The parameter system theory has gained a certain amount of maturity in the past two decades. In the year 1960, the Russian scientists Butkovskii and Lerner have reproduced the root of this very field back to papers. Basically Distributed parameter systems are designed by differential equation. In terms of flexible link robots, the so called distributed nature of mass and rigidity is reflected by the partial differential equations (Wightman, 1972). There are few specific techniques such as eigenfunction expansion, apace quantization, space and time quantization and transfer function approximations which are used to convert the partial differential equations into specific difference equations (DeSaÌ, 2001). In case of a multi-link robot, the equations of motion are non-linear and in general are not specifically known. Therefore, to control a robot can be achievable if each of the controllers joint is robust. Thus, for the control system of a sliding-mode controller is full of disturbance. To achieve a control law a sliding-mode controller has to be arranged according to Lyapunov function. Additionally, to control the non-linear system in a proper order the sliding-mode technique may also be taken under consideration. The technique to control a multi-linked robot is discussed in the later part of this report.
Control philosophy is a part in which the assumption of the robots has to be clarified. In case of the motion related to a multi linked and flexible arm robot, is probably has consisted of two vital parts. The first said part is the gross motion or the average motion of the robot which is specifically the motion of the rigid body of the robot (Gagliardi, 2009). The second part is the disturbance related to the average motion of the multi-linked robot such as the vibration of the flexible arm of the robot. At the same time the motion is controlled by a controller. In the after step will be to accelerate the linked robot. To explain the control philosophy the sliding-mode and shaped-input controllers are taken into consideration.
The motion related equations of any kind of robot are linear in respect to the potential control, which is, the major system can be easily represented in the underneath given form
x= f (x) + B (x) u,
Controller- Sliding Mode
Basically to be precise the particular motion of the major system that is controlled by a major mode controller can be evaluated potentially in two particular phrases (Potvin, 1985). The first basically includes the major forcing of the potentially important trajectory of the state, typically at any subsequent condition to a surface that is already pre-defined. Secondly to be brief it particularly involves sliding potentially from the identified surface to the subsequent state space or gap origin (Balasubramanian, Sivakumaran and Radhakrishnan, 2008). The major design of the needful controller is basically folded in two halves; basically both are for different purposes that are the subsequent selection of the desired surface eventually to produce the dynamics that are desired and the major selection of a law control which eventually forces the surface that is selected to be the major global attraction.
Shaped Input Control
Basically the next prolific step in the process of designing majorly involve the modification of the command input to the desired system in such a way that the system response must not contain any sort of harmonic thing or content (Arthur, 1982). Basically to systematically produce the periodic response that is needed to any of the major command input, the impulse way or sequence is adjusted with the input command, and this basic modification of the input prolifically produces the response that is desired or needed. To be very specific this controller can be prolifically used to control certain parts like the hand of the robot which is subjected to the motion of point to point. Basically the two inputs that are impulse shaped prolifically cancels the vibrations only in the instance if the frequency which is natural and damping of the desired system are exactly be known (Bartelt, 2007). The frequencies that are natural of the link that are multi-flexible basically are the major functions of the link positions, basically implying that the frequencies that are natural prolifically change with the position of the link.
Results of Experiment
Basically the needful test-bed for the control-strategy is actually a flexible link. To be very precise it is actually a two-flexible-link mechanism (Lees, 1993). Every needful link is much less flexible when prolifically compared to the other link and it is potentially elongated and driven on a directly basis by a motor termed as servo and it is different from the other second link which prolifically employs a major gear train basically which helps the prolific use of the motor which is smaller in size. The necessary system which is sensory authorized mainly contains two small cameras, whose work is to detect the major deflection of the links from the tip from their rigid, tough body positions (Applied technology and instrumentation for process control, 2004). The other CCD cameras which are also very important with other motor shafts prolifically detect the major deflection through the major infra-red light emitting diodes which are basically mounted at the uppermost tip of the links.
Prolifically a single link was used of the experiment basically to make understand and evaluate the controllers that are proposed. At the initial stage the major system was prolifically controlled using the most simple feedback controller termed as PD which actually damps out the major vibration and which can be positively proved and explained o be virtually stable via the work energy rate principle (Instrumentation fundamentals for process control, 2002). The outcome or the feedback was potentially chosen to bring out or produce the response that is under damped.
In the above mentioned report, few generalized concepts such as the sliding-mode and shaped-input techniques have been suggested to control the flexible or rigid multi-linked robots (Chopey, 1996). The design process which is described here is two-fold; which has showed the specific design to control a rigid body as well as the design to control a flexible multi-linked robot. The controller is designed for the rigid body motion that requires producing proper dynamics. Mainly, at the point when the controller of the rigid part is designed, the required system equation can be assigned with the rigid body to the operating point (Johnson, 1982). This is a suggested control strategy on an experimental basis to be executed to run a flexible or rigid multi-linked robot.
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