Simple Closed-Loop System with Simulated Plant

    Before the implementation of a wireless control loop on a physical plant was undertaken, we began by performing wireless control on a simulated plant.  The primary goal of this study was to examine the effects of time delays and explore ways of compensating for them. 

Application of a Smith Predictor for Overcoming Delayed Feedback

   In order to compensate for the effects of delayed feedback, we next implemented a Smith Predictor.  It is well documented that the use of a Smith Predictor can significantly improve performance in the control of systems with significant time delays, but its application to the present single-sample-period delay has not to our knowledge been demonstrated.  Through experimentation we found that implementation of a Smith Predictor works nicely in our case when the following conditions are satisfied: a) The plant is reasonably well modeled.  b) The time delay (in our case the sampling interval) is well known.  c) The plant is "fast" in comparison to the time delay.  d) Gain or saturation constraints do not severely limit achievable performance.  These conditions are met in the case of the previously mentioned 1/(s+1) plant sampled at 10Hz (assuming control saturation is reasonably high), making the application of a Smith Predictor quite effective in improving performance.  By nearly negating the effects of delayed feedback, more precise pole-zero cancellation is obtained and gains can be increased.  In this case the system was found to give excellent performance with the PI controller K_P = 7, K_I = 8.4 inside the predictive loop.  Gains could actually be raised further without giving significant overshoot, but we chose these as conservative values.  A comparison of both step and sine tracking is shown for the classic PI and Smith PI controllers in the plots below.  Again the classical PI controller is shown in blue with the Smith Predictor PI controller now shown in black.

We see that the application of the Smith Predictor gives improved performance in both cases, verifying its applicability to the problem of time delay compensation.

Modeling of Packet Loss and its Effect on Performance 

   The above testing demonstrates achievable performance using an ideal network (i.e. one that never loses data or suffers from traffic-induced delays).  For the two-node peer-to-peer wireless network used in our system, the true network behavior is actually quite similar to this ideal model, since there are no other users or environmental factors to disrupt performance.  Nevertheless, we are interested in developing control strategies that demonstrate robustness to the type of packet loss that would occur over a real-world network.  For this reason, we chose to implement a model of data loss into our communication blocks.  After reviewing literature on a variety of network models, we chose the two-state Markov model for it's combination of simplicity and accuracy.  Specifically, the Markov model is one of the simplest network models to accurately capture the "bursty" behavior of real networks.  By "bursty" we mean that real networks tend to be characterized by relatively long periods of good performance separated by shorter periods of bad performance.  The two-state Markov model accurately represents this type of behavior by transitioning between a "good" and a "bad" state, each having a different probability of losing any particular packet of data.  The results of a pulse reference signal under conditions of severe and mild packet loss are shown below for both controllers under identical loss of data (Smith PI in black, classical PI in blue).  

In the above example over 25% of transferred data was lost, which is quite high for a real system.