and proportional derivative controllers are nowadays quite often used in research studies regarding the control of various types of processes, with several papers demonstrating t...
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Fractional order proportional integral and proportional derivative controllers are nowadays quite often used in research studies regarding the control of various types of processes, with several papers demonstrating their advantage over the traditional proportional integral/proportional derivative controllers. The majority of the tuning techniques for these fractional order proportional integral/fractional order proportional derivative controllers are based on three frequency-domain specifications, such as the open-loop gain crossover frequency, phase margin and the iso-damping property. The tuning parameters of the controllers are determined as the solution of a system of three nonlinear equations resulting from the performance criteria. However, as with any system of nonlinear equations, it might occur that for a certain process and with some specific performance criteria, the computed parameters of the fractional order proportional integral/fractional order proportional derivative controllers do not fall into a range of values with correct physical meaning. In this article, a study regarding this limitation, as well as the existence conditions for the fractional order proportional integral/fractional order proportional derivative parameters are presented. The method could also be extended to the more complex fractional order proportional-integral-derivative controller. The aim of this research is directed toward demonstrating that when designing fractional order proportional integral/fractional order proportional derivative controllers, the choice of the performance specifications should be done based on some specific design constraints. The article shows that given a specific process and open-loop modulus and phase specifications, the gain crossover frequency (or in general, a certain test frequency used in the design), specified as a performance specification, must be selected such that the process phase fulfills an important condition (design constraint). Once
This article focuses on the control of a group of nonholonomic mobile robots. A leader-follower coordinated control scheme is developed to achieve formation maneuvers of such a multi-robot system. The scheme adopts th...
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This article focuses on the control of a group of nonholonomic mobile robots. A leader-follower coordinated control scheme is developed to achieve formation maneuvers of such a multi-robot system. The scheme adopts the methodology of integral sliding mode control to form up and maintain the robots in predefined trajectories. The dynamic equations of the scheme are subject to mismatched uncertainties. The mismatched uncertainties challenge formation stabilization because they cannot be suppressed by the invariance of integral sliding mode control. In light of Lyapunov's direct method, a sufficient condition is drawn to guarantee the reachability condition of integral sliding mode control in the presence of the mismatched uncertainties. To verify the feasibility and effectiveness of the proposed strategy, simulation results are illustrated by an uncertain multi-robot system composed of three nonholonomic mobile robots.
In applications, usually sampled data controllers are employed. If the sampling time is sufficiently small, the sampled data structure may be neglected and the system is treated quasi-continuously. If the sampling tim...
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In applications, usually sampled data controllers are employed. If the sampling time is sufficiently small, the sampled data structure may be neglected and the system is treated quasi-continuously. If the sampling time is longer, the system is treated in discrete time neglecting the behaviour in between the sample instances and the z-transform is used. This article combines these two approaches. The plant is driven by an input which consists of a sequence of values and a function forming the actuating variable. By use of the modified z-transform, the plant is modelled by a parametric transfer function matrix, whose additional parameter discloses the behaviour between sampling instances. Thus, the output signal is calculated not only at the points of sampling. A right co-prime matrix-fraction description is derived. Building on that description, basis variables are defined in the z-domain. The corresponding basis sequences can be chosen arbitrarily and with them the input sequences and the output functions are fixed and can be calculated without solving a differential or difference equation. This mathematical fact is applied to plan trajectories in continuous time. Hence, the entire output trajectory in continuous time can be taken into account. A tracking controller may be added to ensure that the disturbed system complies with the plan.
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