introduction

Summation of [Alstrom, K.J., Murray, R.M., Feedback Systems: An Introduction for Scientists and Engineers, 2006.]

..what is feedback?
Feedback occurs when outputs of a system are “fed back” as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to “feed back” into itself.

In this context, the term “feedback” has also been used as an abbreviation for:
• Feedback signal – the conveyance of information fed back from an output, or measurement, to an input, or effector, that affects the system.
• Feedback loop – the closed path made up of the system itself and the path that transmits the feedback about the system from its origin (for example, a sensor) to its destination (for example, an actuator).
• Negative feedback – the case where the fed-back information acts to control or regulate a system by opposing changes in the output or measurement.

..what is control?
Emerging applications include high confidence software systems, autonomous vehicles and robots, real-time resource management systems, and biologically engineered systems. At its core, control is an information science, and includes the use of information in both analogue and digital representations.
A modern controller senses the operation of a system, compares that against the desired behaviour, computes corrective actions based on a model of the system’s response to external inputs, and actuates the system to effect the desired change. Uncertainty enters the system through noise in sensing and actuation subsystems, external disturbances that affect the underlying system physics, and uncertain dynamics in the physical system (parameter errors, un-modelled effects, etc). The algorithm that computes the control action as a function of the sensor values is often called a control law.
Control engineering relies on and shares tools from physics (dynamics and modelling), computer science (information and software) and operations research (optimization and game theory), but it is also different from these subjects in both insights and approach. Perhaps the strongest area of overlap between control and other disciplines is in modelling of physical systems, which is common across all areas of engineering and science. Control relies on input/output modelling that allows many new insights into the behaviour of systems, such as disturbance rejection and stable interconnection.
Model reduction, where a simpler (lower-fidelity) description of the dynamics is derived from a high fidelity model, is also very naturally described in an input/output framework. Perhaps most importantly, modelling in a control context allows the design of robust interconnections between subsystems, a feature that is crucial in the operation of all large engineered systems.
Control is also closely associated with computer science, since virtually all modern control algorithms for engineering systems are implemented in software.
..feedback examples
Feedback has many interesting and useful properties. It makes it possible to design precise systems from imprecise components and to make physical variables in a system change in a prescribed fashion. An unstable system can be stabilized using feedback and the effects of external disturbances can be reduced.
.robotics and intelligent machines
Early robots were primarily used for manufacturing, modern robots include wheeled and legged machines capable of competing in robotic competitions and exploring planets, unmanned aerial vehicles for surveillance and combat, and medical devices that provide new capabilities to doctors. Together, these works and others of that time form much of the intellectual basis for modern work in robotics and control.
Two accomplishments that demonstrate the successes of the field are the Mars Exploratory Rovers and entertainment robots such as the Sony AIBO. The Sony AIBO robot debuted in June of 1999 and was the first “entertainment” robot to be mass marketed by a major international corporation. This “higher level” of feedback is key element of robotics, where issues such as task-based control and learning are prevalent.
Despite the enormous progress in robotics over the last half century, the field is very much in its infancy. Today’s robots still exhibit extremely simple behaviours compared with humans, and their ability to locomote, interpret complex sensory inputs, perform higher level reasoning, and cooperate together in teams is limited. While advances are needed in many fields to achieve this vision—including advances in sensing, actuation, and energy storage—the opportunity to combine the advances of the AI community in planning, adaptation, and learning with the techniques in the control community for modelling, analysis, and design of feedback systems presents a renewed path for progress.
.materials and processing
Process manufacturing operations require a continual infusion of advanced information and process control technologies in order for the chemical industry to maintain its global ability to deliver products that best serve the customer reliably and at the lowest cost. In addition, several new technology areas are being explored that will require new approaches to control to be successful. The payoffs for new advances in these areas are substantial, and the use of control is critical to future progress in sectors from semiconductors to pharmaceuticals to bulk materials.
There are several common features within materials and processing that pervade many of the applications. And control techniques must make use of increased in situ measurements to control increasingly complex phenomena.
In addition to the continuing need to improve product quality, several other factors in the process control industry are drivers for the use of control. Environmental safety considerations have led to the design of smaller storage capacities to diminish the risk of major chemical leakage, requiring tighter control on upstream processes and, in some cases, supply chains. All of these trends increase the complexity of these processes and the performance requirements for the control systems, making the control system design increasingly challenging.
As in many other application areas, new sensor technology is creating new opportunities for control. Many of these sensors are already being used by current process control systems, but more sophisticated signal processing and control techniques are needed to more effectively use the real-time information provided by these sensors.
..feedback properties
Feedback is a powerful idea which, as we have seen, is used extensively in natural and technological systems. The use of feedback has often resulted in vast improvements in system capability and these improvements have sometimes been revolutionary, as discussed above. In this section we will discuss some of the properties of feedback that can be understood intuitively.
.robustness to uncertainty
By measuring the difference between the sensed value of a regulated signal and its desired value, we can supply a corrective action. If the system undergoes some change that affects the regulated signal, then we sense this change and try to force the system back to the desired operating point.
.design of dynamics
Through feedback, we can alter the behavior of a system to meet the needs of an application: systems that are unstable can be stabilized, systems that are sluggish can be made responsive, and systems that have drifting operating points can be held constant. Control theory provides a rich collection of techniques to analyze the stability and dynamic response of complex systems and to place bounds on the behavior of such systems by analyzing the gains of linear and nonlinear operators that describe their components.
.drawbacks of feedback
This is tricky because of the uncertainty that feedback was introduced to compensate for: not only must we design the system to be stable with the nominal system we are designing for, but it must remain stable under all possible perturbations of the dynamics.
In addition to the potential for instability, feedback inherently couples different parts of a system. In engineering systems, measurements must be carefully filtered so that the actuation and process dynamics do not respond to it, while at the same time insuring that the measurement signal from the sensor is properly coupled into the closed loop dynamics (so that the proper levels of performance are achieved).
Another potential drawback of control is the complexity of embedding a control system into a product. While the cost of sensing, computation, and (to a lesser extent) actuation has decreased dramatically in the past few decades, the fact remains that control systems are often very complicated and hence one must carefully balance the costs and benefits. An early engineering example of this is the use of microprocessor-based feedback systems in automobiles.
.feedforward
Feedforward is particularly useful to shape the response to command signals because command signals are always available. Since feedforward attempts to match two signals, it requires good process models otherwise the corrections may have the wrong size or it may be badly timed.
The ideas of feedback and feedforward are very general and appear in many different fields. In economics, feedback and feedforward are analogous to a market-based economy versus a planned economy. In business a pure feedforward strategy corresponds to running a company based on extensive strategic planning while a feedback strategy corresponds to a pure reactive approach. The experience in control indicates that it is often advantageous to combine feedback and feedforward. A typical example is in chemical process control where disturbances in one process may be due to processes upstream.
.positive feedback
In most of this text, we will consider the role of negative feedback, in which we attempt to regulate the system by reacting to disturbances in a way that decreases the effect of those disturbances. In some systems, particularly biological systems, positive feedback can play an important role. In a system with positive feedback, the increase in some variable or signal leads to a situation in which that quantify is further through its dynamics.