there's many lectures about control systems early on in the course i mentioned how control systems are important for maintaining a constant internal environment within the body and a statement i made early on was that physiology is dynamic it allows you to run and leap and do all kinds of dynamic things behaviors etc but of course the cells and the molecules within those cells are fragile in the body so that's the challenge for these control systems to maintain homeostasis a constant internal state against the changes in environment and activity that you may impose on that physiology so that is resolved by control systems physiological control systems and in order to consider those control systems we're going to start talking about the nervous system on a broader scale not just individual neurons but how the nervous system works in conjunction with physiological systems in order to facilitate homeostasis now before we get into the specifics of how your physiology does that we want to establish some basic intuition for how control systems work at all so the question for this mini lecture is what kind of control generates homeostasis and we're going to contrast that kind of control with a couple of alternatives so we're largely going to be talking here about control systems pretty abstractly for this lecture but then in future lectures it's really a theme that's going to pervade all the rest of this course we'll talk about the physiology okay so starting with a non-physiological example a thermostat and a thermostat illustrates negative feedback which is a form of control so here's an old school thermostat which has two readings of temperature two displays of temperature one is the current temperature so think of that as a thermometer and in control language which we need to introduce we would call temperature here our state variable our state variable is the measure that our control system cares about it's what is being controlled and so that's temperature in this case and the thermostat itself is making computations in order to control a furnace that serves to maintain the temperature around a comfortable target and that target is known as the set point so that's what you dial in on the thermostat that's your desired temperature in this case but of course we're just using temperature as an illustration for control in general set point state variable and integrating center are all generic terms that we apply apply to a variety of physiological control systems this old school thermometer works mechanically it has a mercury switch on its interior it has a temperature sensitive coil it all works mechanically so the behavior that i'm going to describe is really a mechanical phenomenon of course this is all done digitally with electronics these days all right so how does our state variable of temperature change over time we're going to consider a scenario where you're in a really cold house and you dial in the thermostat to turn on heat so that you get to a more comfortable temperature the goal is to maintain the temperature around a desirable set point as best possible so we start off with that really cold temperature zero degrees c and we walk into this house and we set our set point on that dial on the left to 35 degrees celsius here it's shown as fahrenheit we're going to dial in a celsius temperature um the furnace will kick on in response to that the heat that it generates will elevate the temperature of course and at a certain point we exceed the set point so here we've got the set point as the horizontal line we can see that the temperature goes goes above that that's intentional that's in the nature of our controller but we don't want to go too high because of course our goal is to stay at the set point so the furnace will turn off and then the building will start to cool the temperature will therefore drop until it goes uh low enough to re-trigger the thermostat and thereby turn the furnace back on again like that okay that heats it up and then we have these oscillations through time so our control system doesn't do a perfect job of keeping our state variable at the set point there's oscillations around that that's typical for control systems so some control systems are very uh have very narrow tolerances and are capable of maintaining uh variation around that set point over a very narrow range and other control systems are sloppier and allow for these oscillations okay now we need to introduce some more jargon and some concepts here to really understand what's going on first of all the difference between the temperature our state variable and our set point which we're denoting with the letter p that difference is critical to how a control system works initially we're really far away from our set point and so the difference between s and p indicates how well the controller is doing at any point in time we call that difference the error it's telling us you can think of it as just like how poorly our state variable is relative to our set point now i mentioned that the furnace turns on it overshoots the set point and then it eventually turns off that overshoot occurs up to some measure of the error and that difference is known as a high threshold or the letter tau so you can think of tau as being a particular value so that's the letter tau you can think of tau which is shown by the height of that arrow it's the error value at which something happens so in this case the furnace turns off when the error reaches that high threshold then again as the temperature drops and the furnace turns back on which occurs right there and drives the temperature to increase again that occurs at another threshold that's the low threshold and in the simplest case the high threshold is just the inverse of the low threshold so we're going to denote the low threshold as negative tau it's the error value that occurs when the furnace turns on so now that we have these quantitative concepts we can articulate what the thermostat is doing in terms of a set of rules and there's two rules in this case the first rule has to do with turning the furnace on and that rule is like this if the error the difference between the state variable and the set point is less than the lower threshold minus tau then turn the furnace on so if the furnace was off turn it on if it was our if it's already on you leave it on um but this rule has to do with changing the state of the furnace on off to on the second rule has to do with what occurs at the the high threshold and there if the error exceeds the high threshold of tau then turn the furnace off now that first rule of what occurs relative to the low threshold let me change my pointer here that first rule occurs here because we are below that low threshold and then it occurs again right there and the reason why it looks different is just that we were starting off at such a low temperature value and here it just peaks a little bit below the lower threshold in order to trigger the same rule so this rule here applies both to this event where the furnace initially turns on and then the second turning on of the furnace the same rule works for both instances and then eventually as this temperature would rise then the second rule would apply because we would exceed the high threshold so we've got two rules together they allow us to formulate an algorithm so control systems need a set of instructions how to respond in this case to a temperature measurement with either turning the furnace on or turning it off so we can represent control systems as flowcharts and in the center of these flow charts or in this case at the top of the flowchart we have our integrating center that's the thermostat now as an output we have the furnace that's an action that is recruited by the integrating center and that furnace has an effect on the state variable the state variable is monitored by the thermometer within the thermostat or a temperature sensor now we're beginning to see why there's a feedback in the term negative feedback because the temperature sensor is compared against a set point in this case 35 degrees celsius the difference between those two quantities gives us our error and it's the error that the integrated integrating center does something with in determining how the furnace should be controlled the furnace is an example of what we call something along an efferent pathway efferent pathways with a with an e have an effect on the state variable the temperature sensor on the other hand is with an a and a an example of something along an afferent pathway afferent pathways are sensory efferent pathways are actions that influence the state variable the temperatures um there the sensing of temperature by that thermometer illustrates feedback and it sets up a situation where the efferent response and the influence on the state variable is detected by the afferent pathway in other words the afferent pathway influences or modulates the efferent response so this is a control loop the furnace heats up the room that affects the temperature it's detected by the sensor the difference between the set point and the reported temperature are considered by the integrating center and then it decides whether or not to change the state of the furnace from off to on or on to off according to these rules so it's the algorithm feeding into the integrating center that determines the actions along the efferent pathway so we can say that a negative feedback loop acts to maintain a state variable around a set point okay again it's not perfect but by virtue of these actions by the controller we're maintaining temperature around the set point so negative feedback loops are the kinds of control systems that facilitate homeostasis if it's a system where something is regulated we're talking about temperature regulation blood pressure regulation regulation of ion balance in the body regulation of sex hormones if whatever it is if it is the term regulation then that suggests a negative feedback loop and a negative feedback controller now we can contrast negative feedback with positive feedback all right a lot of the same parts still apply um we've got two notable differences here first of all uh there is the threshold okay this actually should be tau not p because it's the difference between a threshold and the state variable that determines the actions by the integrating center okay in this case in this case the threshold is a little bit different it's not defined as a particular value of the error but instead it's a particular value of the state variable itself now the algorithm is where things are really different the algorithm says there's two rules the first one says if the state variable exceeds the threshold in other words if the difference between s the state variable and tau the threshold is greater than zero then activate our efferent pathway turn it on in this case we're going to turn on the furnace now this furnace is different from the one that we consider for the negative feedback loop because it has a variable intensity it can we're going to call that the furnace level it can uh run at low medium high and very high levels and the level that the furnace runs at is proportional to the state variable itself so let's consider how that works first of all let's say that the temperature rises above the threshold this would require some action in order to turn it on so we get let's just say in this scenario we turn it on low then it reaches the threshold okay so now we've turned the furnace on the first rule has been satisfied now we're in a situation where the efferent pathway depends on the state variable so the level of the furnace is now being dictated by the temperature as read by the temperature sensor so as the temperature goes up that is then going to drive the furnace to run at a higher level so now we're at level medium that rise in temperature in turn drives the integrating center to turn the furnace up even more so the furnace is now at a high level and this would just keep on going until our state variable approaches of infinity okay it goes up and up and up of course this is not possible eventually the furnace would burn out it could it has a maximum level that it can operate at and so there is the need for an external shutoff of some sort to prevent this from going to infinity but what this illustrates is the characteristic curve an exponential rise that is characteristic of positive feedback loops so even though the flow chart looks vaguely similar to a negative feedback loop if our efferent output is proportional or a function of the state variable then you've created a situation for positive feedback the third type of control is a feed forward controller okay so here we've got the correct uh towel again there's a threshold that's what's going to turn on our system and we can see that here if we exceed the threshold then we turn on but um and so let's see how that plays out over time we turn the furnace on and the temperature rises and we have it rising if the furnace is on low or if it's on high but it's at a fixed level and the temperature just goes up over time the key distinction between feed forward control and the other two controllers that we've mentioned is that there is actually no feedback the temperature um is monitored only in order to initiate the efferent response once initiated then that efferent response no longer depends on the afferent pathway so there is no feedback in a feed forward control system the efferent output is independent of the afferent input the afferent input is useful just to initiate a feed forward controller after it has initiated then it just plays out in a very consistent way so let me summarize we have the feed forward control that i just described it's relatively simple you don't have a feedback loop and feed forward controllers tend to be fast acting they're just playing out a pattern on the efferent side and it's not modulated so we'll see examples of this when we consider uh reflex arcs such as in the musculoskeletal system and autonomic reflex arcs we've considered negative feedback these are more complicated because of a feedback loop but they offer a modulated response and so this is good for regulatory functions this will achieve homeostasis positive feedback loops have the same essential parts as a negative feedback loop but they have a very rapid rise that is un well it's uh it's um exponential and by virtue of being exponential it quite uh quickly uh sort of moves out of control and so that requires some sort of external shutoff in our example of the furnace the furnace would have to fail or reach its maximum in the case we've actually considered a positive feedback loop example which is the sodium voltage-gated channels that drive an action potential so when the cell membrane is depolarizing on the rise of an action action potential it has exponential growth like this but the inactivation gate in the voltage-gated channels shut off the system now positive feedback loops are no good for homeostasis but they are beneficial for very rapid action so we're going to see very few examples of them as we consider physiological systems homeostasis is generated by negative feedback control so most of the control systems that we'll talk about focus on negative feedback but we'll see some examples of the other two as well