Sensory Systems/Control Systems

An Introduction to Control Systems

What is a control system?

Control systems are virtually everywhere. From technical equipment such as cars and phones to kitchen appliances such as a toasters and fridges, or bathroom amenities such as a temperature regulation in the shower and faucet – no matter what part of your house your glance falls on, chances are very high you will find a device that is making use of a control system.

Definition of Control Systems

In general, control systems can be seen as an interconnection of components that take an input and transform it into the desired output - similarly to a function, but more complicated in real life. Think for instance of a very simplified traffic light system. Our input could be a channel that takes 1,2 or 3 as an input, corresponding to red, orange and green lights, and outputs a light signal on one of the three light signal channels. The control system would assure that only one of the lights is on, while the others must be switched off for the duration of the phase.

Essentially, a control system takes an input and converts it into an output by controlling a process, through which the input must pass.

A more complicated example would be a thermostat. The thermostat responds to the room temperature and ensures that the desired temperature is met. It does this by means of a feedback loop, which we will explain in more depth later. In short, the thermostat will have a detector that measures the temperature and passes this on to the comparator, which will compare the desired and measured temperature. If the comparator detects a difference between the measured and desired temperature, it will pass this information on to an effector, for instance an air conditioner, which is turned on via this information and subsequently cools the room. Of course, this would happen in loops, which means that the thermostat's detector would send a new signal after a certain period of time and the cycle begins again. For more engineering examples, see the book by Dorf and Bischop.

Contrary to what one may think, control systems are not only artificial constructs, but can also be identified in biological systems. In balance control, for instance, a very delicate and complex system with many input and output channels, the cerebellum acts as an important integration stage. We will see in later sections that the cerebellum, however, acts not only as a simple feedforward or a feedback control system, but as both simultaneously.

Biological Control Systems – The Balance System

The balance system is essentially a biological control system, integrating three sensory systems, which produce a mainly musco-skeletal output that is designed to maintain posture and stability of the body.

Simplified flow diagram of the inputs and outputs that lead to what we commonly understand by the term ‘balance’.

The inputs to the balance system are:

1. Somatosensory system (proprioceptive & tactile)
2. Vestibular system
3. Visual System

At the level of integration, the cerebellum is responsible for the coordination of motor behavior and is not accessible by our consciousness. It is, however, strongly influenced by the cerebral cortex, the projections of which make up the largest stream of inputs to the cerebellum. Additionally, the brainstem is another important relay point for incoming and outgoing sensory information from all three inputs to the balance system. Its role is mostly to sort the incoming information and to enable the cerebellum to respond most efficiently to the current situation.

The final motor outputs are mediated by the brainstem and the cerebellum and include the vestibulo-ocular reflex, the movement of the eye muscles to maintain line of sight and finally also the necessary muscoskeletal control to make postural adjustments and maintain overall balance.

Control Systems - Overview

Continuous-time and Discrete-time Systems

In general, all control systems are either continuous-time or discrete-time systems, based on their types of input. An input is continuous if it is defined for every value in the range of interest. Practically, what this meant is there is a constant stream of incoming information which is used to generate a constant stream of output (Constant in this context is not the same meaning as in the mathematical definition).

A discrete input would be one or more separate signals that are separated by a certain amount of time larger than the sampling time in continuous systems. Discrete systems have a countable number of states and are also often called analog systems. The countable states each produce a countable output.

SISO and MIMO Systems

As the name already suggests, “Single Input Single Output” (SISO) Systems have one single input and one single output only. MIMO systems are “Multiple Input Multiple Output” Systems that have more than one input and more than one output. Due to their rapidly changing interactions, MIMO system dynamics are difficult to trace in detail for the human observer. For SISO systems, one can make use of Bode, Nyquist and Nichols plots to analyze the system. Examples of MIMO systems can be found in the realm of wireless communication that we are very familiar with when using our smartphone, namely 3G, 4G and LTE systems. Contrarily, one can image a SISO system by thinking about a radio system with only one antenna in the transmitter and also the receiver (so input and output streams).

Open and Closed Loop Systems

Open loop control systems use a controller to influence the process depending on the desired output.

Open loop systems are probably the simplest of the control system family, as they do not take any feedback signal into account. Open systems use an actuating device, also called a controller, to control the process output. Closed loop systems are more complex, as they use measurement entity that feeds the output or feedback signal back into a comparator at the beginning of the loop. The comparator then compares the desired output with the feedback signal and thus sends a downstream message to the controller ordering him to take action for the maintenance of or approach to the desired output.

Feedback and Feedforward Systems

Feedback Systems

We have already briefly seen feedback control in the closed loop description, but we will discuss it again as it is important to explicitly distinguish between feedback and feedforward systems. Feedback control systems are usually designed to maintain a certain relationship between an input and an output signal via the aforementioned feedback signal and a constant matching process between the feedback signal and the desired output at the level of the comparator. Feedback systems are highly effective if the speed of feedback transmission and processing is larger than the actual output. This inequality is necessary to provide enough time for the comparison to take place and have an effect on the produced output, otherwise it would be oblivious.

Closed Loop Feedback Control Systems

Closed loop feedback systems include a measurement entity as well as a comparator, which compares the signal from the measurement device to the desired output and sends a corresponding downstream signal to the controller in order to match measurement and desired output.

A thermostat example of a closed feedback loop control system. A desired output is set manually – e.g. 22 degrees Celsius. The comparator compares the feedback signal from the thermometer and sends an error signal to either the air conditioner or the furnace, effectuating a temperature change. This output is then again measured by the sensor and the cycle continues until the desired temperature is equal to the measured temperature.

Feedforward Systems

Feedforward systems, however, are capable of dealing with very high speed outputs. The main principle of feedforward systems is that no output is generated until the computation has been completed that takes into account only its inputs or environmental factors. The evaluation of the current system and the inputs then gives rise to a control signal that cannot be altered any further once it has passed the evaluation stage. Therefore, in pure feedforward systems, the current output has no influence on the next output, enabling fast reaction of the system to its surroundings. However, the disadvantage of such a system is that there is always a lag between its first employment with a trial and error phase and the stage at which it is well established. Thus, to achieve the best results a feedforward system must undergo a learning phase, the length of which varies depending on the task.

Closed Loop Feedforward Control Systems

In feedforward control systems, additional input is used in order to calculate the necessary control signal that will lead to the desired output. No direct feedback from the output stage is necessary for the process, which makes the feedforward control system generally faster than the feedback system.

An extended thermostat example of a feedforward control system. A desired output is set manually – e.g. 22 degrees Celsius. Next to the current temperature, the comparator receives many different types of information, e.g. room size, humidity or the number of people in the room. This information would then be sufficient to turn on the furnace or air conditioner for a given period of time. The amount of time necessary would be subject to long periods of training.

In summary:The difference between feedback and feedforward systems is that feedback systems use sensory information to generate an error signal during the control of movement, whilst feedforward systems use the sensory information before generating a movement control signal.

Linear and Nonlinear Systems

Linear Control Systems

Linear control deals with systems that follow the superposition principle, that is, the output of the system being proportional to the input. One major subclass to the linear control systems is the linear time-invariant system (LTI system). The fundamental features of the LTI systems can be summarized into linearity and time invariance.

Linearity:

Changing the input linearly, such as scaled or summed, will change the output in the same linear way.

Time invariance:

The output is independent of when the input is applied. In other words, a time invariant system takes an input X(t) that produces an output Y(t) will produce Y(t+t)  when taking in an input as X(t+t) where t is the elapsed time.

In addition, the LTI systems can have memory, can be inverted, are only dependent on current and past events, have real inputs and outputs, and can produce bounded output for each bounded input. As a sum of all these features, a general form of a LTI system output is defined as follows, in which y[n] is the system output and x[n] current input at time n, and constants c_k and d_j stand for previous outputs and inputs respectively:

$$y[n]=c_{0}y[n-1]+c_{1}y[n-2]+...+c_{k-1}y[n-k]+d_{0}X[n]+d_{1}x[n-1]+...+d_{j}x[n-j]$$

General form of LTI system in an operator equation:

$${\begin{alignedat}{2}Y&=c_{0}RY+c_{1}R^{2}Y+...+c_{k-1}R^{k}Y+d_{0}X+d_{1}RX+...+d_{j}R^{j}X\\&=Y(c_{0}R+c_{1}R^{2}+...+c_{k-1}R^{k})+X(d_{0}+d_{1}R+...+d_{j}R^{j})\\\end{alignedat}}$$

The quotient of the output and input signals:

$${\frac {Y}{X}}={\frac {d_{0}+d_{1}R+...+d_{j}R^{j}}{1-c_{0}R-c_{1}R^{2}-...-c_{k-1}R^{k}}}$$

The system function of the LTI system:

$${\frac {Y}{X}}={\frac {d_{0}+d_{1}R+d_{2}R^{2}+...}{n_{0}+n_{1}R+n_{2}R^{2}+...}}$$

The transfer function for any LTI system:

$${\frac {Y(S)}{X(S)}}={\frac {n_{0}+n_{1}S+n_{2}S^{2}+...}{d_{0}+d_{1}S+d_{2}S^{2}+...}}$$

The coefficients of the numerator (n) and denominator (d) uniquely characterizes the transfer function. This notation is used by some computational tools, such as Simulink, Matlab, to simulate the response of such a system to a given input.

Nonlinear Control Systems

The nonlinear control systems are of more importance than linear control systems, for most real-world systems are nonlinear-disobeying superposition rules, being time variant, or satisfying both cases. For instance, the thermo-stat system mentioned in previous session is an example of the nonlinear control. The human balance system, which is a complex and delicate model, is also predominated by nonlinear systems.

Among many nonlinear approaches, the gain scheduling is one of the most popular nonlinear control methods. This mechanism employs a family of linear controllers to decompose a nonlinear task into a number of linear sub-tasks, thus simplifying the complicated nonlinear analysis into smaller and more plausible tasks.

The gain-scheduling controller can be designed with Simulink as in the following three steps quoted from Matlab:

1. Linearize nonlinear plant model at the same time as a linear model
2. Tune controller gains for all the linear plant models
3. Implement a gain-scheduled controller architecture, where controller gains are “scheduled” with a scheduling variable, such as a measured output or a system state

Although nonlinear system can resemble the real-world issues better than the linear model, the complexity accompanied with the nonlinear model makes it harder for scientists and researchers to explore the unknown parts in fields such as human postural control and robotics. Thus, linear control mechanisms are often implemented in analyzing a nonlinear task for the sake of simplicity.

The Cerebellum as a Master Controller in Feedforward and Feedback Loops

Position of the cerebellum in the human brain.

Often underestimated, the cerebellum can be seen as one of the most important relay points (or comparators in control theory terms) in our brain, regulating not only vital cognitive functions, but also motor control and balance. It receives projections from the cerebral cortex, but also directly from other regions, such as the superior colliculus, the inferior olivary nucleus, the spinal cord and the vestibular labyrinth and their nuclei. The latter two structures are of special interest with regards to the balance control system, as the spinal cord carries the axons from the proprioceptive and tactile somatosensory systems and the nerve coming from the vestibular labyrinth provides the cerebellum with information about the vestibular system status.

Sensory Information Integration by the Cerebellum

Purkinje cells are some of the largest nervous cells in the human body with their vast network of dendritic endings. They receive information from many different parts of the brain and play an important role in the orchestration of the balance control system.

Simplified feedforward control system model of the cerebellum. The cerebellum acts as the controller, which receives sensory inputs from mossy and climbing fibers and sends a feedforward signal to the effectors, which are mostly the muscle nerves that control limb position or eye movement.

If you were to understand the exact workings of each and every neuron in the cerebellum, you would certainly receive the Nobel Prize right away. As with all brain-related control systems, we need to zoom out and look at a slightly higher level of abstraction. The cerebellum is home to two special types of neurons, namely the Purkinje cells and the deep cerebellar nuclear cells, which are essentially our sensors in the control system sense and are fed with sensory information via mossy fibers and climbing fibers. Mossy fibers mostly transmit the information about the desired output, whilst climbing fibers are specialized to transfer sensory information about the current state of the system as well as already processed error signals.

All this information is processed mainly by the Purkinje and deep cerebellar nuclear cells, whose activation patterns are characteristic of different types of movement. If we consider just a simple hand movement, it turns out that the firing patterns of these cells are characteristic for this specific movement. That is, a certain group of these cells will undergo an even stronger, characteristic activation in comparison to their ground-state tonic activation. Each and every movement and aspect of it, let it be the extension or contraction of a specific muscles, the position of a joint, the stability configuration of a foot, is encoded in these firing patterns of the Purkinje and deep cerebral nuclear cells.

In addition to sensing ongoing movement, the aforementioned cells also have the capability to recognize potential errors in the movement pattern, thus correcting a faulty position to maintain balance. The cells essentially compare the patterns of convergent activity amongst each other. If their results do not match, they detect an error. In this case, the Purkinje cells may facilitate corrective signals to be sent downstream in order to attempt to correct the movement before the body falls out of balance, thus acting as a control system comparator. As we can already see, this system appears to be a mixture of a feedforward and a feedback system, as error signal information is combined with advanced sensory information that is not dependent on the loop's direct output. The advantage of this is that the biological system can combine the advantages of both systems in order to respond to different types of environmental demands – that is, the cerebellum employs the feedback mechanism for slower movement control and the feedforward system for movements that require fast responses. Posture control, for instance, is a task of the cerebellum that requires feedback from the body's somatosensory system and is relatively slow in comparison to e.g. the vestibulo-ocular reflex (VOR), which requires feedforward control.

What is striking though, is that instead of directly sending the signals to the motor effector systems themselves, all information passes through the other parts of the cerebellum to a central computational node, the small cerebral nuclei, which are the bottleneck integrators and processors in this delicate circuitry. The exact workings of these nuclei are poorly understood, but it is known that all the temporal and spatial features of the downstream signaling are controlled here. This comparison could not take place if there were no memory of ‘correct’ positionings of the limbs and joints for balance maintenance, which is why the cerebellum has also often been described to play a key role in the formation and retrieval of dynamic muscle memory.

However, the cerebellum also receives more information from higher-level brain areas, which, in a real-life setting, adds multiple levels of complexity to our control system model and we have omitted it from the simplified model. One must therefore always acknowledge that, after all, biological systems are usually more complex than their artificial partners and conclusions drawn from limited modelling knowledge must always be qualified to accommodate for the unknown parameters that remain to be discovered.

Computer Simulations on Human Postural Control

Multisensory integration

The human balance control requires the collective efforts of sensory and central nervous system (CNS), and the human body to work against the external disturbances such as gravity; any changes in multisensory inputs will trigger immediate alterations in CNS so as to maintain balance. More importantly, such alterations are a result of estimations of the unforeseen scenarios based on changes in multisensory inputs. This intriguing control behavior has inspired neurologists and engineers with models to explore the myths in understanding human postural control and to develop algorithms being implemented in robotics. Multisensory integration is probably the most fascinating aspect in understanding balance control system. This concept has been well represented in human experiments in which subjects were tested under different conditions with a modulated combined stimulation of vision, vestibular sensation, and touch; each modulation on sensory inputs altered the postures of the subjects significantly. This study provides evidence for the multisensory integration.

Weighting and re-weighting system

The myths in understanding integrating mechanism lead us to the key framework in understanding the multiple integration, “weighting and re-weighting system”. The sensory re-weighting process plays a critical role in helping human maintain postural control, during which various sensory inputs are integrated and regulated dynamically based on different conditions and sensory information. In computer simulations, the model with parameters representing different components of the environmental conditions can adjust dynamically to the changes in the environment. In the model, the weights of visual, vestibular, and proprioceptive sensory systems are represented by W_v, W_g and W_p respectively. By modelling this sensory re-weighting system, the simulation is able to make adjustment according to the changes in environmental conditions, and therefore the system is capable of providing a relative representation of each sensory channel's contribution to the balance behavior control. A key hypothesis of this mechanism is that all sensory channels contributing to the balance control sum up to a unity. For instance, during an eyes-open quiet stance, the effective overall sensory weight of the system, W, equals to the sum of W_v, W_g and W_p, while W = W_g + W_p under an eyes-closed standing because there is no contribution from visual channel. Nevertheless, this hypothesis does have exclusions when the system is under transient conditions, in which the effective overall weights W will be different from the unity. The weights of sensory systems will be adjusted in the integration process to make up for the changes taken place in the transient period, after which W will return to unity again.

Currently, the reweighting process is performed through two types of modelling, one adjusting externally and the other automatically, with the Independent Sensory Channel (IC) Model being an example of the former the Disturbance Estimation and Compensation (DEC) Model the latter.

Independent Sensory Channel Model

The IC model is a linear model developed by Peterka. The IC model can descriptively imitate human balance behavior in steady stance condition, which is supported by studies. During the experiments, the IC model was implemented in Simulink, Matlab, and a single inverted pendulum model was used to represent human body. Both human subjects and the inverted pendulum model had gone through balancing tests, and the parameters obtained from human subjects were compared with the estimations generated by the IC model. The result showed that two sets of parameters are comparable to one another, providing sounded evidence to support the IC model's qualification in representing human balance behaviors. The result showed that two sets of parameters are comparable to one another, providing sounded evidence to support the IC model's qualification in representing human balance behaviors. However, this IC model is only applicable under a steady state. When the model is exposed to a more complex environment, the amount of the required parameters to describe the model will increase markedly, with decreased confidence in estimating parameters and in attributing to specific behaviors. The limitations undermine the eligibility of the IC model in clinical studies.

Disturbance Estimation and Compensation Model

Unlike the IC model which requires different sets of parameters to describe the sensory reweighting feature, the DEC model can accomplish the prediction of data obtained from different environmental contexts with one set of parameters. The fundamental feature of the DEC model is its ability to compensate for the external and self-produced disturbances so as to assist the motion execution in balance control. The four types of external disturbances are the field gravity, contact forces such as a push or pull affecting the body, and motion of the body supporting surface including rotation as well as translational acceleration. When being exposed to external disturbances, the DEC model can recap from the library of learned external events to make anticipations, and thus compensates for the disturbances to avoid falling. The higher level mechanisms represented by the DEC can benefit both neurologists and engineers, and provide more interdisciplinary insights into understanding the human balance control and building more efficient robots.

Weaknesses and Advantages of Control Systems

Biological Control Systems

Sensory Conflict Theory

Whoever has enjoyed a roller coaster ride or just plainly travelled by boat or car has probably once in their lifetime experienced motion sickness. Whereas our balance system performs very well in natural environments, these situations have in common that they can cause distortions of the whole equilibrium by creating conflicting signals for the visual, somatosensory and vestibular system. For instance, riding in a car evokes the visual sensations of movement, whereas the vestibular and somatosensory systems experience a notion of stationarity.

This mismatch of information is captured in sensory conflict theory, which describes that the contrast between habitually experienced patterns of sensory information and the contradicting, perceived information give rise to the sensation of motion sickness. Although the balance system itself remains intact in its motor outputs – that is, the person on the boat or in the car is still able to maintain his or her posture – the feedback supplied to higher order perception areas elicits a feeling of motion sickness. This clearly underlines that the balance system in humans is much more than just a control system and due to it being integrated with perceptual areas, can elicit negative effects in humans despite proper functioning.

Diseases Affecting the Balance Control System

Parkinson's disease impairments

However, as the human balance control is a biological system, diseases can heavily impede the workings of the system. In general, nearly all of neuromusculoskeletal diseases, such as Parkinson's disease or cerebral ataxia, as well as heard injury, deafness and ear infections, such as labyrinthritis, can elicit an impairment of the balance control system. Phenotypically, this impairment can take many different forms, depending on which of the balance system's components is most strongly affected and which other component or components might temporarily and partially compensate for the loss.

In Parkinson's disease, for instance, the basal ganglia that are involved in balance control via a thalamic-cortical-spinal loop (essentially a connection from the cortex to the brainstem as discussed above) are affected by neurodegeneration and thus the patient's balance system can be impaired. From early age on, children with auditory dysfunctions due to labyrinthritis or surgeries such as cochlear implants may also have difficulties with their balance system. It has been shown that children with these conditions learn to stand and walk significantly later than their peers, but often the condition improves with age, as a neuroplastic process sets in to compensate for the lacking information from the inner ear. In these cases, the proprioceptive and visual systems take over the input stream from the vestibular system. Similarly, blind children and blinded adults develop coping mechanisms to maintain balance control despite the loss of the visual information.

This flexibility is a great advantage of the biological system over the artificial control system. The biological system has the capability to make use of neuroplasticity in order to alter the input streams as a response to them being damaged.

Weaknesses in Simulating Models

Inability to Fully Replicate the Human Balancing Mechanism

Current simulations implemented in robots enable them to perform standing and walking or even jumping without troubles, but these models are insufficient for providing direct insights in understanding the human balance control. Although the current models can reproduce mechanisms from lower level to higher level, such as central pattern generators for gait and movement synergies, a large part in understanding the role of the central nervous system in balancing control remains unknown. The most critical drawback in current simulating models for human postural control is that none of the produced model is capable of mimicking the exact mechanisms used in the human body balance, and to handle multiple inputs and to provide reactions simultaneously in response to external disturbances as timely and precisely as humans can do. Because these models can merely explain the human balance system partially, they still leaves mechanisms taking place in the cortical level unexplored. In addition, the hardware used to build the robots also limits the values of understanding human balance behavior through robotics, for the hardware may trigger troubles that are not seen in the human body. Nevertheless, despite the current models can only reveal part of what is going on in the human body, neurologists can still benefit from studying and comparing these models to test their hypotheses, and in turn provide directions for engineers to improve their models.   

Further reading

1. Control Systems Wikibook
2. Matlab Control System Toolbox
3. Gain Scheduling
4. Independent Sensory Channel Model