Month: August 2017

Integral Control

Integral Control

Integral Control

08/17/17

“How can control systems be based on the summation of error levels over time?”

 

Control systems respond to an error between feedback and setpoints by making changes to the next output. However, sometimes the error does not change fast enough or it changes too quickly. So how could we devise a mechanism to solve this issue? Well, let’s start with a simple idea. We know that if an error value were to persist over time it would show easily on a graph. So what if we were to just take the area of the error under this graph and modify our outputs accordingly? This is the fundamental idea behind integral control and is one of the prime factors in the ever so often used PID control system.

Derivative Control

Derivative Control

Derivative Control

08/16/17

“How can control the rate of change of our control system?”

 

Proportional control systems are great for correcting the error of simple applications. However, one major drawback is that this method does not control the rate of change of the control system. For example, let’s say that we have a self-driving car that needs to accelerate to the speed limit of a roadway. Proportional Control might accelerate so fast that it actually overshoots the speed limit and causes an accident! To solve this, we can introduce a factor called a derivative control which modulates the rate of change of the system. If we were to introduce it to the self-driving car, then its rate of change would be held in a sustainable manner and decrease to zero as it becomes closer to the setpoint.

 

Proportional Control

Proportional Control

Proportional Control

08/16/17

“How can we have a control method proportional to the error?”

 

Closed loop control systems respond to external stimuli with the use of an error compared to a setpoint. So how can we use this information to make an easy to use control system? Well, what if we were to base our adjustment to be proportional to the error, such that the higher the error the higher the restoring force? Well, engineers have implemented exactly this in a form known as proportional control and are used in applications such as self-driving vehicles and valve systems.

Polytropic process

Polytropic process

Polytropic process

08/16/17

“What process in Thermodynamics holds the pressure and volume to a constant?”

 

Thermodynamics is known for its intense reliance on processes. Some of the most important types are classified as Polytropic processes. In polytropic processes, the pressure and volume are held to the constant given by the relation pv^n=c, where p is pressure, v is volume, n is the polytropic index, and c is a constant. A process is polytropic if it obeys the ideal gas law and if the heat to energy transfer as work at each infinitesimal step of the process is kept constant

 

Part-load efficiency

Part-load efficiency

Part-load efficiency

08/15/17

“Can machines operating at part loads have different efficiencies than full loads?”

 

Machines can operate at variable loads. For example, an electric grid might be providing electricity to its entire network during the daytime and only a few houses at night. Because these different loads have different parameters, machines operating at partial loads have something called a part-load efficiency, or the efficiency when not at full (100%) loading.

Routh–Hurwitz stability criterion

Routh–Hurwitz stability criterion

Routh–Hurwitz stability criterion

08/15/17

“How can we analytically estimate the stability of a transfer function?”

 

We know that transfer functions have a certain level of stability afforded to them. However, sometimes the functions can be quite complicated. So how can we analytically analyze their stability? Well, let’s think about it. First, let’s take our polynomial. Then, let’s take the coefficients for all of our functions. Then, let’s make a graph with the number of rows equal to the highest exponent and number of columns equal to half rounded up of that. Afterward, let’s place the coefficients on the first two columns such that the greatest coefficient goes on the top left, the next one goes beneath, the next one goes to the right of the first one, the next one goes below, and so on. Now let’s fill in the rest of the table by taking the difference between the coefficient in the first column two rows up multiplied by the coefficient up and right one, and then let’s subtract it from the value directly up two and right one minus the one at the first column one row up while dividing everything by the number directly up one row and put the result in place of the column . Let’s now repeat this pattern until we have the entire table filled out. If any coefficients in the first column are of a different sign, then the system will be unstable. This mathematical tool is known as the Routh–Hurwitz stability criterion and is used in designing all sorts of control systems.

Duty Cycles

Duty Cycles

Duty Cycles

08/15/17

“What described the on and off period for a digital signal?”

 

Digital signals have only two modes: on and off. And sometimes they cycle through each at a constant period. So how can we describe this phenomenon? Well, after much research, engineers have come up with the concept of a duty cycle. A duty cycle determines for what time periods the signal is on duty and can be quantified by the percentage on vs off (for example, a signal that is active for 3/4ths of the time has a duty cycle of 75%)

Cutoff frequency

Cutoff frequency

Cutoff frequency

08/14/17

“What is the frequency that causes machines to stop working efficiently?”
Many modern electrical machines depend on a frequency for some input. However, sometimes we don’t want it to be accessible to all inputs. To achieve this, we implement something called a cutoff frequency into the system. A cutoff frequency is the frequency point in which a machine’s output will stop working efficiently.

Control System Stability

Control System Stability

Control System Stability

08/14/17

“How can we measure the stability of a control system?”

 

Control systems are necessary for the function of society. However, if our system proves to be unstable, then it can cause serious harm to its operation. So how can we measure the control system stability? Well if we take the Laplace transform of the transfer function and observe that there are poles in the right-hand plane, then the exponential part of the function will grow to infinity over time, thereby causing a system malfunction. Control system stability is used to analyze a diverse range of fields ranging from aerospace controls to robotics and even building energy management.