Lecture 1: Open and closed loop systems, Laplace Transforms, impulse responses, pole locations

An open loop dynamical system put together for an application, while it responds to forces and initial conditions may not satisfy conditions required in that application because of several reasons: a full model is never available, there are uncertainties in the system, the response is sensitive to certain parameters and their variations, the design requirement for response may interfere with the functionality of the system, etc. General requirements on a system include: The system has to be stable, adequately damped, capable of rejecting disturbance and quick to respond, less sensitive to parametric variations. While open loop systems may fail to satisfy the above requirements, feedback systems provide a very good solution. For e.g., an open loop robot hand, modelled as a double pendulum, even with motors at every joint and elbow may not perform according to the specs because: 1) The model is inadequate (rigid body model vs flexible body model). There may be joint uncertainties. 2) Model may be adequate but system values EI, ρ are uncertain. 3) The system values are known with reasonable accuracies but day to day variations exist. When you assemble, the system behaves one way, when your friend assembles, it behaves another way. 4) Due to the above reasons system may actually be unstable. 5) Open loop systems cannot handle disturbances. 6) And the system may be uncontrollable after all the design and assembly due to the above reasons. This necessitates a method of including control system design during the system design stage, iteratively. The above issues are largely corrected by using closed loop systems. Closed loop systems can be made stable even when the open loop system is unstable, artificial electronic damping can be built into the system, closed loop systems are relatively less sensitive to disturbances, and also can be made insensitive to parametric variations. In order to achieve the requirements above, in addition to the physical system (which for us are usually mechanical systems) one needs electronic systems which can effectively modify (improve) the response. We will see soon, in the next lecture that the system poles determine the system response. This additional system effectively modifies the total pole locations of the combined physical and the electronic system. In order to achieve this, an adequate continuous corrective action is built into the system. Important response information is continuously measured and fed back for comparison